| Lecture |
Section(s) |
Topics Covered |
| 1 |
1.1-1.3 |
Introduction: Mathematical modeling with ODE, Classification
of ODE and PDE |
| 2 |
2.1 |
Linear equations; Method of Integrating Factors |
| 3 |
2.2 |
Separable Equations |
| 4 |
2.3,2.4 |
Modeling with First Order Equations; Differences
Between Linear and Nonlinear Equations |
| 5 |
2.5 |
Autonomous Equations and Population Dynamics |
| 6 |
2.6 |
Exact Equations and Integrating Factors |
| 7 |
3.1,3.2 |
Second Order Linear Equations:
Fundamental Solutions of Linear Homogeneous Equations |
| 8 |
3.3 |
Linear Independence and the Wronskian |
| 9 |
3.4 |
Complex Roots of the Characteristic Equation |
| 10 |
3.5 |
Repeated Roots; Reduction of Order |
| Week 4 |
Midterm 1 |
TOPICS COVERED: Boyce and DiPrima 1.1-3.4.
|
| 11 |
3.6 |
Nonhomogeneous Equations;
Method of Undetermined Coefficients |
| 12 |
3.7 |
Variation of Parameters |
| 13 |
7.1,7.2 |
Systems of First Order Linear Equations: Introduction,
Review of Matrices |
| 14 |
7.3 |
Linear Algebraic Equations; Linear Independence,
Eigenvalues, Eigenvectors |
| 15 |
7.4 |
Basic Theory of Systems of First Order Linear Equations |
| 16 |
7.5 |
Homogeneous Linear Systems with Constant Coefficients |
| 17 |
7.6 |
Complex Eigenvalues |
| 18 |
7.7,7.8 |
Fundamental Matrices, Repeated Eigenvalues |
| 19 |
7.9 |
Nonhomogeneous Linear Systems |
| 20 |
5.1 |
Review of Power Series;
Using Power Series to Solve ODEs |
| Week 8 |
Midterm 2 |
TOPICS COVERED: Boyce and DiPrima 3.5-3.7,7.1-7.9.
|
| 21 |
5.2,5.3 |
Series Solutions Near an Ordinary Point |
| 22 |
6.1 |
The Laplace Transform: Definition of the Laplace Transform |
| 23 |
6.2 |
Solution of Initial Value Problems |
| 24 |
6.3,6.4 |
Step Functions; Differential Equations with
Discontinuous Forcing Functions |
| 25 |
6.5 |
Impulse Functions. |
| Week 10 |
Review |
REVIEW for Final Exam |
| Week 11 |
Final Exam |
TOPICS COVERED: Boyce and DiPrima 1.1-7.9.
|
