Math 0290: Differential Equations

Schedule and practice problems

Approximate schedule for lectures. References of the form a.b refer to sections in the main textbook.

Week 1
August 26: Introduction to Differential Equations (DE)
dfield.jar
1.1 Number 1-11. Homework: 1,2,5,7,11
August 28: First Order Initial Value Problems
2.1 Number 1-6, 12-15. Homework: 1,3,5,12,13,15
August 30: Numerical methods and computer tools including Matlab for DEs
6.1 Number 1-5 Homework: 3,5
Solutions

Week 2
September 4: Numerical Methods. Runge-Kutta Methods
6.2 Number 1-9. Homework: 5, 23
September 6: Numerical Methods. Numerical Error.
6.3 Number 1-6, 11-13.
Solutions

Week 3
September 9 Separable Equations
2.2 Number 1-22, 23-29, 33-35 Homework: 3,5,9,33
September 11: Models of Motion
2.3 Number 1-10 Homework: 9
September 13: First Order Linear Equations
2.4 Number 1-21 Homework: 5,15,19
Solutions

Week 4
September 16: Mixing Problems
2.5 Number 1-7, 9-10 Homework: 5, 9b
September 18: Electrical Circuits
3.4 Number 1-19 Homework: 1,3,5,7,11
September 20: Second Order Equations
4.1 Number 1-20, 26-30 Homework: 1,3,9,17
Solutions

Week 5
September 23: Linear Homogeneous Equations with Constant Coefficients
4.3 Number 1-36 Homework: 1,9,17,35
September 25: Harmonic Motion
4.4 Number 1-12, 14-16, 18 Homework: 1,7
September 27: Inhomogeneous second order equations. Undetermined Coefficients
4.5 Number 1-29 Homework: 1,5,11
Solutions

Week 6
September 30: Inhomogeneous second order equations. Undetermined Coefficients (continued)
4.5 (cont.) Number 1-29 Homework: 15,19
October 2: Inhomogeneous Equations. Variation of Parameters
4.6 Number 1-10 Homework: 1,3,5
October 4: Forced harmonic motion
4.7 Number 3-11 Homework: 3,11
Solutions

Week 7
October 7: Review
October 9: Midterm 1
October 11: Laplace Transform
5.1 Number 1-29 Homework: 7,13,15,29
Solutions

Week 8
October 14: Fall Break for students (No Classes)
October 16: Laplace Transform. Basic properties
5.2 Number 1-41 Homework: 5,11,19,29
October 18: The Inverse Laplace Transform
5.3 Number 1-36 Homework: 3,7,11,19
Solutions

Week 9
October 21: Using the Laplace Transform to solve DEs
5.4 Number 1-26 Homework: 7,11,21
October 23: Discontinuous Forcing Term
5.5 Number 1-25 Homework: 1,3,11,17
October 25: The Dirac Delta Function
5.6 Number 1-9 Homework: 2,3,5,7
Solutions

Week 10
October 28: Convolutions
5.7 Number 4-24 Homework: 6,8,10
October 30: Introduction to Systems
8.1 Number 1-16 Homework: 5,7,13,15
November 1: Systems (continued)
8.2 Number 1-6, 13-16 Homework: 11,13,15 (use pplane.jar)
Solutions

Week 11
November 4: Systems of differential equations, Constant coefficient homogeneous 2x2 systems
8.3 Number 1-6 Homework: 1,3,5
November 6: Linear Systems with Constant Coefficients
9.1 Number 1-8, 16-23 Homework: 3,5,17,19
November 8: Planar Systems
9.2 Number 1-27, 58-61 Homework: 3,13,15,59
Solutions

Week 12
November 11: Phase Plane Portraits
9.3 Number 20-23 Homework: 21
November 13: Nonlinear Systems: Equilibria, Linearization
10.1 Number 1-16 Homework: 3,7,15
November 15: Review
Solutions

Week 13
November 18: Midterm 2
November 20: Fourier series
12.1 Number 1-22 Homework: 5,7,13,17
November 22: Fourier Cosine and Sine Series
12.3 Number 1-32 Homework: 3,7,19,31
Solutions

Week 14
December 2: Heat Equation
13.1 Number 1-9 Homework: 3
December 4: Separation of variables for the heat equation
13.2 Number 1-18
December 6: Separation of variables for the heat equation (continued)
13.2 Number 1-18
Solutions

December 9: Review