Starting a new Lecture Notes Series on MIT Learn Differential Equations
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MIT Learn Differential Equations By Lecture Notes together!
Lecture 1: Gilbert and Cleve Introduction
Lecture 2: Overview of Differential Equations
Lecture 3: The Calculus You Need
Lecture 4: Response to Exponential Input
Lecture 5: Response to Oscillating Input
Lecture 6: Solution for Any Input
Lecture 7: Step Function and Delta Function
Lecture 8: Response to Complex Exponential
Lecture 9: Integrating Factor for Constant Rate
Lecture 10: Integrating Factor for a Varying Rate
Lecture 11: The Logistic Equation
Lecture 12: The Stability and Instability of Steady States
Lecture 13: Separable Equations
Lecture 14: Second Order Equations
Lecture 15: Forced Harmonic Motion
Lecture 16: Unforced Damped Motion
Lecture 17: Impulse Response and Step Response
Lecture 18: Exponential Response – Possible Resonance
Lecture 19: Second Order Equations with Damping
Lecture 20: Electrical Networks: Voltages and Currents
Lecture 21: Method of Undetermined Coefficients
Lecture 22: An Example of Undetermined Coefficients
Lecture 23: Variation of Parameters
Lecture 24: Laplace Transform: First Order Equation
Lecture 25: Laplace Transform: Second Order Equation
Lecture 26: Laplace Transforms and Convolution
Lecture 27: Pictures of Solutions
Lecture 28: Phase Plane Pictures: Source, Sink, Saddle
Lecture 29: Phase Plane Pictures: Spirals and Centers
Lecture 30: Two First Order Equations: Stability
Lecture 31: Linearization at Critical Points
Lecture 32: Linearization of two nonlinear equations
Lecture 33: Eigenvalues and Stability: 2 by 2 Matrix, A
Lecture 34: The Tumbling Box in 3-D
Lecture 35: The Column Space of a Matrix
Lecture 36: Independence, Basis, and Dimension
Lecture 37: The Big Picture of Linear Algebra
Lecture 38: Graphs
Lecture 39: Incidence Matrices of Graphs
Lecture 40: Eigenvalues and Eigenvectors
Lecture 41: Diagonalizing a Matrix
Lecture 42: Powers of Matrices and Markov Matrices
Lecture 43: Solving Linear Systems
Lecture 44: The Matrix Exponential
Lecture 45: Similar Matrices
Lecture 47: Second Order Systems
Lecture 48: Positive Definite Matrices
Lecture 49: Singular Value Decomposition (the SVD)
Lecture 50: Boundary Conditions Replace Initial Conditions
Lecture 51: Laplace Equation
Lecture 52: Fourier Series
Lecture 53: Examples of Fourier Series
Lecture 54: Fourier Series Solution of Laplace's Equation
Lecture 55: Heat Equation
Lecture 56: Wave Equation
Lecture 57: Euler, ODE1
Lecture 58: Midpoint Method, ODE2
Lecture 59: Classical Runge-Kutta, ODE4
Lecture 60: Order, Naming Conventions
Lecture 61: Estimating Error, ODE23
Lecture 62: ODE45
Lecture 63: Stiffness, ODE23s, ODE15s
Lecture 64: Systems of Equations
Lecture 65: The MATLAB ODE Suite
Lecture 66: Tumbling Box
Lecture 67: Predator-Prey Equations
Lecture 68: Lorenz Attractor and Chaos