Free Online Lectures and Courses for Mathematics
40 Courses
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Algebra
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Simple Equations
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Equations Part 2
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Equations Part 3
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Linear Equations
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Graphing Lines Part 1
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Slope and Y-intercept Intuition
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Slope Part 1
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Slope Part 2
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Slope Part 3
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Averages
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Integer Sums
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Taking Percentages
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Growing by a Percentage
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Another Percent Word Problem
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More Percent Problems
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Systems of Equations
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Ratio Problem with Basic Algebra
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Ratio Problem: Advanced
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Alternate Solution to Ratio Problem
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Introduction to Ratios
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Advanced Ratio Problems
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Age Word Problems Part 1
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Age Word Problems Part 2
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Age Word Problems Part 3
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Level 1 Multiplying Expressions
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Solving a Quadratic by Factoring
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i and Imaginary Numbers
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Complex Numbers Part 1
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Complex Numbers Part 2
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Introduction to the Quadratic Equation
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Quadratic Equation Part 2
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Completing the Square
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Quadratic Formula
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Quadratic Inequalities
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Functions Part 1
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Functions Part 2
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Functions Part 3
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Functions Part 4
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Domain of a Function
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Proof: log a + log b = log ab
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Proof: A(log B) = log (B^A), log A - log B = log (A/B)
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Proof: log_a (B) = (log_x (B))/(log_x (A))
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Algebraic Long Division
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Introduction to Conic Sections
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Conic Sections: Circles
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Conic Sections: Ellipses
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Conic Sections: Hyperbolas Part 1
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Conic Sections: Hyperbolas Part 2
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Conic Sections: Hyperbolas Part 3
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Identifying Conics Part 1
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Identifying Conics Part 2
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Identifying Conics Part 3
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Foci of an Ellipse
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Foci of a Hyperbola
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Hyperbola Foci
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Partial Fraction Expansion Part 1
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Partial Fraction Expansion Part 2
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Partial Fraction Expansion Part 3
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Parabola Focus and Directrix Part 1
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Parabola Focus and Directrix Part 2
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Two Passing Bicycles Word Problem
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Passed Bike Word Problem
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Passing Trains
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Overtaking Word Problem
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Early Train Word Problem
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Officer on Horseback
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Rational Inequalities Part 1
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Rational Inequalities Part 2
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Interesting Polynomial
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Geometric Series Sum to Figure Out Mortgage Payments
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Algebra I Worked Examples
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Solving Equations 1
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Solving Equations 2
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Solving Equations with the Distributive Property
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Solving Equations with the Distributive Property 2
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Algebraic Word Problem
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Sum of Consecutive Odd Integers
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Example of Solving for a Variable
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Solving for a Variable 2
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Absolute Value 1
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Absolute Value and Number Lines
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Absolute Value Equations 1
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Absolute Value Equations 2
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Patterns in Sequences 1
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Patterns in Sequences 2
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Equations of Sequence Patterns
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Finding the 100th Term in a Sequence
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Functional Relationships 1
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Testing if a Relationship is a Function
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Domain and Range 1
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Domain and Range 2
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Direct Variation 1
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Basic Rate Problem
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Basic Linear Function
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Exploring Linear Relationships
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Recognizing Linear Functions
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Exploring Nonlinear Relationships
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Slope of a Line
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Slope Example
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X and Y Intercepts
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X and Y Intercepts 2
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Graphing a Line in Slope Intercept Form
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Equation of a Line
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Converting to Slope Intercept Form
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Point-slope and Standard Form
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Parallel Lines 1
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Parallel Lines 2
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Parallel Lines 3
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Perpendicular Lines 1
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Perpendicular Lines 2
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Interpreting Inequalities
