14 Jun 2007 ... FOR ENGINEERING AND THE SCIENCES ... to Fourier series and learn how to
apply the theory to solving partial differential equations. [A1, A2 ...
MA 303 DIFFERENTIAL EQUATIONS AND PARTIAL DIFFERENTIAL EQUATIONS FOR ENGINEERING AND THE SCIENCES
Course Outcomes 1. Students are introduced to more advanced techniques for solving differential equations and systems. These include series solutions and applications to Bessel’s equation. [A1, A2, A3] 2. Students use Laplace transform methods to solve differential equations. [A1, A2, A3] 3. Students are introduced to Fourier series and learn how to apply the theory to solving partial differential equations. [A1, A2, A3] 4. Students learn how to use standard numerical methods to solve differential equations. [A1, A2, A3]
Methods 1. Power Series 2. Numerical Methods 3. Laplace Transforms 4. Fourier Series
Ordinary Differential Equations
Partial Differential Equations
1. Solving by Power Series (ordinary and regular singular points, Bessel functions)
1. Separation of Variables
2. Solving by Laplace Transforms
3. Wave Equation
3. Solving Numerically 4. Solving Linear Systems
2. Heat Equation
4. Laplace Equation
COURSE NUMBER: MA 303
COURSE TITLE: Differential Equations and Partial Differential Equations for Engineering and the Sciences
REQUIRED COURSE OR ELECTIVE COURSE: Required
TERMS OFFERED: Fall, Spring, and Summer
TEXTBOOK/REQUIRED MATERIAL: Boyce and DiPrima, Elementary Differential Equations and Boundary Value Problems, 8th ed., Wiley, 2006 (interactive CD is recommended but not required)
PRE-REQUISITES: MA 262 Linear Algebra and Differential Equations, or MA 272 Differential Equations and Linear Algebra
COORDINATING FACULTY: A. Yip, Chair, Advanced Services Committee COURSE DESCRIPTION: This is a methods course for juniors in any branch of engineering and science, designed to follow MA 262. Basic techniques for solving systems of linear ordinary differential equations. Series solutions for second order equations, including Bessel functions, Laplace transform, Fourier series, numerical methods, separation of variables for partial differential equations and Sturm-Louisville theory. Not open to students with credit in MA 304. ASSESSMENTS TOOLS: 1. Daily homework 2. Quizzes 3. Three one-hour exams 4. Comprehensive final exam. PROFESSIONAL COMPONENT: 1. Mathematics – 3 credits (100%) NATURE OF DESIGN CONTENT: N/A
COURSE OUTCOMES: 1. Students are introduced to more advanced techniques for solving differential equations and systems. These include series solutions and applications to Bessel’s equation. [A1, A2, A3] 2. Students use Laplace transform methods to solve differential equations. A1, A2, A3] 3. Students are introduced to Fourier series and learn how to apply the theory to solving partial differential equations. [A1, A2, A3] 4. Students learn how to use standard numerical methods to solve differential equations. [A1, A2, A3]
RELATED ME PROGRAM OUTCOMES: A1. Math and science A2. Engineering fundamentals A3. Analytical skills
COMPUTER USAGE: None COURSE STRUCTURE/SCHEDULE: 1. Lecture – 3 days per week at 50 minutes. PREPARED BY: A. Weitsman
REVISION DATE: June 14, 2007
