A Guide to Maple

A Guide to Maple

by Ernic Kamerich

Paperback(Softcover reprint of the original 1st ed. 1999)

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Product Details

ISBN-13: 9781461264361
Publisher: Springer New York
Publication date: 09/08/2012
Edition description: Softcover reprint of the original 1st ed. 1999
Pages: 325
Product dimensions: 6.10(w) x 9.25(h) x 0.03(d)

Table of Contents

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 in graphics.- 8 Taylor or Laurent expansion and limits.- 8.1 Taylor expansion.- 8.2 The order of a series expansion.- 8.3 Estimating the order term.- 8.4 The subexpression structure of results from series.- 8.5 The leading term.- 8.6 Laurent, Puisseux, and generalized truncated power series.- 8.7 Application of series to integration.- 8.8 Numerical evaluation of a series.- 8.9 Multivariate Taylor expansion.- 8.10 Calculating limits.- 8.11 Multiple limits.- 8.12 Continuity, singularities, and residues.- 8.13 Other facilities for series calculations.- 9 Numerical calculations with Maple.- 9.1 Accuracy.- 9.2 Speeding up by optimizing.- 9.3 Speeding up with floating-point facilities of the system.- 9.4 Some special procedures.- 9.5 Using Fortran and C in combination with Maple.- 9.6 Data files.- 10 Manipulating several objects at once.- 10.1 Creation of sequences, sets, and lists.- 10.2 Selecting elements of sequences, sets, and lists.- 10.3 Applying a procedure to several objects at once.- 10.4 Finding a special element in a set or a list.- 10.5 Finding the minimal or the maximal element.- 10.6 Selecting the elements that satisfy a special condition.- 10.7 Generating sequences as values of a function or an expression.- 10.8 Manipulating sequences, sets, and lists.- 10.9 Conversions between sequences, sets, and lists.- 10.10 Tables.- 11 Substitution and subexpressions.- 11.1 Some examples of substitution.- 11.2 A substitution that fails.- 11.3 Subexpressions of polynomials, substitution.- 11.4 Subexpressions of rational expressions, substitution.- 11.5 Subexpressions of unevaluated function calls.- 11.6 The procedure eval.- 11.7 The procedures subs and eval—a survey.- 11.8 More than one substitution at once.- 11.9 The procedure PDEtools [dchange] for changing variables.- 11.10 Substitution of algebraic subexpressions.- 11.11 Applying side relations.- 11.12 Finding the structure and subexpressions of large expressions.- 11.13 Selecting suboperands.- 11.14 Substituting something for one component of an expression.- 12 Manipulating and converting numbers.- 12.1 Real and imaginary parts of a complex number.- 12.2 Argument and absolute value of a complex number.- 12.3 The sign of a real or a complex number.- 12.4 Manipulating products and quotients of radicals.- 12.5 Nested radicals and roots of complex numbers.- 12.6 An example: substituting expressions with radicals in polynomials.- 12.7 Converting floating-point numbers to rational numbers.- 12.8 Rounding rational numbers to integers.- 13 Polynomials and rational expressions.- 13.1 Polynomials and the standard arithmetic operators.- 13.2 Division of polynomials with a remainder.- 13.3 The greatest common divisor and the least common multiple.- 13.4 The resultant of two polynomials.- 13.5 The coefficients of a polynomial.- 13.6 Truncating a polynomial above some degree.- 13.7 Sorting a polynomial.- 13.8 Simplifying rational expressions.- 13.9 Numerator and denominator.- 13.10 More tools.- 13.11 Reliability.- 14 Polynomial equations and factoring polynomials.- 14.1 Solving polynomial equations symbolically.- 14.2 Solving modest systems of polynomial equations.- 14.3 Finding or approximating the elements represented by a RootOf expression.- 14.4 Calculating with RootOf expressions.- 14.5 RootOf expressions versus radicals.- 14.6 Factoring with the procedure factor.- 14.7 More tools for factoring.- 14.8 Solving with numerical tools.- 14.9 Solving complicated systems of polynomial equations with Gröbner basis.- 14.10 Algebraic extensions of the rational number field.- 14.11 Polynomial rings modulo ideals.- 14.12 Polynomials over Z mod p.- 15 Manipulating algebraic expressions.- 15.1 Options for simplify and combine.