Symbolic Mathematics for Chemists

An essential guide to using Maxima, a popular open source symbolic mathematics engine to solve problems, build models, analyze data and explore fundamental concepts

Symbolic Mathematics for Chemists offers students of chemistry a guide to Maxima, a popular open source symbolic mathematics engine that can be used to solve problems, build models, analyze data, and explore fundamental chemistry concepts. The author -- a noted expert in the field -- focuses on the analysis of experimental data obtained in a laboratory setting and the fitting of data and modeling experiments. The text contains a wide variety of illustrative examples and applications in physical chemistry, quantitative analysis and instrumental techniques.

Designed as a practical resource, the book is organized around a series of worksheets that are provided in a companion website. Each worksheet has clearly defined goals and learning objectives and a detailed abstract that provides motivation and context for the material. This important resource:

• Offers an text that shows how to use popular symbolic mathematics engines to solve problems

• Includes a series of worksheet that are prepared in Maxima

• Contains step-by-step instructions written in clear terms and includes illustrative examples to enhance critical thinking, creative problem solving and the ability to connect concepts in chemistry

• Offers hints and case studies that help to master the basics while proficient users are offered more advanced avenues for exploration

Written for advanced undergraduate and graduate students in chemistry and instructors looking to enhance their lecture or lab course with symbolic mathematics materials, Symbolic Mathematics for Chemists: A Guide for Maxima Users is an essential resource for solving and exploring quantitative problems in chemistry.

Auteur

Professor Fred Senese is a computational chemist at Frostburg State University with a particular focus on chemical education. His research interests include applications of artificial intelligence in chemical education, development of web-based narratives and construction kits for chemical education, remote control and access of instrumentation, and environmental chemical analysis applied to problems in ethnobotany.

Contenu
Preface xiii

1 Fundamentals 1

1.1 Getting Started With wxMaxima 1

1.1.1 Input Cells 2

1.1.2 The Toolbar 3

1.1.3 The Menus 3

1.1.4 Command History 4

1.1.5 Basic Arithmetic 5

1.1.6 Mathematical Functions 7

1.1.7 Assigning Variables 8

1.1.8 Defining Functions 10

1.1.9 Comments, Images, and Sectioning 12

1.2 A Tour of the General Math Pane 12

1.2.1 Basic Plotting 13

1.2.1.1 Plotting Multiple Curves 14

1.2.1.2 Parametric Plots 15

1.2.1.3 Discrete Plots 15

1.2.1.4 Three-Dimensional Plots 17

1.2.2 Basic Algebra 18

1.2.2.1 Equations 18

1.2.2.2 Substitutions 18

1.2.2.3 Simplification 20

1.2.2.4 Solving Equations 21

1.2.2.5 Simplifying Trigonometric and Exponential Functions 21

1.2.3 Basic Calculus 22

1.2.3.1 Limits 22

1.2.3.2 Differentiation 23

1.2.3.3 Series 24

1.2.3.4 Integration 25

1.2.4 Differential Equations 28

1.3 Controlling Execution 28

1.4 Using Packages 30

2 Storing and Transforming Data 33

2.1 Numbers 33

2.1.1 Floating Point Numbers 33

2.1.2 Integers and Rational Numbers 37

2.1.3 Complex Numbers 38

2.1.4 Constants 42

2.1.5 Units and Physical Constants 43

2.2 Boolean Expressions and Predicates 47

2.2.1 Relational Operators 47

2.2.2 Logical Operators 48

2.2.3 Predicates 49

2.3 Lists 51

2.3.1 List Assignments 51

2.3.2 Indexing List Items 52

2.3.3 Arithmetic with Lists 52

2.3.4 Building and Editing Lists 54

2.3.4.1 Adding Items 54

2.3.4.2 Deleting Items 55

2.3.5 Nested Lists 55

2.3.6 Sublists 56

2.4 Matrices 57

2.4.1 Row and Column Vectors 57

2.4.2 Indexing Matrices 58

2.4.3 Entering Matrices 59

2.4.4 Assigning Matrices 60

2.4.5 Editing Matrices 61

2.4.6 Reading and Writing Matrices From Files 63

2.4.7 Transforming Data in a Matrix 65

2.5 Strings 66

2.5.1 Using String Functions toWork with Files 67

3 Plotting Data and Functions 71

3.1 Plotting in Two Dimensions 71

3.1.1 Changing Plot Size and Resolution 71

3.1.2 Plotting Multiple Curves 73

3.1.3 Changing Axis Ranges 74

3.1.4 Plotting Complex Functions 74

3.1.5 Plotting Data 74

3.1.5.1 Plotting Data in Separate X, Y Lists 75

3.1.5.2 Plotting Data as Lists of X, Y Points 75

3.1.5.3 Plotting Data in Matrices 76

3.1.5.4 Plotting Data with Units 76

3.1.5.5 Plotting Functions and Data Together 77

3.1.6 Adding Text Labels to Graphs 77

3.1.7 Plotting Rapidly Rising Functions 78

3.1.7.1 Solving Axis Scaling Problems 81

3.1.7.2 Positioning the Legend 83

3.1.8 Parametric Plots 84

3.1.9 Implicit Plots 87

3.1.10 Histograms 89

3.2 Plotting inThree Dimensions 91

3.2.1 Plotting Functions of x, y, andz 91

3.2.2 Plotting Multiple Surfaces 93

3.2.3 Plotting in Spherical Coordinates 94

3.2.4 Plotting in Cylindrical Coordinates 95

3.2.5 Parametric Surface Plots 96

3.2.6 Plotting DiscreteThree-Dimensional Data 98

3.2.7 Contour Plotting 99

4 Programming Maxima 103

4.1 Nouns and Verbs 103

4.2 Writing Multiline Functions 106

4.3 Decision Making 108

4.4 Recursive Functions 109

4.5 Contexts 110

4.6 Iteration 114

4.6.1 Indexed Loops 114

4.6.2 Conditional Loops 116 4.6.3 Looping Over Lists 117</p&g...