Department of Mathematics - RHIT
Topics Outline for MA212 - Matrix Algebra and Systems of Differential Equations - 2010-11

last posted to site: 08/19/10

Text and Text Materials

Text: Advanced Engineering Mathematics 4th edition by Zill and Wright

Approximate Timing and Pace

There should be 2 or 3 tests, perhaps a review day or two.

The topics break up into three main pieces.

Topics Sections Time
Chapter 8 - Matrix Algebra
Chapter 17 - Complex Arithmetic
8.1-8.6, 8.8.
17.1,17.2
11 days

Chapter 2 - First-Order Differential Equations

1.1, 1.2, 2.2-2.3 5 days

Chapter 10 - Systems of Linear Differential Equations

10.1, 10.2 10.3, 10.4.1, 10.4.3 9 days
Chapter 11 - Systems of Non-Linear Differential Equations 11.1-11.4 6 days
Chapter 12 - Orthogonal Functions and Fourier Series 12.1-12.3 4 days
Tests, Review and Spare days   5 days

  8. Matrices

     8.1 Matrix Algebra

     8.2 Systems of Linear Algebraic Equations

     8.3 Rank of a Matrix

     8.4 Determinants

     8.5 Properties of Determinants

     8.6 Inverse of a Matrix
        8.6.1 Finding the Inverse
        8.6.2 Using the Inverse to Solve Systems

  17. Complex Numbers

     17.1 Complex Numbers

     17.2 Powers and Roots

  10. Systems of Linear Differential Equations

    10.1 Theory of Linear Systems

    10.2 Homogeneous Linear Systems
        10.2.1 Distinct Real Eigenvalues
        10.2.2 Repeated Eigenvalues
        10.2.2 Complex Eigenvalues

     10.3 Solution by Diagonalization

     10.4 Nonhomogeneous Linear Systems
        10.4.1 Undetermined Coefficients
        10.4.3 Diagonalization

  11. Systems of Nonlinear Differential Equations

     11.1 Autonomous Systems

     11.2 Stability of Linear Systems

     11.3 Linearization and Local Stability

     11.4 Autonomous Systems as Mathematical Models

  12. Orthogonal Functions and Fourier Series

    12.1 Orthogonal Functions

    12.2 Fourier Series

    12.3 Fourier Cosine and Sine Series