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Solving Inequalities
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Inequalities
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Absolute Value Inequalities
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Absolute Inequalites 2
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Absolute Value Inequalities 3
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Writing and Using Inequalities 1
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Writing and Using Inequalities 2
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Writing and Using Inequalities 3
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Solving and Graphing Linear Inequalities in Two Variables
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Graphing Linear Inequalities in Two Variables 1
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Graphing Linear Inequalities in Two Variables 2
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Solving Systems By Graphing 1
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Solving Systems By Graphing 2
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Solving Systems By Graphing 3
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Solving Systems By Substitution 1
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Solving Systems By Substitution 2
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Solving Systems By Substitution 3
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Solving Systems By Elimination 1
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Solving Systems By Elimination 2
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Solving Systems By Elimination 3
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Systems and Rate Problems 1
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Systems and Rate Problems 2
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Systems and Rate Problems 3
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Mixture Problems 1
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Mixture Problems 2
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Mixture Problems 3
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Graphing Systems of Inequalities 1
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Graphing Systems of Inequalities 2
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Graphing Systems of Inequalities 3
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Exponent Rules 1
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Exponent Rules 2
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Exponent Rules 3
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Scientific Notation 1
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Scientific Notation 2
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Scientific Notation 3
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Simplifying Expressions with Exponents 1
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Simplifying Expressions with Exponents 2
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Simplifying Expressions with Exponents 3
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Pythagorean Theorem 1
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Pythagorean Theorem 2
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Simplifying Radical Expressions 1
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Simplifying Radical Expressions 2
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Simplifying Radical Expressions 3
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Solving Radical Expressions 1
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Solving Radical Expressions 2
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Solving Radical Expressions 3
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Applying Radical Equations 1
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Applying Radical Equations 2
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Applying Radical Equations 3
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Fractional Exponent Expressions 1
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Fractional Exponent Expressions 2
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Multiplying and Dividing Monomials 1
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Multiplying and Dividing Monomials 2
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Multiplying and Dividing Monomials 3
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Polynomials 1
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Polynomials 2
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Adding and Subtracting 1
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Adding and Subtracting 2
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Adding and Subtracting 3
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Multiplying Polynomials 1
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Multiplying Polynomials 2
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Multiplying Polynomials 3
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Special Products of Polynomials 1
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Special Products of Polynomials 2
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Special Products of Polynomials 3
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Bay Area CBS Station with Slaman Khan
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Factoring and the Distributive Property 1
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Factoring and the Distributive Property 2
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Factoring and the Distributive Property 3
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Factoring Trinomials By Grouping 1
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Factoring Trinomials By Grouping 2
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Factoring Trinomials By Grouping 3
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Factoring Trinomials By Grouping 4
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Factoring Trinomials By Grouping 5
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Factoring Trinomials by Grouping 6
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Factoring Special Products 1
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Factoring Special Products 2
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Factoring Special Products 3
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Solving Quadratic Equations By Factoring 1
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Solving Quadratic Equations By Factoring 2
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Solving Quadratic Equations By Factoring 3
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Quadratic Functions 1
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Quadratic Functions 2
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Quadratic Functions 3
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Completing the Square 1
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Completing the Square 2
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Completing the Square 3
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Completing the Square 4
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Quadratic Formula 1
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Quadratic Formula 2
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Quadratic Formula 3
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Applying Quadratic Functions 1
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Applying Quadratic Functions 2
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Applying Quadratic Functions 3
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Non-Linear Systems of Equations 1
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Non-Linear Systems of Equations 2
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Non-Linear Systems of Equations 3
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Simplifying Rational Expressions 1
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Simplifying Rational Expressions 2
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Simplifying Rational Expressions 3
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Multiplying and Dividing Rational Expressions 1
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Multiplying and Dividing Rational Expressions 2
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Multiplying and Dividing Rational Expressions 3
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Adding and Subtracting Rational Expressions 1
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Adding and Subtracting Rational Expressions 2
