Maple V

Maple V Mathematics Learning Guide is the fully revised introductory documentation for Maple V Release 5. It shows how to use Maple V as a calculator with instant access to hundreds of high-level math routines and as a programming language for more demanding or specialized tasks. Topics include the basic data types and statements in the Maple V language. The book serves as a tutorial introduction and explains the difference between numeric computation and symbolic computation, illustrating how both are used in Maple V Release 5. Extensive "how-to" examples are presented throughout the text to show how common types of calculations can be easily expressed in Maple. Graphics examples are used to illustrate the way in which 2D and 3D graphics can aid in understanding the behaviour of problems.

1. Interactive Use of Maple.- 1.1 The Worksheet Interface.- 1.2 Tutorial 1: Solving Problems.- 1.3 Tutorial 2: Managing Expressions through the Worksheet Interface.- Spreadsheets.- Palettes.- Smart Plots.- 1.4 Tutorial 3: Documenting Your Work.- Adding a Title.- Adding Headings.- In-line Mathematics.- 1.5 Tutorial 4: Multiple Worksheets.- Drag and Drop.- Adding Hyperlinks.- Bookmarks.- 1.6 Tutorial 5: Getting Help.- The Contents of the Help System.- Searching by Topic.- Full Text Searching.- 1.7 Conclusion.- 2. Mathematics with Maple: the Basics.- 2.1 Introduction.- 2.2 Numerical Computations.- Integer Computations.- Exact Arithmetic—Rationals, Irrationals, and Constants.- Floating-Point Approximations.- Arithmetic with Special Numbers.- Mathematical Functions.- 2.3 Basic Symbolic Computations.- 2.4 Assigning Names to Expressions.- 2.5 More Basic Types of Maple Objects.- Expression Sequences.- Lists.- Sets.- Operations on Sets and Lists.- Arrays.- Tables.- Strings.- 2.6 Expression Manipulation.- The simplify Command.- The factor Command.- The expand Command.- The convert Command.- The normal Command.- The combine Command.- The map Command.- The lhs and rhs Commands.- The numer and denom Commands.- The nops and op Commands.- Common Questions about Expression Manipulation.- 2.7 Conclusion.- 3. Finding Solutions.- 3.1 Simple solve.- Verifying Solutions.- Restricting Solutions.- Exploring Solutions.- The unapply Command.- The assign Command.- The RootOf Command.- 3.2 Solving Numerically: fsolve.- Limitations on solve.- 3.3 Other Solvers.- Finding Integer Solutions.- Finding Solutions Modulo m.- Solving Recurrence Relations.- 3.4 Polynomials.- Sorting and Collecting.- Mathematical Operations.- Coefficients and Degrees.- Root Finding and Factorization.- 3.5 Calculus.- 3.6 Differential Equations: dsolve.- 3.7 The Organization of Maple.- 3.8 The Maple Packages.- List of Packages.- The Student Calculus Package.- The Linear Algebra Package.- The Matlab Package.- The Statistics Package.- The Linear Optimization Package.- 3.9 Conclusion.- 4. Graphics.- 4.1 Graphing in Two Dimensions.- Parametric Plots.- Polar Coordinates.- Functions with Discontinuities.- Multiple Plots.- Plotting Data Points.- Refining Plots.- 4.2 Graphing in Three Dimensions.- Parametric Plots.- Spherical Coordinates.- Cylindrical Coordinates.- Refining Plots.- Shading and Lighting Schemes.- 4.3 Animation.- Animation in Two Dimensions.- Animation in Three Dimensions.- 4.4 Annotating Plots.- 4.5 Composite Plots.- Placing Text in Plots.- 4.6 Special Types of Plots.- 4.7 Manipulating Graphical Objects.- 4.8 Conclusion.- 5. Evaluation and Simplification.- 5.1 Mathematical Manipulations.- Expanding Polynomials as Sums.- Collecting the Coefficients of Like Powers.- Factoring Polynomials and Rational Functions.- Removing Rational Exponents.- Combining Terms.- Factored Normal Form.- Simplifying Expressions.- Simplification with Assumptions.- Simplification with Side Relations.- Sorting Algebraic Expressions.- Converting Between Equivalent Forms.- 5.2 The Assume Facility.- 5.3 Structural Manipulations.- Mapping a Function onto a List or Set.- Choosing Elements from a List or Set.- Merging Two Lists.- Sorting Lists.- The Parts of an Expression.- Substitution.- Changing the Type of an Expression.- 5.4 Evaluation Rules.- Levels of Evaluation.- Last-Name Evaluation.- One-Level Evaluation.- Commands with Special Evaluation Rules.- Quotation and Unevaluation.- Using Quoted Variables as Function Arguments.- Concatenation of Names.- 5.5 Conclusion.- 6. Examples from Calculus.- 6.1 Introductory Calculus.- The Derivative.- A Taylor Approximation.- The Integral.- Mixed Partial Derivatives.- 6.2 Ordinary Differential Equations.- The dsolve Command.- Example: Taylor Series.- When You Cannot Find a Closed Form Solution.- Plotting Ordinary Differential Equations.- Discontinuous Forcing Functions.- 6.3 Partial Differential Equations.- The pdsolve Command.- Changing the Dependent Variable in a PDE.- Plotting Partial Differential Equations.- 6.4 Conclusion.- 7. Input and Output.- 7.1 Reading Files.- Reading Columns of Numbers from a File.- Reading Commands from a File.- 7.2 Writing Data to a File.- Writing Columns of Numerical Data to a File.- Saving Expressions in Maple’s Internal Format.- Converting to LATEX Format.- 7.3 Exporting Whole Worksheets.- Plain Text.- Maple Text.- LATEX.- HTML.- 7.4 Printing Graphics.- 7.5 Conclusion.