232 Courses
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Differential Equations
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The Geometrical View of y'=f(x,y): Direction Fields, Integral Curves
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Euler's Numerical Method for y'=f(x,y) and its Generalizations
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Solving First-order Linear ODE's; Steady-state and Transient Solutions
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First-order Substitution Methods: Bernouilli and Homogeneous ODE's
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First-order Autonomous ODE's: Qualitative Methods, Applications
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Complex Numbers and Complex Exponentials
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First-Order Linear with Constant Coefficients
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Applications to Temperature, Mixing, RC-circuit, Decay, and Growth Models
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Solving Second-Order Linear ODE's with Constant Coefficients
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Complex Characteristic Roots; Undamped and Damped Oscillations
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Second-Order Linear Homogeneous ODE's: Superposition, Uniqueness, Wronskians
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Inhomogeneous ODE's; Stability Criteria for Constant-Coefficient ODE's
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Inhomogeneous ODE's: Operator and Solution Formulas Involving Ixponentials
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Interpretation of the Exceptional Case: Resonance
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Introduction to Fourier Series; Basic Formulas for Period 2(pi)
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More General Periods; Even and Odd Functions; Periodic Extension
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Finding Particular Solutions via Fourier Series; Resonant Terms
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Derivative Formulas; Using the Laplace Transform to Solve Linear ODE's
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Convolution Formula: Proof, Connection with Laplace Transform, Application
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Using Laplace Transform to Solve ODE's with Discontinuous Inputs
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Impulse Inputs; Dirac Delta Function, Weight and Transfer Functions
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First-Order Systems of ODE's; Solution by Elimination, Geometric Interpretation
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Homogeneous Linear Systems with Constant Coefficients: Solution via Matrix Eigenvalues
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Continuation: Repeated Real Eigenvalues, Complex Eigenvalues
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Sketching Solutions of 2x2 Homogeneous Linear System with Constant Coefficients
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Matrix Methods for Inhomogeneous Systems
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Matrix Exponentials; Application to Solving Systems
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Decoupling Linear Systems with Constant Coefficients
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Non-linear Autonomous Systems: Finding the Critical Points and Sketching Trajectories
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Limit Cycles: Existence and Non-existence Criteria
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Non-Linear Systems and First-Order ODE's
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Digital Typography
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Directed Evolution: Engineering Biocatalysts
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Discrete Stochastic Processes
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Introduction and Probability Review
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More Review: The Bernoulli Process
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Law of Large Numbers, Convergence
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Poisson (the Perfect Arrival Process)
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Poisson Combining and Splitting
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From Poisson to Markov
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Finite-state Markov Chains: The Matrix Approach
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Markov Eigenvalues and Eigenvectors
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Markov Rewards and Dynamic Programming
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Renewals and the Strong Law of Large Numbers
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Renewals: Strong Law and Rewards
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Renewal Rewards, Stopping Trials, and Wald's Inequality
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Little, M/G/1, Ensemble Averages
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The Last Renewal
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Renewals and Countable-State Markov
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Countable-State Markov Chains
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Countable-State Markov Chains and Processes
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Countable-State Markov Processes
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Markov Processes and Random Walks
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Hypothesis Testing and Random Walks
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Random Walks and Thresholds
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Martingales (Plain, Sub, and Super)
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Martingales: Stopping and Converging
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Putting It All Together
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Drugs, Politics, and Culture
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Dynamic Optimization & Economic Applications (Recursive Methods)
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Dynamic Optimization Methods with Applications
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Dynamic Systems and Control
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Dynamics of Nonlinear Systems