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Adding and Subtracting Rational Expressions 3
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Solving Rational Equations 1
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Solving Rational Equations 2
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Solving Rational Equations 3
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Applying Rational Equations 1
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Applying Rational Equations 1 Extra
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Applying Rational Equations 2
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Applying Rational Equations 3
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Number Sets 1
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Number Sets 2
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Number Sets 3
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Understanding Logical Statements 1
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Understanding Logical Statements 2
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Understanding Logical Statements 3
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Understanding Logical Statements 4
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Understanding Logical Statements 5
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Inductive Reasoning 1
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Inductive Reasoning 2
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Inductive Reasoning 3
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Deductive Reasoning 1
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Deductive Reasoning 2
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Deductive Reasoning 3
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Events and Outcomes 1
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Events and Outcomes 2
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Events and Outcomes 3
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Independent Events 1
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Independent Events 2
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Independent Events 3
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Permutations and Combinations 1
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Permutations and Combinations 2
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Permutations and Combinations 3
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Permutations and Combinations 4
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Probability of Dependent Events 1
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Probability of Dependent Events 2
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Absolute Value Equations
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Graphing Systems of Inequalities
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Solving Systems By Graphing
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Graphing Linear Inequalities in Two Variables
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Representing Functions as Graphs
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Inductive Patterns
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Arithmetic
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Basic Addition
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Addition 2
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Level 2 Addition
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Addition 3
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Addition 4
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Basic Subtraction
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Subtraction 2
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Subtraction 3: Introduction to Borrowing or Regrouping
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Alternate Mental Subtraction Method
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Why Borrowing Works
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Level 4 Subtraction
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Adding Decimals
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Subtracting Decimals
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Basic Multiplication
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Multiplication 2: The Multiplication Tables
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Multiplication 3: 10,11,12 Times Tables
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Multiplication 4: 2-digit Times 1-digit Number
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Multiplication 5: 2-digit Times a 2-digit Number
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Multiplication 6: Multiple Digit Numbers
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Multiplication 7: Old Video Giving More Examples
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Mulitplication 8: Multiplying Decimals (Old video)
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Lattice Multiplication
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Why Lattice Multiplication Works
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Division 1
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Division 2
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Division 3: More Long Division and Remainder Examples
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Level 4 Division
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Converting Fractions to Decimals
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Percent and Decimals
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Dividing Decimals
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Ordering Numeric Expressions
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Greatest Common Divisor
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Least Common Multiple
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Equivalent Fractions
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Mixed Numbers and Improper Fractions
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Calculus
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Epsilon Delta Limit Definition Part 1
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Epsilon Delta Limit Definition Part 2
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Calculus: Derivatives 1
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Calculus: Derivatives 2
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Calculus: Derivatives 2.5
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Derivatives Part 1
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Derivatives Part 2
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Derivatives Part 3
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Derivatives Part 4
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Derivatives Part 5
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Derivatives Part 6
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Derivatives Part 7
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Derivatives Part 8
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Derivatives Part 9
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Proof: d/dx(x^n)
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Proof: d/dx(sqrt(x))
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Proof: d/dx(ln x) = 1/x
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Proof: d/dx(e^x) = e^x
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Proofs of Derivatives of Ln(x) and e^x
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Extreme Derivative Word Problem
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Implicit Differentiation Part 1
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Implicit Differentiation Part 2
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More Implicit Differentiation
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More Chain Rule and Implicit Differentiation Intuition
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Trig Implicit Differentiation Example
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Derivative of x^(x^x)
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Maxima Minima Slope Intuition
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Inflection Points and Concavity Intuition
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Monotonicity Theorem
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Maximum and Minimum Values on an Interval
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Graphing Using Derivatives
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Graphing with Derivatives Example
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Graphing with Calculus
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Optimization with Calculus Part 1
