Mathematical Computing

1 Preliminaries.- 1.1 Maple as a Programming Language.- 1.2 Analyzing Programming Tasks.- 1.3 Documentation and Coding.- 1.4 Maple/Calculus Notes.- 2 Basic Aspects of Maple.- 2.1 Variables and Constants.- 2.2 Expressions and Assignments.- 2.3 Notation in Mathematics and in Maple.- 2.4 Sequences, Lists, Sets, and Arrays.- 2.5 The Do Loop.- 2.6 Procedures: A First Glance.- 2.7 Evaluation Rules.- 2.8 Maple/Calculus Notes.- 3 Looping and Repetition.- 3.1 The Basic Loop.- 3.2 The Do Loop with All Its Features.- 3.3 Case Study: Iterated Maps.- 3.4 Maple/Calculus Notes.- 4 Conditionals — Flow of Control.- 4.1 Logic in Mathematics.- 4.2 Relational and Logical Operators.- 4.3 Boolean Expressions.- 4.4 The if-then-else Statement.- 4.5 The if-then-elif-then Statement.- 4.6 Case Study: Riemann Sums for a Double Integral.- 4.7 Maple/Calculus Notes.- 5 Procedures.- 5.1 Maple’s Procedure Statement.- 5.2 Procedures — Some Details.- 5.3 Groups of Related Procedures.- 5.4 Case Study: Trig Integrals.- 5.5 Maple/Calculus Notes.- 6 Data Structures.- 6.1 Expressions and Operands.- 6.2 Quotes and Strings.- 6.3 Numbers.- 6.4 Lists: Vector Methods in Geometry.- 6.5 Arrays and Tables.- 6.6 Sets: The Cantor Set and Limiting Covers.- 6.7 Polynomials.- 6.8 Case Study: Partial Fractions.- 7 Graphics Programming.- 7.1 Preliminary Examples.- 7.2 Maple’s Plot Structures.- 7.3 Approximating Curves and Surfaces.- 7.4 The GRID and MESH Objects.- 7.5 Animations.- 7.6 Maple/Calculus Notes.- 8 Recursion.- 8.1 Recurrence Relations — Series Solutions.- 8.2 Reduction Formulas for Integration.- 8.3 Sorting.- 8.4 Numbers.- 8.5 Maple/Calculus Notes.- 9 Programming Projects.- 9.1 Projects on Crystal Growth.- 9.2 Projects on Inscribed Polygons.- 9.3 Projects on Random Walks.- 9.4 Projects on Newton’sSecond Law.- A Maple Reference.- A.1 Expressions and Functions.- A.2 Plotting and Visualization.- A.3 Programming.- A.4 Packages.