M.I.T. 18.03 Ordinary Differential Equations
18.03 Notes and Exercises

D. Definite Integral Solutions
G. Graphical and Numerical Methods
C. Complex Numbers
IR. Input Response Models
O. Linear Differential Operators
S. Stability
I. Impulse Response and Convolution
H. Heaviside Coverup Method
LT. Laplace Transform
CG. Convolution and Green's Formula
LS.1. Linear Systems: Review of Linear Algebra
LS.2. Homogeneous Linear Systems with Constant Coefficients
LS.3. Complex and Repearted Eigenvalues
LS.4.  Decoupling Systems
LS.5. Theory of Linear Systems
LS.6. Solution Matrices
GS.1-6. Graphing ODE Systems
GS.7-8. Structural stability
LC. Limit Cycles
FR. Frequency Response
P. Poles and Amplitude Response
LA.1. LA.1: Phase Plane and Linear Systems
LA.2. LA.2: Matrix Multiplication, Rank, Solving Linear Systems
LA.3. LA.3: Complete Solutions, Nullspace, Space, Dimension, Basis
LA.4. LA.4: Inverses and Determinants
LA.5. LA.5: Eigenvalues and Eigenvectors
LA.6. LA.6: Diagonalization and Orthogonal Matrices
LA.7. LA.7: Two Dimensional Dynamics
LA.8. LA.8: Trace-determinant plane, Stability
LA.9. LA.9: Decoupling
LA.10. LA.10: The Matrix Exponential
LA.11. LA.11: Inhomogeneous Systems
PDE.1. PDE.1: Fourier's Theory of Heat
PDE.2. PDE.2: Decoupling; Insulated Ends
PDE.3. PDE.3: The Wave Equation

Exercises and Solutions
1.  First Order ODE's Solutions
2. Higher Order ODE's Solutions
3. Laplace Transform Solutions
4. Linear Systems Solutions
5. Graphing Systems Solutions
6. Power Series Solutions
7. Fourier Series Solutions
8. Extra Problems Solutions
9.  Linear Algebra Exercises Solutions
10.  PDE Exercises Solutions

Entire set of notes in one file

©Arthur Mattuck, Haynes Miller, David Jerison, Jennifer French, Jeremy Orloff and M.I.T. 2007, 2013, 2017