Using High Order Finite Differences

Table of contents |epilog= "" /Definitions and Basics#| Definitions and Basics "" Finite Difference Operators "" Shift Operators "" Specialized Norms "" Special Formulas "" <ul> 1. /Definitions and Basics#| Vector Norms "" Matrix Norms "" |epilog=</li> 1.1. /Definitions and Basics#| Definition of a Vector Norm Common Vector Norms Inner Product of Vectors Inequalities Involving Norms |epilog=</li></ul> 1.2. /Definitions and Basics#| Definition of a Matrix Norm Common Matrix Norms Positive definite matrices Consistency of Norms |epilog= 2. /Definitions and Basics#| approximation of a first derivative approximation of a second derivative approximation of higher derivatives effect of the placement of points centered difference operators |epilog=</li> 3. /Definitions and Basics#| Trigometric polynomials Definition of a shift operator Approximation by trigometric polynomials Fundamental Property Error Estimation Simple Functions |epilog= 4. /Definitions and Basics#| Discrete Heat Norms "" Energy and Heat Norms |epilog=</li> 4.2. /Definitions and Basics#| appendix a) appendix b) appendix c) |epilog= 5. /Definitions and Basics#| Definitions and Basics Vector Norms Definition of a Vector Norm Common Vector Norms Inner Product of Vectors Inequalities Involving Norms Matrix Norms Definition of a Matrix Norm Common Matrix Norms Positive definite matrices Consistency of Norms Finite Difference Operators approximation of a first derivative approximation of a second derivative approximation of higher derivatives effect of the placement of points centered difference operators Shift Operators Trigometric polynomials Definition of a shift operator Approximation by trigometric polynomials Fundamental Property Error Estimation Simple Functions Specialized Norms Energy and Heat Norms appendix a) appendix b) appendix c) save scratch none Mathematics 25%