Prerequisite material (brief version)
Review of Algebra (Note: Partial fractions are on page 18.)
Review of Review of Integration by Parts (look at the tabular method)
Examples of partial fractions: with a repeated factor and using partial fractions for integration including a prime quadratic factor
Review of Calculus I and II
Hyperbolic Functions explained
Newton's Law of Cooling
Video lectures on Linear Algebra at MIT - These are really good. Check them out.
Video lectures on Differential Equations at MIT
Homework set
Class Notes
Class notes for section 1.1 Differential Equations and Mathematical Models
Class notes for section 1.2 Integrals as General and Particular Solutions
Class notes for section 1.3 Slope Fields and solutions Curves
Class notes for section 1.4 Separable Equations and Applications
Class notes for section 1.5 Linear First Order Equations and a Supplement on the integrating factor method
Class notes for section 1.6 Substitution Methods and Exact Equations
Class notes for section 2.1 Populations Models
Class notes for section 2.2 Equilibrium Solutions and Stability
Class notes for section 2.3 Acceleration-Velocity Models
Class notes for section 3.1 Introduction to Linear Systems
Class notes for sections 3.2 and 3.3 Matrices and Gaussian Elimination as well as Reduced Row-Echelon Matrices (RREF)
Class notes for section 3.4 Matrix Operations
Class notes for section 3.5 Inverse Matrices
Class notes for section 3.6 Determinants and a supplement on Determinant Properties
Current notes for sections 4.1 and 4.2 (and OLD notes for sections 4.1 and 4.2)
Notes for section 4.3 and revised notes
Notes for section 4.4
Notes for section 4.5 and a worksheet on the row space, column space, and nullspace of A and solutions
Notes for section 4.7
Summary of Chapter 4
Notes for section 5.1 and additional derivation of the Euler Equation solution
Notes for section 5.2
Notes for section 5.3 and nth roots of complex numbers
Using software packages Maple, Mathematica or Matlab for computer-aided representations and solutions
Notes for section 5.4
Satellite orbit calculator link for 5.4 Problem 12
Notes for section 5.5: The Annihilator Method and for when that fails, Variation of Parameters
Notes for section 6.1
Notes for section 7.1
Notes for section 7.3 as well as a complex eigenvalue example
Additional notes for section 7.3
Notes for section 7.5
Maple Commands for problems 5 and 6 in section 7.5
Notes for section 10.1
Supplement on the Gamma Function
Notes for section 10.2
Notes for section 10.3 as well as an another example involving partial fractions
Notes for section 10.4
Supplemental Notes for the First Shift Theorem
Table of Laplace Transforms
Convolution explained visually (Wikipedia)
Notes for section 10.5
REview for Chapter 10 on Laplace transforms
Final Exam Schedule Spring 2009:
11:30 MTWF Section 002: Final Exam: 9:30 am Monday, April 27
9:30 MTWF Section 003: Final Exam: 9:30 am Wednesday, April 29