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Air Date
Episode Name
Watched?
E1
Overview of Differential Equations
E2
The Calculus You Need
E3
1.4b: Response to Exponential Input, exp(s*t)
E4
1.4c: Response to Oscillating Input, cos(w*t)
E5
1.4d: Solution for Any Input, q(t)
E6
1.4e: Step Function and Delta Function
E7
1.5: Response to Complex Exponential, exp(i*w*t) = cos(w*t)+i*sin(w*t)
E8
1.6: Integrating Factor for a Constant Rate, a
E9
1.6b: Integrating Factor for a Varying Rate, a(t)
E10
1.7: The Logistic Equation
E11
1.7c: The Stability and Instability of Steady States
E12
1.8: Separable Equations
E13
2.1: Second Order Equations
E14
2.1b: Forced Harmonic Motion
E15
2.3: Unforced Damped Motion
E16
2.3c: Impulse Response and Step Response
E17
2.4: Exponential Response - Possible Resonance
E18
2.4b: Second Order Equations With Damping
E19
2.5: Electrical Networks: Voltages and Currents
E20
2.6: Methods of Undetermined Coefficients
E21
2.6b: An Example of Method of Undetermined Coefficients
E22
2.6c: Variations of Parameters
E23
2.7: Laplace Transform: First Order Equation
E24
2.7b: Laplace Transform: Second Order Equation
E25
2.7c: Laplace Transforms and Convolution
E26
3.1: Pictures of the Solutions
E27
3.2: Phase Plane Pictures: Source, Sink Saddle
E28
3.2b: Phase Plane Pictures: Spirals and Centers
E29
3.2c: Two First Order Equations: Stability
E30
3.3: Linearization at Critical Points
E31
3.3b: Linearization of y'=f(y,z) and z'=g(y,z)
E32
3.3c: Eigenvalues and Stability: 2 by 2 Matrix, A
E33
3.3d: The Tumbling Box in 3-D
E34
5.1: The Column Space of a Matrix, A
E35
5.4: Independence, Basis, and Dimension
E36
5.5: The Big Picture of Linear Algebra
E37
5.6: Graphs
E38
5.6b: Incidence Matrices of Graphs
E39
6.1: Eigenvalues and Eigenvectors
E40
6.2: Diagonalizing a Matrix
E41
6.2b: Powers, A^n, and Markov Matrices
E42
6.3: Solving Linear Systems
E43
6.4: The Matrix Exponential, exp(A*t)
E44
6.4b: Similar Matrices, A and B=M^(-1)*A*M
E45
6.5: Symmetric Matrices, Real Eigenvalues, Orthogonal Eigenvectors
E46
6.5b: Second Order Systems, y''+Sy=0
E47
7.2: Positive Definite Matrices, S=A'*A
E48
7.2b: Singular Value Decomposition, SVD
E49
7.3: Boundary Conditions Replace Initial Conditions
E50
7.4: Laplace Equation
E51
8.1: Fourier Series
E52
8.1b: Examples of Fourier Series
E53
8.1c: Fourier Series Solution of Laplace's Equation
E54
8.3: Heat Equation
E55
8.4: Wave Equation