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Optimization with Calculus Part 2
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Optimization with Calculus Part 3
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Optimization with Calculus Part 4
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Introduction to Rate-of-change
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Equation of a Tangent Line
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Rates-of-change Part 2
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Ladder rate-of-change Problem
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Mean Value Theorem
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Indefinite Integrals Part 1
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Indefinite Integrals Part 2
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Indefinite Integrals Part 3
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Indefinite Integrals Part 4
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Indefinite Integrals Part 5
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Indefinite Integrals Part 6
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Indefinite Integrals Part 7
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Another U-substitution Example
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Definite Integrals Part 1
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Definite Integrals Part 2
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Definite Integrals Part 3
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Definite Integrals Part 4
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Definite Integrals Part 5
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Definite Integral with Substitution
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Integrals: Trig Substitution Part 1
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Integrals: Trig Substitution Part 2
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Integrals: Trig Substitution Part 3
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Introduction to Differential Equations
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Solid of Revolution Part 1
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Solid of Revolution Part 2
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Solid of Revolution Part 3
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Solid of Revolution Part 4
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Solid of Revolution Part 5
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Solid of Revolution Part 6
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Solid of Revolution Part 7
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Solid of Revolution Part 8
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Polynomial Approximation of Functions Part 1
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Polynomial Approximation of Functions Part 2
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Polynomial Approximation of Functions Part 3
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Polynomial Approximation of Functions Part 4
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Polynomial Approximation of Functions Part 5
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Polynomial Approximation of Functions Part 6
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Polynomial Approximation of Functions Part 7
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Taylor Polynomials
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AP Calculus BC Exams: 2008 1 A
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AP Calculus BC Exams: 2008 1 B & C
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AP Calculus BC Exams: 2008 1 C & D
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AP Calculus BC Exams: 2008 1 D
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Calculus BC 2008 2 A
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Calculus BC 2008 2 B & C
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Calculus BC 2008 2 D
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Partial Derivatives Part 1
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Partial Derivatives Part 2
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Gradient
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Gradient of a Scalar Field
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Divergence Part 1
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Divergence Part 2
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Divergence Part 3
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Curl Part 1
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Curl Part 2
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Curl Part 3
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Double Integrals Part 1
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Double Integrals Part 2
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Double Integrals Part 3
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Double Integrals Part 4
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Double Integrals Part 5
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Double Integrals Part 6
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Triple Integrals Part 1
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Triple Integrals Part 2
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Triple Integrals Part 3
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(2^ln x)/x Antiderivative Example
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Line Integrals
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Line Integral Example 1
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Line Integral Example 2 Part 1
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Line Integral Example 2 Part 2
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Position Vector Valued Functions
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Derivative of a Position Vector Valued Function
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Differential of a Vector Valued Function
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Differential of a Vector Valued Function Example
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Line Integrals and Vector Fields
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Using a Line Integral to Find a Vector Field Example
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Parametrization of a Reverse Path
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Scalar Field Line Integral Independent of Path Direction
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Vector Field Line Integral Dependent of Path Direction
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Path Independence for Line Integrals
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Closed Curve Line Integrals of Conservative Vector Fields
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Example of Closed Line Integral of Conservative Field
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Second Example of Line Integral of Conservative Vector Field
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Green's Theorem Proof Part 1
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Green's Theorem Proof Part 2
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Green's Theorem Example Part 1
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Green's Theorem Example Part 2
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Introduction to Parametrizing a Surface with Two Parameters
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Position Vector-Valued Function for a Parametrization of Two Parameters
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Partial Derivatives of Vector-Valued Functions
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Introduction to the Surface Integral
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Calculating a Surface Integral Example Part 1
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Calculating a Surface Integral Example Part 2
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Calculating a Surface Integral Example Part 3
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L'Hopital's Rule
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L'Hopital's Rule Example 1
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L'Hopital's Rule Example 2
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L'Hopital's Rule Example 3
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Calculus / First Semester - Limits, Continuity, Derivatives
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A way to remember the Entire Unit Circle for Trigonometry
