Math 340-220 - Spring 2012

Introduction to Ordinary Differential Equations

Colorado State University

This is the syllabus for Math 530. See the links to the right for updated information. Here you'll find information on prerequisites, grading policy, homework, study resources and a tentative course calender. See the box in the upper right for more links and information for the course. The required textbook is pictured above, and can be found in the library or online.

### Textbook

J. Polking, A. Boggess, and D. Arnold: Differential Equations(2nd edition). Prentice Hall, 2006, ISBN 0-13-143738-0. Available at the University Bookstore, or online: click the image above.

### Office Hours

I am often in my office **Weber 214**, you are free to stop by and see if I am available. My official office hours are :

### Other Resources

One co-author of the textbook, **John Polking** maintains a website for the text containing computing resources, and other information helpful for the course. Another co-author David Arnold has some other computing resources which are cool.Last year's course page contains sets of notes on each section, some nice matlab notes as well as several links to good Matlab tutorials.

### Prerequisites

You **should be familiar** with the ideas on this sheet. Want other free sources to freshen up your linear algebra? Look here.

### Grading

### Exams

**no calculator, no books**

**no calculator, no books**

*Please make sure that you will be able to attend the exams at the given dates and times. Exceptions can only be accepted in case of time conflicts with other courses, or serious illness with a physician's certification.*

### Course Description

The construction of mathematical models to address real-world problems has been one of the most important aspects of each of the branches of science. It is often the case that these mathematical models are formulated in terms of equations involving functions as well as their derivatives. Such equations are called differential equations. If only one independent variable is involved, often time, the equations are called ordinary differential equations. The course will demonstrate the usefulness of ordinary differential equations for modeling physical and other phenomena. Complementary mathematical approaches for their solution will be presented, including analytical methods, graphical analysis and numerical techniques. The basic content of the course includes

- first order equations
- mathematical models
- linear equations of second order
- the Laplace transform
- linear systems of arbitrary order and matrices
- nonlinear systems and phase plane analysis
- numerical methods

**Chapter 1 - Differential Equation Models.**

**Chapters 2, 3, 6 - First-Order Equations and Applications:**Solution techniques for linear, separable and exact equations. Modeling Examples. Stability of equilibrium solutions. Numerical methods.

**Chapter 7 - Linear Algebra and Linear Systems of Equations:**Matrices. Matrix notation of linear systems of algebraic equations. Gaussian elimination. Subspaces and Bases. Determinants.

**Chapters 8, 9 - Systems of Differential Equations:**General properties. Linear systems with constant coefficients. Eigenvalues, eigenvectors and characteristic equation. Fundamental set of solutions. Fundamental matrices and matrix exponential. Nonhomogeneous linear systems. The phase plane.

**Chapter 4 - Second-Order Linear Equations:**Constant coefficient equations. Homogeneous and nonhomogeneous equations. Linear independence of solutions, characteristic equation. Superposition principle. Reduction of order, undetermined coefficients, variation of parameters. Applications from mechanical and electrical vibrations.

**Chapter 5 - The Laplace transform:**Laplace transforms and their properties. Initial-value problems. Delta or impulse function and Heaviside or step function.

**Chapter 10 - Nonlinear systems:**Linearization of a nonlinear system. Phase plane analysis and stability. Applications to biological model systems. Nonlinear Mechanics.