Differential Equations - with Computer Methods

M427K-C * 60055 * Fall 2007

---

This is a first-course in Differential Equations. The subject is a basic tool in mathematical science. Computer methods, including both computation and graphics will be used in developing the topics. Beginning with Newton's mechanics and extending to our present knowledge of relativity, particle physics and cosmology, differential equations have been the principal method to describe natural phenomena. In mathematics this theory is central to understanding many problems in analysis and geometry. Computers increasingly play a significant role in the way mathematicians, engineers and scientists solve problems and develop theoretical models. Examples include the description of chaotic behavior, the search for pattern and structure in mathematical phenomena, and the continuing effort to understand the observed world with quantitative precision.

The course objective is to develop an understanding of differential equations and to show how computers can be used to gain mathematical intuition about problems in science.

Topics

• 1) First-order differential equations
  

• 2) Second-order linear equations and linear systems
  

• 3) Series solutions, numerical methods and Laplace transforms
  

• 4) Non-linear equations and dynamical systems
  

• 5) Partial differential equations and Fourier series
  

Class Schedule

• Text: Polking, Boggess & Arnold, Differential Equations with Boundary Value Problems , 2nd edition [used copies are fine]
  

• Scientific Calculator: highly recommended; an inexpensive choice is Sharp EL-531W for about $10
  

• Suggested Reading: Gleick, Chaos; Feynman, The Character of Physical Law; Gleick, Isaac Newton
  

• Prerequisite: one-year calculus course equivalent to M408C & M408D
  

• Course work: 3 hour exams (60%), final exam (32%). problem sets (8%). Grades are roughly based on percentages marked above. Exception: in order to receive an A for the course, final exam grade must be at least a B.
  

• Hour exams are scheduled for Sept 21, Oct 19, Nov 16 in Welch 1.308..
  

• Final exam: Monday Dec 17, 2-5pm.
  

• Office hours: By appointment. RLM 12.154 - William Beckner
  

• Email: beckner@math.utexas.edu
  

• TA: Emanuel Carneiro
  

The University of Texas at Austin recognizes that students with disabilities should have full access to educational opportunity on the Austin campus, and provides upon request appropriate academic adjustments for qualified students with disabilities. For more information, contact the Office of the Dean of Students at 471-6259, 471-4641 TTY.

---