Free Online Lectures and Courses for Mathematics
40 Courses
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Precalculus
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Introduction to Limits
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Limit Examples (Part 1)
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Limit Examples (Part 2)
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Limit Examples (Part 3)
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Squeeze Theorem
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Proof: lim (sin x)/x
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More Limits
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Sequences and Series Part 1
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Sequences and Series Part 2
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Permutations
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Combinations
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Binomial Theorem Part 1
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Binomial Theorem Part 2
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Binomial Theorem Part 3
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Exponential Growth
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Parametric Equations 1
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Parametric Equations 2
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Parametric Equations 3
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Parametric Equations 4
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Introduction to Function Inverses
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Probability
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Sequence and Series Video Tutorial
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What is a Sequence? Basic Sequence Info
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Sequences - Examples showing convergence or divergence
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Summation Notation
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What is a Series
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Geometric Series and the Test for Divergence - Part 1
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Geometric Series and the Test for Divergence - Part 2
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Geometric Series - Expressing a Decimal as a Rational Number
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Telescoping Series Example
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Showing a Series Diverges using Partial Sums
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Using the Integral Test for Series
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Remainder Estimate for the Integral Test
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Limit Comparison Test and Direct Comparison Test (Part 1)
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Limit Comparison Test and Direct Comparison Test (Part 2)
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Alternating Series
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More Alternating Series Examples
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Alternating Series Estimation Theorem
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Using the Ratio Test to Determine if a Series Converges #1
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Using the Ratio Test to Determine if a Series Converges #2
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Using the Ratio Test to Determine if a Series Converges #3 (Factorials)
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Root Test for Series
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Strategy for Testing Series - Series Practice Problems
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Absolute Convergence, Conditional Convergence and Divergence
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Power Series Representation of Functions
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Power Series - Finding the Interval of Convergence
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Radius of Convergence for a Power Series
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Differentiating and Integrating Power Series
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Finding the Sum of a Series by Differentiating
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Finding Power Series by Differentiation - 3 examples
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Integrating a Power Series
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Integrating a Power Series, Example 2
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Finding Interval of Convergence for a Given Power Series Representation
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Interval and Radius of Convergence for a Series, Ex 3
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Interval and Radius of Convergence for a Series, Ex 4
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Interval and Radius of Convergence for a Series, Ex 5
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Interval and Radius of Convergence for a Series, Ex 6
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Interval and Radius of Convergence for a Series, Ex 7
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Interval and Radius of Convergence for a Series, Ex 9
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Finding a New Power Series by Manipulating a Known Power Series
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Finding Power Series Representations by Manipulating 1/(1-x) - Another Ex 1
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Finding a New Power Series by Manipulating a Known Power Series, Ex 2
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Finding a Maclaurin Series Expansion - Another Example 1
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Taylor's Remainder Theorem - Finding the Remainder, Ex 1
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Taylor's Remainder Theorem - Finding the Remainder, Ex 2
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Taylor's Remainder Theorem - Finding the Remainder, Ex 3
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Finding a Maclaurin Polynomial - Ex 1
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Finding a Maclaurin Polynomial - Ex 2
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Finding a Taylor Polynomial to Approximate a Function, Ex 1
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The Root Test - Another Example, #3
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Finding a Taylor Polynomial to Approximate a Function, Ex 2
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Finding a Taylor Polynomial to Approximate a Function, Ex 3
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Finding a Taylor Polynomial to Approximate a Function, Ex 4
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The Root Test - Another Example, #2
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The Ratio Test , Another Example #1
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The Ratio Test , Another Example #2
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The Ratio Test , Another Example #3
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The Ratio Test , Another Example #4
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Absolute Convergence, Conditional Convergence, Another Example 1
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Absolute Convergence, Conditional Convergence, Another Example 2
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Absolute Convergence, Conditional Convergence, Another Example 3
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Alternating Series - Another Example 1
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Alternating Series - Another Example 2
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Alternating Series - Another Example 3
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Alternating Series - Another Example 4
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Intro to Summation Notation and Infinite Series, Ex 1
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Limit Comparison Test for Series - Another Example 1
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Limit Comparison Test for Series - Another Example 2
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Limit Comparison Test for Series - Another Example 3
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Limit Comparison Test for Series - Another Example 4
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Limit Comparison Test for Series - Another Example 5
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Intro to Monotonic and Bounded Sequences, Ex 1
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The Squeeze Theorem and Absolute Value Theorem, #1
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The Squeeze Theorem and Absolute Value Theorem, #2
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The Squeeze Theorem and Absolute Value Theorem, #3
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Finding the Limit of a Sequence, 3 more examples
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Multiplication and Division of Power Series
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Taylor and Maclaurin Series - Example 1
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Taylor / Maclaurin Series for Sin (x)
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Taylor and Maclaurin Series - Example 2
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Using Series to Evaluate Limits
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Using Maclaurin/Taylor Series to Approximate a Definite Integral
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The Binomial Series - Example 1
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The Binomial Series - Example 2
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Integrating a Function as a Power Series
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Finding a Power Series Representation for a Logarithm Function
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Finding a Function to Match a Given Power Series by Integrating
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Finding a Power Series by Differentiation
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Interval and Radius of Convergence for a Series, Ex 2
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Direct Comparison Test - Another Example 2
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Direct Comparison Test - Another Example 1
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Direct Comparison Test - Another Example 3
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P-Series
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Integral Test to Evaluate Series, Ex 4
