Finite Differences - Numerical Analysis (Undergraduate Advanced)
Numerical differentiation (finite difference calculus) and its applications.
Enrolment valid for 12 months
Course Chapters
1. Introduction
1. Introduction
Welcome and course outline. Review of elementary calculus concepts, including Taylor's series.
2. Divided Differences
2. Divided Differences
Definition and use of divided differences.
3. First Forward and Backward Differences
3. First Forward and Backward Differences
Definition, geometric interpretation and use of the first forward and backward differences of error order h.
4. Higher Forward and Backward Differences
4. Higher Forward and Backward Differences
Definition and use of second and higher forward and backward differences of error order h.
5. Higher-Error-Order Forward and Backward Differences
5. Higher-Error-Order Forward and Backward Differences
Definition and use of forward and backward differences of error order h-squared and higher.
6. Central Differences
6. Central Differences
Definition and use of first and higher central differences of error order h.
7. Differences and Polynomials
7. Differences and Polynomials
Fitting data at a series of equally-spaced points with a polynomial, using difference expressions.