Table of Contents
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.
