232 Courses

Differential Equations

The Geometrical View of y'=f(x,y): Direction Fields, Integral Curves

Euler's Numerical Method for y'=f(x,y) and its Generalizations

Solving Firstorder Linear ODE's; Steadystate and Transient Solutions

Firstorder Substitution Methods: Bernouilli and Homogeneous ODE's

Firstorder Autonomous ODE's: Qualitative Methods, Applications

Complex Numbers and Complex Exponentials

FirstOrder Linear with Constant Coefficients

Applications to Temperature, Mixing, RCcircuit, Decay, and Growth Models

Solving SecondOrder Linear ODE's with Constant Coefficients

Complex Characteristic Roots; Undamped and Damped Oscillations

SecondOrder Linear Homogeneous ODE's: Superposition, Uniqueness, Wronskians

Inhomogeneous ODE's; Stability Criteria for ConstantCoefficient ODE's

Inhomogeneous ODE's: Operator and Solution Formulas Involving Ixponentials

Interpretation of the Exceptional Case: Resonance

Introduction to Fourier Series; Basic Formulas for Period 2(pi)

More General Periods; Even and Odd Functions; Periodic Extension

Finding Particular Solutions via Fourier Series; Resonant Terms

Derivative Formulas; Using the Laplace Transform to Solve Linear ODE's

Convolution Formula: Proof, Connection with Laplace Transform, Application

Using Laplace Transform to Solve ODE's with Discontinuous Inputs

Impulse Inputs; Dirac Delta Function, Weight and Transfer Functions

FirstOrder Systems of ODE's; Solution by Elimination, Geometric Interpretation

Homogeneous Linear Systems with Constant Coefficients: Solution via Matrix Eigenvalues

Continuation: Repeated Real Eigenvalues, Complex Eigenvalues

Sketching Solutions of 2x2 Homogeneous Linear System with Constant Coefficients

Matrix Methods for Inhomogeneous Systems

Matrix Exponentials; Application to Solving Systems

Decoupling Linear Systems with Constant Coefficients

Nonlinear Autonomous Systems: Finding the Critical Points and Sketching Trajectories

Limit Cycles: Existence and Nonexistence Criteria

NonLinear Systems and FirstOrder ODE's


Digital Typography

Directed Evolution: Engineering Biocatalysts

Discrete Stochastic Processes

Introduction and Probability Review

More Review: The Bernoulli Process

Law of Large Numbers, Convergence

Poisson (the Perfect Arrival Process)

Poisson Combining and Splitting

From Poisson to Markov

Finitestate Markov Chains: The Matrix Approach

Markov Eigenvalues and Eigenvectors

Markov Rewards and Dynamic Programming

Renewals and the Strong Law of Large Numbers

Renewals: Strong Law and Rewards

Renewal Rewards, Stopping Trials, and Wald's Inequality

Little, M/G/1, Ensemble Averages

The Last Renewal

Renewals and CountableState Markov

CountableState Markov Chains

CountableState Markov Chains and Processes

CountableState Markov Processes

Markov Processes and Random Walks

Hypothesis Testing and Random Walks

Random Walks and Thresholds

Martingales (Plain, Sub, and Super)

Martingales: Stopping and Converging

Putting It All Together


Drugs, Politics, and Culture

Dynamic Optimization & Economic Applications (Recursive Methods)

Dynamic Optimization Methods with Applications

Dynamic Systems and Control

Dynamics of Nonlinear Systems