Course Description
Numerical solutions of ordinary and partial differential equations, higher-dimensional Newton's method, and splines.
Additional Requirements for Graduate Students:
Extra problems on weekly homework.
Athena Title
NUMER ANALYSIS II
Prerequisite
(MATH 2270 or MATH 2500 or MATH 3510 or MATH 3510H) and MATH 2700 and MATH 4500/6500
Semester Course Offered
Offered spring
Grading System
A - F (Traditional)
Course Objectives
Continuing Differential Calculus with Theory, the student will understand different numerical methods for solving linear algebra problems, differential equations, and data fitting using splines. Again, the student will understand the trade-off between efficiency (time) and accuracy (error analysis).
Topical Outline
1. Numerical linear algebra: Vector and matrix norms, Gaussian elimination, Gaussian elimination with pivoting, iterative methods, Gauss-Seidel method. 2. Splines and applications: First degree, second degree, Subbotin quadratic spline, third degree, natural cubic spline, Bernstein polynomials. 3. Numerical solution of differential equations: Euler method, Runge-Kutta methods, systems of differential equations, adaptive methods, including Runge-Kutta-Fehlberg and Adams-Bashforth- Moulton.
Syllabus