Rose-Hulman - Department of Mathematics - Course Syllabus MA211 - Differential Equations - 2010-11

 Description & Prerequisites Course Goals Texts and Other Materials Course Topics Course Policies Links last posted to site: 05/29/12

Parts of the web page to be completed or determined by the instructor are in green.

Catalogue Description and Prerequisites

MA 211 (starting Fall 2010) Differential Equations 4R-0L-4C F,W,S Pre: MA 113
First order differential equations including basic solution techniques and numerical methods. Second order linear, constant coefficient differential equations, including both the homogeneous and non-homogeneous cases. Laplace transforms, Introduction to complex arithmetic, as needed. Applications to problems in science and engineering.

Prerequisite: All of the topics in MA112, as well some topics in MA113, will be assumed. In addition, familiarity with some Maple commands from Calculus is assumed. The Maple files  MapleIntRGL.mws (introduction) and calcrev.mws (review for DE) may be helpful. These files are available on Angel in the (Rose-Only) Mathematics Course Information Repository.

Course Goals

1. Develop a deeper understanding of scalar differential equations and their solutions.
2. Provide an introduction to Laplace transform methods.
3. Develop a deeper understanding and appreciation of transformation methods by studying Laplace methods.
4. Improve mathematical modeling and analytical problem solving skills.
5. Develop ability to communicate mathematically.
6. Improve skill using the computer as a tool for mathematical analysis and problem solving.
7. Introduce applications of mathematics, especially to science and engineering.

Textbook and other required materials

Textbook: Text: Advanced Engineering Mathematics, 4th edition by Zill and Wright
Computer Usage:  Maple14 must be available on your laptop.

Course Topics

The topics below follow the approximate book order.

1. First order differential equations
• Review basic notions (e.g., separation of variables, initial value problems)
• Review dx/dt = ax and dx/dt = ax + b and show structure of solution as particular solution plus homogeneous solution
• Other solution methods
• Applications as appropriate

2. Second order linear differential equations
• Constant coefficient, homogeneous case (solving the characteristic equation requires basics of complex arithmetic through Euler's formula)
• Method of undetermined coefficients for non-homogeneous case
• Resonance
• Applications as appropriate

3. Laplace Transforms
• Definition of Laplace transform and standard table; inverse transform
• Basic properties and theorems
• Delta and Heaviside functions
• Convolution
• Transfer functions
• Applications as appropriate - e.g., salt tanks, spring-mass systems, and electrical circuits.

4. Numerical Methods
• Euler Method and Error Analysis
• Higher Order Systems and Equations

Course Requirements and Policies

The following policies and requirements will apply to all sections and classes:

Computer Policy

A summary of the computer policy page: Students will be expected to demonstrate a minimal level of competency with a relevant computer algebra system. The computer algebra system will be an integral part of the course and will be used regularly in class work, in homework assignments and during quizzes/exams. Students will also be expected to demonstrate the ability to perform certain elementary computations by hand. (See Performance Standards below.)

Performance Standards

Paper and pencil
1. Demonstrate skill using complex numbers
• basic arithmetic and geometric interpretation
2. Solve linear differential equations including
• direct integration
• separate and integrate involving simple integrations
• integrating factors with simple integration
• graphing and interpreting the solutions
• constant coefficient, second order equations with simple driving functions
• compute elementary Laplace transforms from the definition and standard table.
• solve simple scalar differential equations using Laplace transforms
Maple

Use Maple to solve differential equations symbolically and numerically

• using dsolve
• numerically by using the method=numeric
• using Maple to assist in separate and integrate, undetermined coefficients
• laplace transform methods
• graphing and interpreting the solutions

Final Exam Policy

The following is an extract from the final exam policy page. Consult the policy page for complete details. The final exam will consist of two parts. The first part will be "by hands" (paper, pencil). No computing devices (calculators/computers) will be allowed during the first part of the final exam. This part of the exam will cover both computational fundamentals as well as some conceptual interpretation, though the level of difficulty and depth of conceptual interpretation must take into account that this part of the exam will be shorter than the second part of the exam.  The laptop, starting with a blank Maple work sheet, and a calculator, may be used during the second part of the exam. No "cheat sheets", prepared Maple worksheets or prepared program on the calculator may be used. The second part of the exams will cover all skills: concepts, calculation, modeling, problem solving, and interpretation.