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Ordinary Differential Equations

3 Credits | 200 Level | 38 Contact hours

Elementary Differential Equation, Wiley 10th edition by William E. Boyce & Richard C. DiPrimá. ISBN: 9780-470-45832-7.

Theory and solving techniques for constant and variable coefficient linear equations, a variety of nonlinear equations. Emphasis on those differential equations arising from real-world phenomena, particularly in Engineering applications.

1. Introduction
2. First-order differential equations.
3. Second-order linear equations.
4. Higher-order differential equations.
5. Laplace transform.
6. Systems of first-order differential equations.

If you are from UVA you will also learn (12h-1CRDT):
- Modelling with differential equations

If you are from UIUC you will also learn (12h-1CRDT):
- Fourier Series and The Fourier Convergence Theorem
- Boundary Value Problems and Sturm-Liouville Theory

Upon completion of this course, students will be able to:
• Analyze analytically and graphically first-order differential equations.
• Analyze second differential equations with the help of characteristic polynomials. Applications to spring/mass systems.
• Apply the Laplace transform to solve differential equations with various forcing functions, including piece-wise functions and impulses.
• Analytically solve systems of linear first-order differential equations using Linear Algebra approach.
• Apply theoretical results to model some dynamic problems: Mathematical Modelling using EDOs.

Homework 20%
Midterm Exams 40%
Final Exam 40%