1 Basic elements in the use of Maple.- 1.1 Meeting Maple: symbolic calculations.- 1.2 Meeting Maple: numerical calculations.- 1.3 Meeting Maple: symbolic calculations again.- 1.4 Spaces and asterisks.- 1.5 Terminating commands with semicolons or colons.- 1.6 Names and assignments.- 1.7 Referring to previous results with the ditto.- 1.8 Referring to previous results with other facilities.- 1.9 Using procedures.- 1.10 Procedures that seem to do nothing.- 1.11 The sign % for abbreviations in output.- 1.12 On-line help.- 2 Numbers and algebraic operators.- 2.1 Algebraic operators.- 2.2 Parentheses and precedence rules.- 2.3 Rational numbers.- 2.4 Real constants.- 2.5 Complex numbers.- 2.6 Radicals.- 2.7 Manipulating radicals and complex numbers-an example.- 2.8 Floating-point numbers, approximations.- 2.9 Some effects of automatic simplification of floating-point numbers.- 2.10 Calculations with integers.- 2.11 Integers modulo an integer.- 2.12 Algebraic extensions and general rings.- 3 Names and evaluation 1: mathematical variables.- 3.1 Assigning names to objects and evaluating names to objects.- 3.2 Assigning names and expressions to a name.- 3.3 Unassigning.- 3.4 Names and properties.- 3.5 Combinations of characters that can be accepted as names.- 3.6 Greek letter names.- 3.7 Names with an index.- 3.8 Single back quotes.- 3.9 The concepts of name, symbol, and string in Maple.- 3.10 Recursive definitions of names.- 4 Elementary calculus.- 4.1 Differentiation.- 4.2 The derivative at a point.- 4.3 Some more tools in differential calculus.- 4.4 Antiderivatives.- 4.5 Special elements appearing in the results of the procedure int.- 4.6 Definite integrals.- 4.7 Helping Maple to find a definite integral by restricting the domain of a parameter.- 4.8 Helping Maple to find an antiderivative by conversion to RootOf.- 4.9 Helping Maple to find an antiderivative by substitution.- 4.10 More tools for integration.- 4.11 Reliability of the calculation of antiderivatives.- 4.12 Definite integrals of discontinuous functions.- 4.13 Definite integrals and branch cuts of functions.- 4.14 Reliability of calculations of definite integrals.- 4.15 Numerical integration.- 4.16 Numerical approximations to multiple integrals.- 4.17 Definite and indefinite sums and products.- 4.18 Other tools and pedagogical facilities.- 5 Names and evaluation 2: applying procedures.- 5.1 Evaluation of names in arguments of procedures.- 5.2 Options of procedures.- 5.3 Output and results of procedures.- 5.4 Assigning side results to arguments of procedures.- 5.5 Names referring to procedures.- 5.6 The Maple library of procedures.- 5.7 Asking procedures for additional information with infolevel.- 5.8 Printing standard procedures from Maple's library.- 6 Creating and using mathematical functions.- 6.1 Standard mathematical functions.- 6.2 Definitions of inverse functions, branch cuts.- 6.3 Denotation of the functions exp, Gamma, and Zeta.- 6.4 Expressions versus functions, creating functions.- 6.5 Creating functions in several arguments.- 6.6 A pitfall in creating mathematical functions.- 6.7 Using existing expressions for creating mathematical functions.- 6.8 Evaluation of names of procedures.- 6.9 Derivative functions.- 6.10 Derivatives of functions of more than one variable.- 6.11 Conversion between diff and D.- 6.12 Piecewise-defined functions and expressions.- 6.13 Creating functions by elementary operations on functions.- 7 Graphics.- 7.1 Graphs of real functions in one real parameter.- 7.2 Graphs of real functions in two real parameters.- 7.3 Assigning, manipulating, and printing graphical objects.- 7.4 Vertical asymptotes and discontinuities.- 7.5 Graphs with ranges to infinity.- 7.6 Logarithmic scalings.- 7.7 Parameterized curves and surfaces.- 7.8 Different types of coordinates.- 7.9 Empty plots caused by complex values.- 7.10 Plotting data.- 7.11 Graphs of relations or implicitly defined functions.- 7.12 Combining graphs.- 7.13 Maple's movies.- 7.14 More tools
This "hands-on" book is for people who are interested in immediately putting Maple to work. The reader is provided with a compact, fast and surveyable guide that introduces them to the extensive capabilities of the software. The book is sufficient for standard use of Maple and will provide techniques for extending Maple for more specialized work. The author discusses the reliability of results systematically and presents ways of testing questionable results. The book allows a reader to become a user almost immediately and helps him/her to grow gradually to a broader and more proficient use. As a consequence, some subjects are dealt with in an introductory way early in the book, with references to a more detailed discussion later on.