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Integral Test to Evaluate Series, Ex 3
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Integral Test to Evaluate Series, Ex 2
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Integral Test to Evaluate Series, Ex 1
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Telescoping Series ,Showing Divergence Using Partial Sums
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Telescoping Series , Finding the Sum, Example 1
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Sum of an Infinite Geometric Series, Ex 3
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Sum of an Infinite Geometric Series, Ex 2
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Sum of an Infinite Geometric Series, Ex 1
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Writing a Geometric Series using Sigma / Summation Notation, Ex 2
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Finding a Formula for a Partial Sum of a Telescoping Series
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Writing a Geometric Series using Sigma / Summation Notation
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Test for Divergence for Series, Two Examples
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Direct Comparison Test - Another Example 4
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Direct Comparison Test - Another Example 5
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The Root Test - Another Example, #1
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Alternating Series - Error Estimation #2
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Alternating Series - Error Estimation
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Limit Comparison Test for Series - Another Example 6
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Limit Comparison Test for Series - Another Example 7
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Limit Comparison Test for Series - Another Example 8
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Single Variable Calculus
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Derivatives, Slope, Velocity, Rate of Change
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Limits, Continuity, Trigonometric Limits
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Derivatives of Products, Quotients, Sine, Cosine
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Chain Rule, Higher Derivatives
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Implicit Differentiation, Inverses
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Hyperbolic Functions (cont.) and Exam 1 Review
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Linear and Quadratic Approximations
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Curve Sketching
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Max-Min Problems
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Related Rates
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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- Many Versus Infinite
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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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Statistics
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Statistics: The Average
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Sample vs. Population Mean
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Variance of a Population
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Sample Variance
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Standard Deviation
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Alternate Variance Formulas
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Introduction to Random Variables
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Probability Density Functions
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Binomial Distribution 3
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Expected Value: E(X)
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Poisson Process 1
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Poisson Process 2
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Law of Large Numbers
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Normal Distribution Excel Exercise
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Introduction to the Normal Distribution
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Qualitative Sense of Normal Distributions
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Z-Score
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Emperical Rule
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Standard Normal Distribution and the Empirical Rule
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More Emperical Rule and Z-Score Practice
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Central Limit Theorem
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Sampling Distribution of the Sample Mean Part 1
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Sampling Distribution of the Sample Mean Part 2
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Standard Error of the Mean
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Sampling Distribution of the Sample Mean
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Confidence Interval 1
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Mean and Variance of Bernoulli Distribution Example
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Bernoulli Distribution Mean and Variance Formulas
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Margin of Error 1
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Margin of Error 2
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Confidence Interval Example
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Small Sample Size Confidence Intervals
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One-Tailed and Two-Tailed Tests
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Z-statistics vs. T-statistics
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Type 1 Errors
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Small Sample Hypothesis Test
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T-Statistic Confidence Interval
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Large Sample Proportion Hypothesis Testing
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Variance of Differences of Random Variables
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Difference of Sample Means Distribution
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Confidence Interval of Difference of Means
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Clarification of Confidence Interval of Difference of Means
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Hypothesis Test for Difference of Means
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Comparing Population Part 1
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Comparing Population Part 2
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Hypothesis Test Comparing Population Proportions
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Squared Error of Regression Line
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Minimizing Squared Error to Regression Line Part 1
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Minimizing Squared Error to Regression Line Part 3
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Minimizing Squared Error to Regression Line Part 4
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Regression Line Example
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Minimizing Squared Error to Regression Line 2
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R-Squared or Coefficient of Determination
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Second Regression Example
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Calculating R-Squared
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Covariance and the Regression Line
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Chi-Square Distribution Introduction
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Pearson's Chi Square Test (Goodness of Fit)
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Contingency Table Chi-Square Test
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Calculating SST (Total Sum of Squares)
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Calculating SSW and SSB (Total Sum of Squares Within and Between)
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Hypothesis Test with F-Statistic
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Statistics 110: Probability
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Probability and Counting
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Story Proofs, Axioms of Probability
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Birthday Problem, Properties of Probability
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Conditional Probability
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Conditioning Continued, Law of Total Probability
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Monty hall, Simpson's Paradox
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Gambler's Ruin and Random Variables
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Random Variables and Their Distributions
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Expectation, Indicator Random Variables, Linearity
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Expectation Continued
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The Poisson Distribution
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Discrete vs. Continuous, the Uniform
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Normal Distribution
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Location, Scale and LOTUS
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Midterm Review
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Exponential Distribution
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Moment Generating Functions
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Moment Generating Functions Continued
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Joint, Conditional, and Marginal Distributions
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Multinominal and Caucchy
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Covariance and Correlation
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Transformations and Convolutions
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Beta Distribution
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Gamma Distribution and Poisson Process
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Order Statistics and Conditional Expectation
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Conditional Expectation Continued
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Conditional Expectation Given an R.V.
