Mathematical Computing

An Introduction to Programming Using Maple®

David Betounes, Mylan Redfern (Autoren)

Buch | Softcover

412 Seiten

2013 | Softcover reprint of the original 1st ed. 2002
Springer-Verlag New York Inc.
978-1-4612-6548-1 (ISBN)

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This book is designed to teach introductory computer programming using Maple. All the important, basic elements of computer programming can be easily learned within the interactive and user friendly environment of a Computer Algebra System (CAS) such as Maple.

This book is designed to teach introductory computer programming using Maple. It aims to infuse more mathematically oriented programming exercises and problems than those found in traditional programming courses while reinforcing and applying concepts and techniques of calculus. All the important, basic elements of computer programming can be easily learned within the interactive and user friendly environment of a Computer Algebra System (CAS) such as Maple. Most chapters feature case studies that provide greater depth on some topics and also serve to illustrate the methodology of analysis and design of code for more complex problems. This book is directed at undergraduates in the fields of math, science, or secondary education.

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.

Zusatzinfo	XII, 412 p.
Verlagsort	New York, NY
Sprache	englisch
Maße	178 x 235 mm
Themenwelt	Mathematik / Informatik ► Informatik ► Programmiersprachen / -werkzeuge
	Mathematik / Informatik ► Informatik ► Theorie / Studium
	Mathematik / Informatik ► Mathematik ► Analysis
ISBN-10	1-4612-6548-7 / 1461265487
ISBN-13	978-1-4612-6548-1 / 9781461265481
Zustand	Neuware