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What is a Limit? Basic Idea of Limits
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Finding Limits From a Graph
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Calculating a Limt By Factoring and Canceling
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Calculating a Limit by Expanding and Simplfiying
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Calculating a Limit by Getting a Common Denominator
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Calculating a Limit Involving sin(x)/x as x approaches zero
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Limits Involving Absolute Value
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The Squeeze Theorem for Limits, Example 1
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Calculus - Infinite Limits
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Limits at Infinity - Basic Idea and Shortcuts
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Shortcut to Find Horizontal Asymptotes of Rational Functions
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Calculating a Limit at Infinity with a Radical
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Continuity - Part 1 of 2
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Continuity - Part 2 of 2
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Understanding the Definition of the Derivative
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Sketching the Derivative of a Function
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Finding a Derivative Using the Definition of a Derivative
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Basic Derivative Examples
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The Product Rule for Derivatives
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The Quotient Rule
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Basic Chain Rule Problems
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Using the Chain Rule - Harder Example #1
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Using the Chain Rule - Harder Example #2
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Using the Chain Rule - Harder Example #3
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Derivatives - Product + Chain Rule + Factoring
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Product Rule, Chain Rule and Factoring - Ex 2
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More Complicated Derivative Examples
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More Complicated Derivative Examples-1
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Finding the Equation of a Tangent Line
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Lots of Different Derivative Examples
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Implicit Differentiation - Basic Idea and Examples
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Using Implicit Differentiation - Extra Examples
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Using Implicit Differentiation - Example
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Using Implicit Differentiation to find a Second Derivative
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More Implicit Differentiation Examples- 2
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More Implicit Differentiation Examples- 3
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Logarithmic Differentiation
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Related Rates #1 Problem Using Implicit Differentiation
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Related Rates #2 Using Cones
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Related Rates #3 - A point on a graph
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Related Rates #4 Involving Trigonometry
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Related Rates #5 Involving Baseball
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Using Differentials
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Finding the Linearization at a Point / Tangent Line Approximation
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Increasing/Decreasing , Local Maximums/Minimums
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The Mean Value Theorem
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Finding Critical Numbers - Example 1
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Finding Critical Numbers - Example 2
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Finding Intervals of Increase/Decrease Local Max/Mins
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Finding Local Maximums/Minimums - Second Derivative Test
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Concavity, Inflection Points and Second Derivatives
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Curve Sketching Using Calculus - Part 1 of 2
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Curve Sketching Using Calculus - Part 2 of 2
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Summary of Curve Sketching - Example 2, Part 1 of 4
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Summary of Curve Sketching - Example 2 - Part 2 of 4
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Summary of Curve Sketching - Example 2 - Part 3 of 4
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Summary of Curve Sketching - Example 2 - Part 4 of 4
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Optimization Problem #1
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Optimization Problem #2
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Optimization Problem #3 - Making a Rain Gutter
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Newton's Method
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The Squeeze Theorem and Absolute Value Theorem, #1
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Calculus Revisited: Single Variable Calculus
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Sets, Functions & Limits- Preface
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Analytic Geometry
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Inverse Functions
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Sets, Functions & Limits- Derivatives and Limits
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A More Rigorous Approach to Limits
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Sets, Functions & Limits- Mathematical Inductions
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Derivatives of Some Simple Functions
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Approximations and Infinitesimals
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Composite Functions and the Chain Rule
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Differentiation of Inverse Functions
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Implicit Differentiation
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Differentiation- Continuity
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Differentiation- Curve Plotting
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Differentiation- Maxima and Minima
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Differentiation- Rolle's Theorem and its Consequences
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Differentiation- Inverse Differentiation
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Differentiation- The "Definite" Indefinite Integral
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The Circular Functions
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Inverse Circular Functions
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The Definite Integral
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Marriage of Differential and Integral Calculus
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Three-Dimensional Area
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One-Dimensional Area
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Logarithms without Exponents
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Inverse Logarithms
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What a Difference a Sign Makes
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Inverse Hyperbolic Functions
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More Integration Techniques- Some Basic Recipes
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More Integration Techniques- Partial Functions
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More Integration Techniques- Integration by Parts
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More Integration Techniques- Improper Integrals
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Infinite Series- Positive Series
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Infinite Series- Absolute Convergence
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Infinite Series- Polynomial Approximations
