## 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.

• Matrix algebra and eigenvalue/eigenvectors
• Linear Systems and Non-Linear Systems of Differential Equations
• Fourier series
 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