Ernic Kamerich

A Guide to Maple (eBook, PDF)

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Springer US
• Seitenzahl: 325
• Erscheinungstermin: 27. Juni 2011
• Englisch
• ISBN-13: 9781441985569
• Artikelnr.: 44179409

Inhaltsangabe

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.