Instructor: Hans Johnston
Office: 1526 LGRT
Phone: (413) 545-2817
Office Hours: T 2:30-3:30, W 4-5
Email: johnston at math.umass.edu
Textbook: Advanced Engineering Mathematics, by Erwin Kreyszig (any edition is fine)
Open Source: MIT OpenCourseWare, MIT Math 18.03: DEs , Miller and Mattuck
Course description: The course is an introduction to ordinary differential equations.
We will cover first and second order linear differential equations,
systems of linear differential
equations, Laplace transforms, numerical methods, and applications.
Homework : We will use an online homework system,
WeBWork . Periodically, written
problems will be assigned and collected to be graded.
Slope Field Calculator : Here is a link to the
Slope Field Calculator
that I used in class.
| 1/23 | First day of class. Read sections 1.1-1.3. |
| 1/25 | What are DEs, and where do they come from?
MIT 18.03 Lecture 1: The Geometrical View of dy/dx = f(x,y) |
| 1/30 | Geometry of DEs and Euler's numerical method.
Assignment: WebWork HW1 due 2/8/13.
MIT 18.03 Lecture 2: Eulers Numerical method for dy/dx = f(x,y) |
| 2/6 | Separable and Exact equations. Read sections 1.4-1.5.
MIT 18.03 Lecture 3: Solving Linear First-order Linear ODEs |
| 2/15 | Linear equations. Assignment: WebWork HW2 due 2/22/13. |
| 2/19 | Integrating factors.
MIT 18.03 Lecture 7: First-order Linear with Constant Coeffs |
| 2/20 | Second order Linear ODES. Read sections 2.1-2.2.
MIT 18.03 Lecture 9: Solving Second-order Linear ODEs with Constant Coeffs |
| 2/22 | Second order linear constant coefficient equations. Assignment: WebWork HW3 due 2/28. |
| 3/8 | Feynman QED lectures.
Douglas Robb Memorial Lectures |
| 3/11 | Mass-Spring systems. Re-read sections 2.4 and 2.8. Assignment: WebWork HW4 due 3/16. |
| 3/25 | Resonance.
MIT 18.03 Lecture 14: Interpretation of the Exceptional Case - Resonance |
| 3/27 | Systems of 1st order ODES, Eigenvalues, Eigenvectors. Read sections 4.0-4.4.
MIT 18.03 Lecture 25: Homogeneous Systems with Constant Coefficients Assignment: WebWork HW5 due 4/5. |
| 4/4 | Matrix Exponentials.
MIT 18.03 Lecture 29: Matrix Exponentials |
| 4/19 | Laplace transforms.
MIT 18.03 Lecture 19: Introduction to the Laplace Transform |
| 5/1 | johnston_HW6.pdf |