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Learn Differential Equations

Res. 18-009 - Learn Differential Equations: Up Close with Gilbert Strang and Cleve Moler (Fall 2015, MIT OCW). Instructors: Prof. Gilbert Strang and Dr. Cleve Moler. This is an in-depth series of videos about differential equations and the MATLAB ODE suite. These videos are suitable for students and life-long learners to enjoy. (from ocw.mit.edu)

Lecture 03 - Response to Exponential Input


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Differential Equations and Linear Algebra
Introduction
Lecture 01 - Overview of Differential Equations
Lecture 02 - The Calculus You Need
First Order Equations
Lecture 03 - Response to Exponential Input
Lecture 04 - Response to Oscillating Input
Lecture 05 - Solution for Any Input
Lecture 06 - Step Function and Delta Function
Lecture 07 - Response to Complex Exponential
Lecture 08 - Integrating Factor for Constant Rate
Lecture 09 - Integrating Factor for a Varying Rate
Lecture 10 - The Logistic Equation
Lecture 11 - The Stability and Instability of Steady States
Lecture 12 - Separable Equations
Second Order Equations
Lecture 13 - Second Order Equations
Lecture 14 - Forced Harmonic Motion
Lecture 15 - Unforced Damped Motion
Lecture 16 - Impulse Response and Step Response
Lecture 17 - Exponential Response ? Possible Resonance
Lecture 18 - Second Order Equations with Damping
Lecture 19 - Electrical Networks: Voltages and Currents
Lecture 20 - Method of Undetermined Coefficients
Lecture 21 - An Example of Undetermined Coefficients
Lecture 22 - Variation of Parameters
Lecture 23 - Laplace Transform: First Order Equation
Lecture 24 - Laplace Transform: Second Order Equation
Lecture 25 - Laplace Transforms and Convolution
Graphical and Numerical Methods
Lecture 26 - Pictures of Solutions
Lecture 27 - Phase Plane Pictures: Source, Sink, Saddle
Lecture 28 - Phase Plane Pictures: Spirals and Centers
Lecture 29 - Two First Order Equations: Stability
Lecture 30 - Linearization at Critical Points
Lecture 31 - Linearization of Two Nonlinear Equations
Lecture 32 - Eigenvalues and Stability: 2 by 2 Matrix, A
Lecture 33 - The Tumbling Box in 3-D
Vector Spaces and Subspaces
Lecture 34 - The Column Space of a Matrix
Lecture 35 - Independence, Basis, and Dimension
Lecture 36 - The Big Picture of Linear Algebra
Lecture 37 - Graphs
Lecture 38 - Incidence Matrices of Graphs
Eigenvalues and Eigenvectors
Lecture 39 - Eigenvalues and Eigenvectors
Lecture 40 - Diagonalizing a Matrix
Lecture 41 - Powers of Matrices and Markov Matrices
Lecture 42 - Solving Linear Systems
Lecture 43 - The Matrix Exponential
Lecture 44 - Similar Matrices
Lecture 45 - Symmetric Matrices, Real Eigenvalues, Orthogonal Eigenvectors
Lecture 46 - Second Order Systems
Applied Mathematics and ATA
Lecture 47 - Positive Definite Matrices
Lecture 48 - Singular Value Decomposition (the SVD)
Lecture 49 - Boundary Conditions Replace Initial Conditions
Lecture 50 - Laplace Equation
Fourier and Laplace Transforms
Lecture 51 - Fourier Series
Lecture 52 - Examples of Fourier Series
Lecture 53 - Fourier Series Solution of Laplace's Equation
Lecture 54 - Heat Equation
Lecture 55 - Wave Equation