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Massachusetts Institute of Technology

Learn Differential Equations: Up Close with Gilbert Strang and Cleve Moler

Massachusetts Institute of Technology via MIT OpenCourseWare

Overview

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*Learn Differential Equations: Up Close with* *\_Gilbert Strang* and\_ *Cleve Moler* 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. About the Instructors Gilbert Strang is the MathWorks Professor of Mathematics at MIT. His research focuses on mathematical analysis, linear algebra and PDEs. He has written textbooks on linear algebra, computational science, finite elements, wavelets, GPS, and calculus. Cleve Moler is chief mathematician, chairman, and cofounder of MathWorks. He was a professor of math and computer science for almost 20 years at the University of Michigan, Stanford University, and the University of New Mexico. These videos were produced by {{% resource_link "154536eb-d4bb-46b6-a7b9-eb8c76859eba" "The MathWorks®" %}} and are also available on {{% resource_link "a65d4362-afac-4b7c-b1ad-b0062e60284b" "The MathWorks website" %}}.

Syllabus

  • An Example of Undetermined Coefficients
  • Boundary Conditions Replace Initial Conditions
  • Diagonalizing a Matrix
  • Eigenvalues and Eigenvectors
  • Electrical Networks: Voltages and Currents
  • Examples of Fourier Series
  • Exponential Response – Possible Resonance
  • Forced Harmonic Motion
  • Fourier Series
  • Fourier Series Solution of Laplace's Equation
  • Gilbert and Cleve Introduction
  • Graphs
  • Heat Equation
  • Impulse Response and Step Response
  • Incidence Matrices of Graphs
  • Independence, Basis, and Dimension
  • Integrating Factor for a Varying Rate
  • Integrating Factor for Constant Rate
  • Laplace Equation
  • Laplace Transform: First Order Equation
  • Laplace Transform: Second Order Equation
  • Laplace Transforms and Convolution
  • Linearization at Critical Points
  • Linearization of two nonlinear equations
  • Lorenz Attractor and Chaos
  • Method of Undetermined Coefficients
  • Order, Naming Conventions
  • Overview of Differential Equations
  • Phase Plane Pictures: Source, Sink, Saddle
  • Phase Plane Pictures: Spirals and Centers
  • Pictures of Solutions
  • Positive Definite Matrices
  • Powers of Matrices and Markov Matrices
  • Predator-Prey Equations
  • Response to Complex Exponential
  • Response to Exponential Input
  • Response to Oscillating Input
  • Second Order Equations
  • Second Order Equations with Damping
  • Second Order Systems
  • Separable Equations
  • Similar Matrices
  • Singular Value Decomposition (the SVD)
  • Solution for Any Input
  • Solving Linear Systems
  • Step Function and Delta Function
  • Symmetric Matrices, Real Eigenvalues, Orthogonal Eigenvectors
  • Systems of Equations
  • The Big Picture of Linear Algebra
  • The Calculus You Need
  • The Column Space of a Matrix
  • The Logistic Equation
  • The MATLAB ODE Suite
  • The Matrix Exponential
  • The Stability and Instability of Steady States
  • Tumbling Box
  • Two First Order Equations: Stability
  • Unforced Damped Motion
  • Variation of Parameters
  • Wave Equation
  • Euler, ODE1
  • Eigenvalues and Stability: 2 by 2 Matrix, A
  • Midpoint Method, ODE2
  • The Tumbling Box in 3-D
  • Classical Runge-Kutta, ODE4
  • Estimating Error, ODE23
  • Stiffness, ODE23s, ODE15s
  • ODE45

Taught by

Dr. Cleve Moler and Prof. Gilbert Strang

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