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Inequalities
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Law of Large Numbers and Central Limit Theorem
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Chi-Square, Student-t, Multivariate Normal
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Markov Chains
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Markov Chains Continued
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Markov Chains Continued Futher
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A Look Ahead
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The Fourier Transform and its Applications
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The Fourier Series
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Periodicity; How Sine and Cosine Can be Used to Model More Complex Functions
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Analyzing General Periodic Phenomena as a Sum of Simple Periodic Phenomena
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Wrapping Up Fourier Series; Making Sense of Infinite Sums and Convergence
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Continued Discussion of Fourier Series and the Heat Equation
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Correction to Heat Equation Discussion
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Review of Fourier Transform (and inverse) Definitions
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Effect on Fourier Transform of Shifting a Signal
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Continuing Convolution: Review of the Formula
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Central Limit Theorem and Convolution; Main Idea
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Cop Story
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Setting Up the Fourier Transform of a Distribution
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Derivative of a Distribution
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Application of the Fourier Transform: Diffraction: Setup
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More on Results From Last Lecture (Diffraction Patterns and the Fourier Transform)
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Review of Main Properties of the Shah Function
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Review of Sampling and Interpolation Results
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Aliasing Demonstration with Music
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Review: Definition of the DFT
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Review of Basic DFT Definitions
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FFT Algorithm: Setup: DFT Matrix Notation
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Linear Systems: Basic Definitions
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Review of Last Lecture: Discrete V. Continuous Linear Systems
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Review of Last Lecture: LTI Systems and Convolution
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Approaching the Higher Dimensional Fourier Transform
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Higher Dimensional Fourier Transforms- Review
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Shift Theorem in Higher Dimensions
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Shahs
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Tomography and Inverting the Radon Transform
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The Mathematics of Everyday Life
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Trigonometry
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Basic Trigonometry Part 1
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Basic Trigonometry Part 2
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Radians and Degrees
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Using Trig Functions Part 1
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Using Trig Functions Part 2
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The Unit Circle Definition of Trigonometric Functions Part 1
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The Unit Circle Definition of Trigonometric Functions Part 2
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Graph of the Sine Function
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Graph of the Trig Function
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Graphing Trig Functions
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Trig Graphs
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Determining the Equation of a Trigonometric Function
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Trigonometric Identities Part 1
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Proof: sin(a+b) = (cos a)(sin b) + (sin a)(cos b)
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Proof: cos(a+b) = (cos a)(cos b)-(sin a)(sin b)
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Trigonometric Identities Part 2
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Trigonometric Identities Part 3
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Trigonometry Word Problems Part 1
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Trigonometry Word Problems Part 2
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Law of Cosines
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Navigation Word Problem
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Proof: Law of Sines
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Ferris Wheel Trig Problem Part 1
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Ferris Wheel Trig Problem Part 2
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Fun Trig Problem
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Inverse Trig Functions: Arcsin
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Inverse Trig Functions: Arctan
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Inverse Trig Functions: Arccos
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Trigonometry Identity Review/Fun
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Vector Calculus
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Applications of Double Integrals
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Path Integrals - How to Integrate Over Curves
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Vector Fields
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Divergence
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Curl
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Line Integrals (2)
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Applications of Line Integrals
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Fundamental Theorem of Line Integrals
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Green's Theorem
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More on Green's Theorem
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Parametrised Surfaces
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Surface Integrals
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More on Surface Integrals
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Surface Integrals and Vector Fields
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Partial Differential Equations
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Separable Differential Equations
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