A Mathematica Primer for Physicists

Jim Napolitano

• Publisher: CRC Press
• Year: 2018
• ISBN:
  9781351979207
• Edition: 1
• Topic: Sciences physiques
• Subtopic: Physique

"…an excellent text for either a short course or self-study… Professor Napolitano has figured out what students really need, and found a way to deliver it… I have found everything he writes to be worthy of my serious attention…"
—Peter D. Persans, Professor of Physics and Director, Center for Integrated Electronics, Rensselaer Polytechnic Institute

Learn how to use Mathematica quickly for basic problems in physics. The author introduces all the key techniques and then shows how they're applied using common examples. Chapters cover elementary mathematics concepts, differential and integral calculus, differential equations, vectors and matrices, data analysis, random number generation, animation, and visualization.

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• Written in an appealing, conversational style

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• Presents important concepts within the framework of Mathematics

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• Gives examples from frequently encountered physics problems

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• Explains problem-solving in a step-by-step fashion

Jim Napolitano is professor and chair in the Department of Physics at Temple University. He is the author of other textbooks, including co-author with Alistair Rae of Quantum Mechanics, Sixth Edition, also published by Taylor & Francis / CRC Press.

Contents

CHAPTER 1 Introduction

1.1 GETTING STARTED

1.2 BUILT-IN OBJECTS

1.3 FUNCTIONS

1.4 SIMPLE PLOTTING

1.5 GOOD HABITS FOR WRITING NOTEBOOKS

1.6 PHYSICS EXAMPLE

1.7 GETTING HELP

1.8 CHAPTER SUMMARY

CHAPTER 2 Solving Algebraic Equations

2.1 SYNTAX FOR EQUATIONS AND SOLUTIONS

2.2 LIST MANIPULATIONS

2.3 SYSTEMS OF EQUATIONS

2.4 COMPLEX NUMBERS

2.5 PHYSICS EXAMPLES

2.6 CHAPTER SUMMARY

CHAPTER 3 Derivatives, Integrals, and Series

3.1 DERIVATIVES

3.2 INDEFINITE INTEGRALS

3.3 DEFINITE INTEGRALS

3.4 NUMERICAL INTEGRATION

3.5 POWER SERIES

3.6 PHYSICS EXAMPLES

3.7 CHAPTER SUMMARY

CHAPTER 4 Differential Equations: Analytic Solutions

4.1 FIRST ORDER ORDINARY DIFFERENTIAL EQUATIONS

4.2 SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS

4.3 SIMULTANEOUS DIFFERENTIAL EQUATIONS

4.4 PARTIAL DIFFERENTIAL EQUATIONS

4.5 PHYSICS EXAMPLES

4.6 CHAPTER SUMMARY

CHAPTER 5 Differential Equations: Numerical Solutions

5.1 ORDINARY DIFFERENTIAL EQUATIONS

5.2 PARTIAL DIFFERENTIAL EQUATIONS

5.3 PLOTTING IN THREE DIMENSIONS

5.4 PHYSICS EXAMPLES

5.5 CHAPTER SUMMARY

CHAPTER 6 Vectors and Matrices

6.1 VECTORS AND MATRICES AS LISTS

6.2 LOGICAL EXPRESSIONS AND OPERATIONS

6.3 VECTOR OPERATIONS

6.4 MATRIX OPERATIONS

6.5 EIGENVALUE PROBLEMS

6.6 PHYSICS EXAMPLES

6.7 CHAPTER SUMMARY

CHAPTER 7 Basic Data Analysis

7.1 NUMBERS IN LISTS

7.2 SELECTING DATA SEGMENTS

7.3 READING DATA FROM A FILE

7.4 MAKING HISTOGRAMS

7.5 PHYSICS EXAMPLE

7.6 CHAPTER SUMMARY

CHAPTER 8 Fitting Data to Models

8.1 LINEAR FITTING

8.2 NONLINEAR FITTING

8.3 HANDLING DATA WITH ERROR BARS

8.4 PHYSICS EXAMPLE

8.5 CHAPTER SUMMARY

CHAPTER 9 Numerical Manipulations

9.1 SIGNIFICANT FIGURES

9.2 NUMERICAL SOLUTIONS TO ALGEBRAIC EQUATIONS

9.3 WORKING WITH UNITS

9.4 ACCESS TO DATABASES

9.5 PHYSICS EXAMPLES

9.6 CHAPTER SUMMARY

CHAPTER 10 Random Numbers

10.1 GENERATING RANDOM NUMBERS

10.2 MONTE CARLO TECHNIQUES

10.3 PROBABILITY DISTRIBUTIONS

10.4 PHYSICS EXAMPLE

10.5 CHAPTER SUMMARY

CHAPTER 11 Animation

11.1 SCOPING

11.2 PLOTS IN MOTION

11.3 DRAWING GEOMETRIC SHAPES

11.4 CARTOON ANIMATION

11.5 PHYSICS EXAMPLES

11.6 CHAPTER SUMMARY

CHAPTER 12 Advanced Plotting and Visualization

12.1 OPTIONS FOR 2D PLOTS

12.2 OPTIONS FOR 3D PLOTS

12.3 CONTOUR AND DENSITY PLOTS

12.4 VECTOR DIFFERENTIAL CALCULUS

12.5 VISUALIZING VECTOR FIELDS

12.6 PHYSICS EXAMPLES

12.7 CHAPTER SUMMARY

Appendix A dditional Exercises

Appendix B Shorthands

Index

How to read this book

Look for bits of Mathematica commands that are set off from the text and in a different font, for example

S o l v e [ { x + y = = 2 a , x - y = = 2 b } , { x , y } ]

(To execute this statement, press Enter while holding down the Shift key.) I generally follow statements like this with the resulting output. In this case,

{ { x - > a + b , y - > a - b } }

The text around these pieces of input and output is there to help you understand the syntax, and to appreciate how to extend it.

Then, look at the example problems. Every chapter concludes with one or more “Physics Examples” that use the material up to that point to solve typical physics problems.

Many commands have “shorthands” and I use them from time to time, more often towards the end of the book. I’ve included an appendix to help you resolve them.

Preface

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