A primer on scientific programming with Python

Contents......Page 7
List of Exercises......Page 17
 1.1 The First Programming Encounter: A Formula......Page 26
 1.2 Computer Science Glossary......Page 38
 1.3 Another Formula: Celsius-Fahrenheit Conversion......Page 43
 1.4 Evaluating Standard Mathematical Functions......Page 47
 1.5 Interactive Computing......Page 51
 1.6 Complex Numbers......Page 56
 1.7 Summary......Page 60
 1.8 Exercises......Page 65
 2.1 Loops and Lists for Tabular Data......Page 75
 2.2 Functions......Page 95
 2.3 If Tests......Page 112
 2.4 Summary......Page 115
 2.5 Exercises......Page 123
3 Input Data and Error Handling......Page 143
 3.1 Asking Questions and Reading Answers......Page 144
 3.2 Reading from the Command Line......Page 151
 3.3 Handling Errors......Page 156
 3.4 A Glimpse of Graphical User Interfaces......Page 163
 3.5 Making Modules......Page 165
 3.6 Summary......Page 174
 3.7 Exercises......Page 184
4 Array Computing and Curve Plotting......Page 192
 4.1 Vectors......Page 193
 4.2 Arrays in Python Programs......Page 198
 4.3 Curve Plotting......Page 202
 4.4 Plotting Difficulties......Page 222
 4.5 More on Numerical Python Arrays......Page 230
 4.6 Higher-Dimensional Arrays......Page 236
 4.7 Summary......Page 242
 4.8 Exercises......Page 248
5 Sequences and Difference Equations......Page 257
 5.1 Mathematical Models Based on Difference Equations......Page 258
 5.2 Programming with Sound......Page 275
 5.3 Summary......Page 278
 5.4 Exercises......Page 282
 6.1 Reading Data from File......Page 291
 6.2 Dictionaries......Page 300
 6.3 Strings......Page 313
 6.4 Reading Data from Web Pages......Page 322
 6.5 Writing Data to File......Page 330
 6.6 Summary......Page 339
 6.7 Exercises......Page 345
7 Introduction to Classes......Page 358
 7.1 Simple Function Classes......Page 359
 7.2 More Examples on Classes......Page 373
 7.3 Special Methods......Page 377
 7.4 Example: Solution of Differential Equations......Page 393
 7.5 Example: Class for Vectors in the Plane......Page 399
 7.6 Example: Class for Complex Numbers......Page 403
 7.7 Static Methods and Attributes......Page 410
 7.8 Summary......Page 412
 7.9 Exercises......Page 418
8 Random Numbers and Simple Games......Page 437
 8.1 Drawing Random Numbers......Page 438
 8.2 Drawing Integers......Page 444
 8.3 Computing Probabilities......Page 452
 8.4 Simple Games......Page 460
 8.5 Monte Carlo Integration......Page 463
 8.6 Random Walk in One Space Dimension......Page 467
 8.7 Random Walk in Two Space Dimensions......Page 473
 8.8 Summary......Page 476
 8.9 Exercises......Page 483
 9.1 Inheritance and Class Hierarchies......Page 499
 9.2 Class Hierarchy for Numerical Differentiation......Page 508
 9.3 Class Hierarchy for Numerical Integration......Page 519
 9.4 Class Hierarchy for Numerical Methods for ODEs......Page 528
 9.5 Class Hierarchy for Geometric Shapes......Page 545
 9.6 Summary......Page 558
 9.7 Exercises......Page 566
 A.1 Discrete Functions......Page 592
 A.2 Differentiation Becomes Finite Differences......Page 598
 A.3 Integration Becomes Summation......Page 602
 A.4 Taylor Series......Page 608
 A.5 Exercises......Page 618
B - Differential Equations......Page 623
 B.1 The Simplest Case......Page 624
 B.2 Exponential Growth......Page 626
 B.3 Logistic Growth......Page 630
 B.4 A General Ordinary Differential Equation......Page 632
 B.5 A Simple Pendulum......Page 633
 B.6 A Model for the Spread of a Disease......Page 637
 B.7 Exercises......Page 639
C - A Complete Project......Page 643
 C.1 About the Problem: Motion and Forces in Physics......Page 644
 C.2 Program Development and Testing......Page 650
 C.3 Visualization......Page 657
 C.4 Exercises......Page 667
 D.1 Using a Debugger......Page 669
 D.2 How to Debug......Page 671
 E.1 Different Ways of Running Python Programs......Page 687
 E.2 Integer and Float Division......Page 691
 E.3 Visualizing a Program with Lumpy......Page 692
 E.4 Doing Operating System Tasks in Python......Page 693
 E.5 Variable Number of Function Arguments......Page 696
 E.6 Evaluating Program E ciency......Page 701
References......Page 705
Index......Page 706