Ordinary differential equations (ODE) are the main tool of applied mathematics that are used to model various processes in physics, engineering, economics, natural and social sciences. The purpose of the course is to learn the basics of the theory of ODE, get familiar with various methods of exact, numerical, and qualitative solutions of ODE, and to learn how to apply mathematical skills to various fields of study. The students will be exposed to both theoretical and applied points of view.

- Classes: MWF 1:00pm-1:50pm, NDSU Dolve Hall 118
- Office hours: MWF 4:00pm-5:00pm
- Syllabus

- 1. Introduction
- 2. Separable ODE
- 3. Direction field
- 4. Linear ODE
- 5. Exact ODE
- 6. Substitutions I
- 7. Substitutions II
- 8. Autonomous ODE
- 9. Numerical methods
- 10. Complex numbers. Solving second order linear ODE
- 11. General theory for linear ODE
- 12. Solving nonhomogeneous ODE. Method of educated guess
- 13. Solving nonhomogeneous ODE. Variation of parameters
- 14. Applications of linear ODE
- 15. Laplace transform. Basic theory
- 16. Laplace transform. Solving linear ODE
- 17. Solving linear ODE with piecewise continuous right hand side
- 18. Systems of ODE
- 19. Review of linear algebra
- 20. Solving systems of ODE. General theory
- 21. Solving systems of ODE. Complex eigenvalues
- 22. Matrix exponent. Generalized eigenvectors
- 23. Phase portraits for planar ODE
- 24. Solving imhomogeneous systems of ODE

- Fall 2012
- Spring 2013
- Fall 2013
- Spring 2014

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