MA**262
LINEAR ALGEBRA AND DIFFERENTIAL EQUATIONS
Course Outcomes
1. Students learn the standard methods for solving differential equations as they arise in engineering and science. [A1, A2, A3]
2. Students learn the linear algebra concepts which are needed to solve linear algebraic systems and linear systems of differential equations.
[A1, A2, A3]
3. Students obtain the computational skills in matrix theory which are needed in computational linear algebra. [A1, A2, A3]
Linear Algebra
Differential Equations
1. First-Order Diff. Equations with and
without Initial Conditions
- separable variables
- exact
- linear
2. Applications of First-Order Diff. Equations
- mixture problems
- growth and decay problems
- falling bodies
- electrical circuits
- orthogonal trajectories
3. Second Order and Higher Diff. Equations
with Constant Coefficients
- undetermined coefficients
- variation of parameters
- initial value problems
4. Applications of Second-Order Diff.
Equations
- Newton’s 2nd law
- electrical circuits
- etc.
1.
2.
3.
4.
5.
Vector Spaces
subspace
basis
spanning set
linear combination
linear independence
Matrix Operations
addition
multiplication
inverse
determinants
Row Reduction of Matrices
row-echelon normal form
rank
Systems of Linear Equations
solve using matrix methods
augmented matrices
Cramer’s rule
solution space
Complex Numbers, Polar Representation, Roots of Complex Numbers
6. Eigenvalues and Eigenvectors
Systems of Differential Equations
1. Matrix Formulation
2. Solutions for Linear Equations
- constant coefficient using eigenvalues
and eigenvectors
3. Variation of Parameters
COURSE NUMBER: MA 262
COURSE TITLE: Linear Algebra and Differential Equations
REQUIRED COURSE OR ELECTIVE COURSE: Required
TERMS OFFERED: Fall, Spring, and Summer
TEXTBOOK/REQUIRED MATERIAL: S. Goode, Differential Equations
and Linear Algebra, 2nd ed., Prentice Hall, 2006.
PRE-REQUISITES: MA 261 Multivariate Calculus
COORDINATING FACULTY: S.K. Yeung, Chair, Calculus Committee
COURSE OUTCOMES:
COURSE DESCRIPTION: Planes, lines, and curves in three dimensions.
Differential calculus of several variables; multiple integrals. Introduction to
vector calculus. Not open to students with credit in MA 174 or MA 271.
1. Students learn the standard methods for solving differential equations as
they arise in engineering and science. [A1, A2, A3]
2. Students learn the linear algebra concepts which are needed to solve linear
algebraic systems and linear systems of differential equations. [A1, A2,
A3]
3. Students obtain the computational skills in matrix theory which are needed
in computational linear algebra. [A1, A2, A3]
ASSESSMENTS TOOLS:
1. Daily homework
2. Quizzes
3. Three one-hour exams
4. Comprehensive final exam.
PROFESSIONAL COMPONENT:
1. Mathematics – 4 credits (100%)
RELATED ME PROGRAM OUTCOMES:
A1. Math and science
A2. Engineering fundamentals
A3. Analytical skills
NATURE OF DESIGN CONTENT:
N/A
COMPUTER USAGE:
None
COURSE STRUCTURE/SCHEDULE:
1. Lecture – 3 days per week at 50 minutes.
2. Recitation – 1 day per week at 50 minutes.
PREPARED BY: A. Weitsman
REVISION DATE: June 14, 2007