Python for Engineering and Scientific Computing

1 ... Introduction ... 17

1.1 ... Development Environments ... 18

1.2 ... The Modules of Python ... 22

1.3 ... The Keywords of Python ... 26

1.4 ... Your Path through This Book ... 27

2 ... Program Structures ... 29

2.1 ... Linear Program Structures ... 29

2.2 ... Functions ... 37

2.3 ... Branching Structures ... 45

2.4 ... Repetitive Structures ... 50

2.5 ... Data Structures ... 63

2.6 ... Functional Program Style ... 76

2.7 ... Object-Oriented Program Style ... 79

2.8 ... Project Task: Dimensions of a Shaft ... 86

2.9 ... Tasks ... 88

3 ... Numerical Calculations Using NumPy ... 91

3.1 ... NumPy Functions ... 91

3.2 ... Vectors ... 101

3.3 ... Matrix Multiplication ... 109

3.4 ... Linear Systems of Equations ... 116

3.5 ... Project Task: Lightning Protection System ... 121

3.6 ... Tasks ... 124

4 ... Function Plots and Animations Using Matplotlib ... 125

4.1 ... 2D Function Plots ... 125

4.2 ... 3D Function Plots ... 166

4.3 ... Vectors ... 171

4.4 ... Displaying Figures, Lines, and Arrows ... 174

4.5 ... Animations ... 182

4.6 ... Project Task: Stirling Cycle ... 190

4.7 ... Project Task: Animating a Thread Pendulum ... 197

4.8 ... Project Task: Animating a Transmission ... 201

4.9 ... Tasks ... 204

5 ... Symbolic Computation Using SymPy ... 207

5.1 ... Basic Mathematical Operations ... 211

5.2 ... Multiplying Matrixes ... 217

5.3 ... Equations ... 220

5.4 ... Simplifications of Terms ... 226

5.5 ... Series Expansion ... 227

5.6 ... Partial Fractions ... 228

5.7 ... Continued Fractions ... 231

5.8 ... Limits ... 234

5.9 ... Differentiation ... 238

5.10 ... Integrations ... 240

5.11 ... Differential Equations ... 245

5.12 ... Laplace Transform ... 254

5.13 ... Project Task: Step Response of a Catenary Circuit ... 262

5.14 ... Project Task: Bending a Beam That Is Fixed at One End ... 265

5.15 ... Project Task: Reaction Kinetics ... 270

5.16 ... Project Task: Dual Mass Oscillator ... 274

5.17 ... Tasks ... 277

6 ... Numerical Computations and Simulations Using SciPy ... 279

6.1 ... Numerical Computation of Zeros ... 280

6.2 ... Optimizations ... 282

6.3 ... Interpolations ... 284

6.4 ... Numerical Differentiation ... 286

6.5 ... Numerical Integration ... 293

6.6 ... Solving Differential Equations Numerically ... 307

6.7 ... Discrete Fourier Transform ... 328

6.8 ... Writing and Reading Sound Files ... 334

6.9 ... Signal Processing ... 337

6.10 ... Project Task: Simulation of a Rolling Bearing Damage ... 342

6.11 ... Project Task: Predator-Prey Model ... 345

6.12 ... Project Task: Simulation of an Epidemic ... 349

6.13 ... Tasks ... 352

7 ... 3D Graphics and Animations Using VPython ... 355

7.1 ... The Coordinate System ... 356

7.2 ... Basic Shapes, Points, and Lines ... 358

7.3 ... Bodies in Motion ... 371

7.4 ... Animation of Oscillations ... 385

7.5 ... Event Processing ... 389

7.6 ... Project Task: Animation of a Coupled Spring Pendulum ... 392

7.7 ... Project Task: Animation of Two Coupled Simple Pendulums ... 395

7.8 ... Tasks ... 398

8 ... Computing with Complex Numbers ... 399

8.1 ... Mathematical Operations ... 400

8.2 ... Euler's Formula ... 402

8.3 ... Calculating with Complex Resistors ... 403

8.4 ... Function Plots with Complex Magnitudes ... 406

8.5 ... Project Task: Electric Power Transmission System ... 410

8.6 ... Tasks ... 415

9 ... Statistical Computations ... 417

9.1 ... Generating, Saving, and Reading Measurement Values ... 419

9.2 ... Frequency Distribution ... 423

9.3 ... Location Parameters ... 426

9.4 ... Dispersion Parameters ... 430

9.5 ... Normal Distribution ... 434

9.6 ... Skew ... 437

9.7 ... Regression Analysis ... 439

9.8 ... Project Task: Simulation of a Quality Control Chart ... 443

9.9 ... Tasks ... 448

10 ... Boolean Algebra ... 449

10.1 ... Logical Operations ... 450

10.2 ... Laws of Boolean Algebra ... 453

10.3 ... Circuit Synthesis ... 456

10.4 ... Project Task: Seven-Segment Coding ... 460

10.5 ... Tasks ... 463

11 ... Interactive Programming Using Tkinter ... 465

11.1 ... Interactions with Command Buttons, Textboxes, and Labels ... 466

11.2 ... The Layout Manager of Tkinter ... 468

11.3 ... Selection with Radio Button ... 475

11.4 ... Slider ... 477

11.5 ... The Canvas Drawing Area ... 478

11.6 ... Project Task: Rotational Frequency Control of an Externally Excited DC Motor ... 484

11.7 ... Tasks ... 496

... Appendix ... 497

A.1 ... Glossary: Basic Applied Computer Science Terminology ... 497

A.2 ... Derivatives of Elementary Functions ... 498

A.3 ... Antiderivative of Elementary Functions ... 499

A.4 ... Fourier Series of Important Electrotechnical Voltage Characteristics ... 500

A.5 ... Correspondence Table of Important Inverse Laplace Transforms ... 500

A.6 ... Bibliography ... 501

... The Author ... 503

... Index ... 505