| L0 |
Terminology and implicit solutions |
(PDF) |
[BR] Sec. 1.1 Terminology & Implicit Solutions |
| Unit I: First-order differential equations |
| L1 |
Integration and solutions |
(PDF) |
[BR] Sec. 1.2 Fundamental Theorem of the Calculus & Method by Quadrature |
| L2 |
Fundamental principles |
(PDF) |
[BR] Sec. 1.9 Fundamental Principles - Linearity, Existence and Uniqueness, Stability |
| L3 |
First-order linear equations |
(PDF) |
[BR] Sec. 1.3 First-order Linear Equations & Logarithmic Spirals |
| L4 |
Separable equations |
(PDF) |
[BR] Sec. 1.4 Separable Equations & Orthogonal Trajectories |
| L5 |
Linear fractional equations |
(PDF) |
[BR] Sec. 1.7 Linear Fractional Equations |
| Unit II: Second-order linear equations |
| L6 |
Second-order linear equations |
(PDF) |
[BR] Sec. 2.1-2.2 Second-order Linear Equations |
| L7 |
Mechanical oscillation |
( PDF) |
|
| L8 |
Uniqueness and the wronskian |
(PDF) |
[BR] Sec. 2.4-2.5 Uniqueness & the Wronskian |
| L9 |
Separation and comparison theorems |
(PDF) |
[BR] Sec. 2.6 Separation and Comparison Theorems |
| L10 |
The maximum principle |
(PDF) |
|
| Unit III: Higher-order linear equations |
| L11 |
Higher-order linear equations |
(PDF) |
[BR] Sec. 3.1-3.3 The Characteristic Polynomial |
| L12 |
Solution bases |
(PDF) |
[BR] Sec. 3.4 Solution Bases - Existence & Uniqueness |
| L13 |
Inhomogeneous equations |
(PDF) |
[BR] Sec. 3.5 Inhomogeneous Equations |
| L14 |
Stability |
(PDF) |
[BR] Sec. 2.3, 3.7 Asymptotic Stability |
| L15 |
Wellposedness; introduction |
|
[BR] Sec. 6.2, 6.6 Wellposedness; Introduction |
| L16 |
Uniform convergence |
|
[BR] Sec. 6.7, 6.9 Picard's Iteration |
| L17 |
Uniqueness and continuity |
|
[BR] Sec. 6.3, SS1.9-1.10 Uniqueness and Continuity |
| L18 |
Remarks on wellposedness |
|
[BR] Sec. 6.5, 6.8, 6.10 Remarks on Wellposedness |
| Unit V: The Laplace transform |
| L19 |
Laplace transform |
(PDF) |
|
| L20 |
Transform and differential equations: generalized solutions, application to ODEs |
(PDF) |
|
| L21 |
Step functions |
(PDF) |
|
| L22 |
Convolution |
(PDF) |
|
| L23 |
The dirac distribution |
(PDF) |
|
| L24 |
The transfer function and the pole diagram |
(PDF) |
|
| Unit VI: The linear systems |
| L25 |
Linear systems |
(PDF) |
[BR] Sec. 5.4 Matrices & Linear Systems |
| L26 |
Eigenvalues and eigenvectors |
(PDF) |
[BR] Sec. 5.4 Eigenvalues & Eigenvectors |
| L27 |
Complex solutions and the fundamental matrix |
(PDF) |
|
| L28 |
Repeated eigenvalues and the matrix exponential |
(PDF) |
[BR] Appendix A1-2 Repeated Eigenvalues & Matrix Exponential |
| L29 |
Phase planes I |
(PDF) |
[BR] Sec. 5.5 Phase Planes |
| L30 |
Phase planes II |
(PDF) |
[BR] Sec. 5.5 Phase Planes; Degenerate cases |
| L31 |
Plane autonomous system |
|
[BR] Sec. 5.1-5.2, 5.7 Plane Autonomous System |
| L32 |
Stability and almost linear systems |
|
[BR] Sec. 5.7-5.8 Stability and Almost linear systems |
| L33 |
Problems from ecology |
|
|
| L34 |
Methods of Lyapunov |
|
[BR] Sec. 5.7-5.8 Methods of Lyapunov |
| L35 |
Nonlinear oscillations |
|
[BR] Sec. 5.9-5.11 Nonlinear Oscillations |
| L36 |
The Poincare-Bendixson theorem |
(PDF) |
[BR] Sec. 5.12 The Poincare-Bendixson Theorem |
