MA 591 Fundamentals of Linear Algebra and Differential Equations

This course covers topics from linear algebra and multivariable calculus. The computational and theoretical linear algebra topics include linear transformations, matrix algebra, bases, eigenvalues and eigenvectors, and first and second order differential equations. Topics from multivariable calculus include multivariable functions, differentiation, Taylorís theorem, optimization and the Inverse Function Theorem. This course is a graduate level survey of the aforementioned topics for engineers and scientists. Not for credit for current math majors. 3 credit hours.


• Prerequisite

Undergraduate courses in the calculus sequence, preferably through multivariable calculus; course in linear algebra and ordinary differential equations; or by consent of the instructor.

• Course Objectives

After completing this course, students should understand the fundamental uses of linear algebra in modeling mathematical and physical problems. In particular, students should be able to

  • Understand why and how linear algebra is used to approximate equations in multidimensional settings.
  • Model and solve problems using matrices and differential equations.
  • Demonstrate the geometric meaning behind matrix operations, determinants, and eigenvalues and eigenvectors.
  • Identify the role of linearization in nonlinear settings with examples from multivariable calculus.

The schedule of topics follows

  • Review of linear algebra (linear transformations, representing linear transformations with matrices, matrix algebra, eigenvalues and eigenvectors). Examples may include stochastic matrices and discrete dynamical systems.
  • Modeling and differential equations.
  • Differential multivariable calculus with a linear algebra framework; in particular the derivative as a linear transformation, optimization, and the Inverse Function Theorem.

• Course Requirements

This course requires homework, three midterms, and a cumulative final. Grades will be based on

  • Midterms = 45%
  • Homework = 20%
  • Cumulative Final Exam = 35%

• Textbook

Instructor notes will be provided. Optional but recommended supplementary text is

  • Matrix Analysis and Applied Linear Algebra Book and Solutions Manual, Carl Meyer, SIAM, 2000, 978-0898714548.

• Computer and Internet Requirements

NCSU and Engineering Online have recommended minimum specifications for computers. For details, click here

• Instructor

Dr. Bevin Maultsby, Teaching Assistant Professor
Department of Mathematics
SAS Hall 3230, Box 8205
NCSU Campus
Raleigh, NC 27695