- 15.2 Simplifications depending on conditions.- 15.3 Sums of exponents, products of powers with equal basis.- 15.4 Powers of powers, products of exponents.- 15.5 Powers of products, products of powers with equal exponents.- 15.6 Radicals.- 15.7 Manipulating logarithmic expressions.- 15.8 An example of the use of the option symbolic.- 15.9 Manipulating trigonometric expressions.- 15.10 Manipulating parts of expressions.- 15.11 An example: converting a complex expression into a real expression.- 15.12 Verifying identities.- 15.13 Reliability.- 15.14 General advice for manipulating.- 16 Solving equations and inequalities in general.- 16.1 General principles in using Maple for solving equations and inequalities.- 16.2 An example: a trigonometric equation.- 16.3 Another example: an exponential equation.- 16.4 No solutions found.- 16.5 Inequalities and systems of inequalities.- 16.6 Manipulating equations and sets of equations.- 16.7 Solving equations numerically.- 16.8 Solving systems of equations numerically.- 16.9 Series of an implicitly defined function.- 16.10 Recurrence relations.- 16.11 Solving identities, matching patterns.- 16.12 Other procedures for solving.- 17 Solving differential equations.- 17.1 Ordinary differential equations (ODEs): denoting, solving, checking solutions.- 17.2 Ordinary differential equations with initial conditions.- 17.3 Implicit solutions and checking them.- 17.4 DESol expressions appearing in solutions.- 17.5 Numerical approximations to solutions.- 17.6 Series development of a solution.- 17.7 Systems of ODEs.- 17.8 Helping Maple in solving ODEs.- 17.9 Symbolic representations of solutions: DESol.- 17.10 Graphic tools for differential equations.- 17.11 More tools.- 18 Vectors and matrices.- 18.1 The linear algebra package.- 18.2 Creating vectors and matrices.- 18.3 Evaluation of vectors and matrices.- 18.4 Elements of vectors and matrices.- 18.5 Matrix and vector arithmetic operators.- 18.6 Manipulating all the elements of a matrix or vector at once.- 18.7 Processing a matrix that contains floating-point numbers.- 18.8 Names contained in elements of matrices and vectors.- 18.9 Determinant, basis, range, kernel, Gaussian elimination.- 18.10 Systems of linear equations.- 18.11 Characteristic polynomials and eigenvalues.- 18.12 Dot product, cross product, norms, and orthogonal systems.- 18.13 Vector calculus.- 18.14 Creating new vectors and matrices from old ones by changing elements.- 18.15 Creating new matrices from old ones by transposing, cutting, and pasting.- 18.16 Alternative ways of creating vectors and matrices.- 18.17 Special types of matrices: (anti)symmetric, sparse, identity.- 18.18 Creating more special types of matrices.- 18.19 Functions yielding vectors and matrices.- 18.20 Vectors and matrices modulo an integer.- 18.21 Reading a matrix of data from a file.- 18.22 Pedagogical facilities.- Appendix A Types, properties, and domains.- A.1 Basic types.- More types.- Selection on type.- Properties, the assume facility.- Derived properties.- Asking for the assumed properties.- Adding properties.- Combining properties.- Properties and assigning.- Properties and formal parameters.- Domains, the Domains package.- Appendix B Names and evaluation 3: some special features.- Changing names, alias.- Finding names used.- Indexed names.- Quotes with table, arrays, vectors, and matrices.- Recovering lost procedures.- Exceptions to the rule of automatic full evaluation.- Appendix C The user interface for text-only versions.- Starting, interrupting, and quitting Maple.- Editing commands.- Pictures.- Maple system messages.- Saving a session and its results.- Appendix D Procedures remembering previous results.- Remember tables of procedures.- Clearing (parts of) the remember table.- An example of side effects of the remember table: infolevel.- Appendix E Control structures.- Procedures.- Searching for causes of odd behavior with trace or printlevel.- Using if ... fi for choices.- Recursion.- Using do od for repeating actions.- An example: checking the results of solve by substituting.- Error messages and warnings.- Catchword index.

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