SUMMARY OF THE TOPICS: Click here
Classification of differential equations :
Click here
First order differential equations:
* Geometrical view of a differential equation: Click here
* Method of Integrating Factors: Click here
* Separable and Exact equations: Click here
* Existence and Uniqueness theorem (first order equations): Click here
* Autonomous equations and Population Dynamics: Click here
Second order equations:
* Introduction, existence & uniqueness theorem, Wronskian: Click here
* Complex roots, repeated roots: Click here
* Inhomogeneous equations - method of undetermined coefficients, variation of parameters: Will be uploaded shortly
* Mechanical Vibrations: Click here
Laplace Transforms (Updated):
* All sections
* Old notes - 1
* Old notes - 2
* Table of Laplace transforms (print and carry to class): Click here
Linear Algebra :
* Notes by Joel Feldman : Click here
* Khan Academy Youtube lectures - contains useful lectures on eigenvalues and eigenvectors: Click here
Notes for chapter 7: Linear system of equations:
* Brief review of matrices (old class notes): Click here
* Real and distinct eigenvalues (saddles, nodes, etc.): Click here
* Complex eigenvalues (how to draw spirals?): Click here
* Repeated eigenvalues: Click here
* Method of undetermined coefficients - system of equations Click here
* Variation of parameters - read from page 2 (skip Method I) Click here
* Notes on autonomous systems and stability (theory on Jacobian, etc.) Click here
* Practice problems for Nonlinear Systems Click here
* More theory on Pendulum - damped cases Damped Simple case , Damped General case
On Delta function (Not for exam, but fun stuff to read though) :
* Article in science education journal Resonance by Prof. V Balakrishnan (IIT Madras) : Click here
Notes and problems on phase plane by Prof. Michael Ward (Competing Species, Predator-Prey, etc):
Notes
Text book problems
Extra useful material
* MIT-OCW lectures by Prof. Arthur Mattuck (Excellent): Linear Systems Note: Skip matrix exponentials, Limit Cycles and Chaos.
* Applet for plotting phase portraits (enable Java in browser): Click here