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Infinite Series- Uniform Convergence
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Infinite Series- Uniform Convergence of Power Series
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Computational Science and Engineering I
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Positive Definite Matrices K = A'CA
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One-Dimensional Applications: A = Difference Matrix
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Network Applications: A = Incidence Matrix
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Applications to Linear Estimation: Least Squares
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Applications to Dynamics: Eigenvalues of K, Solution of MU'' + KU = F(T)
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Underlying Theory: Applied Linear Algebra
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Discrete Vs. Continuous: Differences and Derivatives
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Applications to Boundary Value Problems: Laplace Equation
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Solutions of Laplace Equation: Complex Variables
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Delta Function and Green's Function
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initial Value Problems: Wave Equation and Heat Equation
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Solutions of initial Value Problems: Eigenfunctions
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Numerical Linear Algebra: Orthogonalization and A = QR
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Numerical Linear Algebra: SVD and Applications
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Numerical Methods in Estimation: Recursive Least Squares and Covariance Matrix
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Dynamic Estimation: Kalman Filter and Square Root Filter
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Finite Difference Methods: Equilibrium Problems
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Finite Difference Methods: Stability and Convergence
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Optimization and Minimum Principles: Euler Equation
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Finite Element Method: Equilibrium Equations
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Spectral Method: Dynamic Equations
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Fourier Expansions and Convolution
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Fast Fourier Transform and Circulant Matrices
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Discrete Filters: Lowpass and Highpass
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Filters in the Time and Frequency Domain
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Filter Banks and Perfect Reconstruction
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Multiresolution, Wavelet Transform and Scaling Function
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Splines and Orthogonal Wavelets: Daubechies Construction
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Applications in Signal and Image Processing: Compression
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Network Flows and Combinatorics: Max Flow = Min Cut
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Simplex Method in Linear Programming
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Nonlinear Optimization: Algorithms and Theory
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Convex Optimization I
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Introduction to Convex Optimization I
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Guest Lecturer: Jacob Mattingley
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Logistics
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Vector Composition
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Optimal And Locally Optimal Points
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(Generalized) Linear-Fractional Program
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Generalized Inequality Constraints
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Lagrangian
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Complementary Slackness
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Applications Section of Course
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Statistical Estimation
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Continue On Experiment Design
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Linear Discrimination (Cont.)
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LU Factorization (Cont.)
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Algorithm Section of The Course
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Continue on Unconstrained Minimization
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Newton's Method (Cont.)
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Logarithmic Barrier
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Interior-Point Methods (Cont.)
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Convex Optimization II
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Basic Rules for Subgradient Calculus
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Recap: Subgradients
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Convergence Proof, Stopping Criterion
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Project Subgradient For Dual Problem
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Stochastic Programming
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Addendum: Hit-And-Run CG Algorithm
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Example: Piecewise Linear Minimization
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Recap: Ellipsoid Method
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Comments: Latex Typesetting Style
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Decomposition Applications
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Sequential Convex Programming
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Recap: 'Difference Of Convex' Programming
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Recap: Conjugate Gradient Method
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Methods (Truncated Newton Method)
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Recap: Example: Minimum Cardinality Problem
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Model Predictive Control
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Stochastic Model Predictive Control
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Recap: Branch And Bound Methods, Basic Idea, Unconstrained, Nonconvex Minimization
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Developmental Math
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Place Value 1
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Place Value 2
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Place Value 3
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Rounding Whole Numbers 1
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Rounding Whole Numbers 2
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Rounding Whole Numbers 3
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Comparing Whole Numbers 1
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Comparing Whole Numbers 2
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Comparing Whole Numbers 3
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Adding Whole Numbers and Applications 1
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Adding Whole Numbers and Applications 2
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Adding Whole Numbers and Applications 3
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Adding Whole Numbers and Applications 4
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Rounding to Estimate Difference
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Rounding to Estimate Sums 1
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Rounding to Estimate Sums 2
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Multiplying Whole Numbers and Applications 1
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Multiplying Whole Numbers and Applications 2
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Multiplying Whole Numbers and Applications 3
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Multiplying Whole Numbers and Applications 4
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Multiplying Whole Numbers and Applications 5
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Area of a Circle
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