| Preface Plan of this Book 1 A Tour of Maple V 1.1 Introduction 1.2 Maple's User Interface 1.3 Just a Maple Session 1.3.1 Numerical Calculations 1.3.2 Symbolic Calculations 1.4 Worksheets and Assignments 1.4.1 Worksheet la. Numbers 1.4.2 Assignments la. Numbers 1.4.3 Worksheet lb. Variables and Names 1.4.4 Assignments lb. Variables and Names 1.5 Exercises 1.6 Survey of Used Maple Expressions 2 Functions and Sequences 2.1 Introduction 2.2 Selected Concepts from Analysis 2.3 A Tricky Probability Function 2.3.1 Mathematical Functions 2.3.2 Investigating a Probability Function 2.3.3 Investigating a Strange Sequence 2.4 Workshects and Assignments 2.4.1 Worksheet 2a. Functions 2.4.2 Assignments 2a. Functions 2.4.3 Worksheet 2b. Sequences 2.4.4 Assignments 2b. Sequences 2.5 Exercises 2.6 Survey of Used Maple Expressions 3 Matrices and Vectors 3.1 Introduction 3.2 Selected Concepts from Linear Algebra 3.3 A Least Squares Filter 3.3.1 Matrices and Vectors 3.3.2 Removing Noise from a Data Set 3.4 Worksheets and Assignments 3.4.1 Worksheet 3a. Matrices 3.4.2 Assignments 3a. Matrices 3.4.3 Worksheet 3b. Vectors 3.4.4 Assignments 3b. Vectors 3.5 Exercises 3.6 Survey of Used Maple Expressions 4 Counting and Summation 4.1 Introduction 4.2 Selected Concepts from Discrete Mathematics 4.3 Binomial Coefficients 4.3.1 Maple's binomial Function 4.3.2 Two Binomial Identities 4.3.3 The Binomial Series 4.3.4 The De Moivre-Laplace Limit Theorem 4.4 Worksheets and Assignments 4.4.1 Worksheet 4a. Symbolic Summation 4.4.2 Assignments 4a. Symbolic Summation 4.4.3 Worksheet 4b. Counting and Random Numbers 4.4.4 Assignments 4b. Counting and Random Numbers . . . 4.5 Exercises 4.6 Survey of Used Maple Expressions 5 Derivative and Integral 5.1 Introduction 5.2 Further Concepts from Analysis 5.3 Riemann's Non-differentiable Function 5.3.1 Investigating the Riemann Function 5.3.2 Finding a Primitive Function 5.4 Worksheets and Assignments 5.4.1 Worksheet 5a. Differentiation 5.4.2 Assignment 5a. Differentiation …… 6 Vector Spaces and Linear Mappings A Exercises in Experimentation B Hints and Answers C Quick Guide to Selected Maple Commands Bibliography Index |
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