Numerical solution of nonlinear equations, interpolation, numerical integration and differentiation, numerical solution of initial value problems for ordinary differential equations. The main course objective is to understand and master the basic principles of the numerical analysis --- error analysis, quality of approximation, complexity of an algorithm --- by studying model examples from nonlinear equations, numerical linear algebra, interpolation and approximation, and the initial value problem for ODE.

__Classes:__MWF 10:00am-10:50am, NDSU Elect & Comp Eng, Rm 243__Office hours:__MWF 9:00am-10:00am (Minard 408E32) or by appointment (in my office or through Zoom)- Syllabus
__Textbook (optional):__Sullivan, Eric, Numerical Methods: An Inquiry-Based Approach With Python

- Python Programming and Numerical Methods: A Guide for Engineers and Scientists 1st Edition by Qingkai Kong, Timmy Siauw, Alexandre Bayen
- An Introduction to Numerical Analysis 1st Edition by Endre Suli, David F. Mayers

- Crash course in Python syntax.
- Root finding.
- Solving systems of linear equations.
- Numerical integration. Polynomial interpolation.
- Numerical methods for the initial value problem for ODE.
- Additional topics as time permits.

- 1. Python syntax. Part I
- 2. Python syntax. Part II
- 3. Bisection method. Theory and implementation
- 4. Some other methods. Heuristic discussion
- 5. Contraction mapping principle
- 6. Newton-Raphson method again. Theoretical discussion
- 7. Solving a system of linear algebraic equations (SLAE). Basic methods (Cramer and Gaussian elimination)
- 8. Complexity of an algorithm
- 9. More on Gauss elimination. LU factorization
- 10. Floating point arithmetics and roundoff errors (coming soon)
- 11. Norms of vectors and matrices. Condition number
- 12. Iterative methods to solve SLAE (coming soon)
- 13. Polynomial interpolation. Lagrange interpolation polynomial
- 14. Numerical intergation. Newron-Cotes formulas.
- 15. Ordinary differential equations. Basic theory (see my math 266 notes)
- 16. Euler's method
- Explicit Runge-Kutta methods. Adaptive algorithms
- Stiff problems and implicit methods
- Solving boundary value problems

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