1 Introduction

17

1.1 Development Environments

18

1.1.1 IDLE

18

1.1.2 Thonny

19

1.1.3 Spyder

20

1.1.4 Pip

21

1.2 The Modules of Python

22

1.2.1 NumPy

22

1.2.2 Matplotlib

23

1.2.3 SymPy

24

1.2.4 SciPy

24

1.2.5 VPython

25

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

2.1.1 Linear Programs without Function Calls

30

2.2 Functions

37

2.2.1 Built-In Functions

38

2.2.2 Functions without Parameters and without Return Values

39

2.2.3 Functions with Parameters and a Return

40

2.2.4 Functions with Multiple Return Values

42

2.2.5 Functions Call Other Functions

44

2.3 Branching Structures

45

2.3.1 Single Selection

46

2.3.2 Multiple Selection

47

2.4 Repetitive Structures

50

2.4.1 The while Loop

50

2.4.2 The for Loop

56

2.5 Data Structures

63

2.5.1 Tuples

63

2.5.2 Lists

66

2.5.3 Dictionaries

72

2.5.4 Sets

75

2.6 Functional Program Style

76

2.7 Object-Oriented Program Style

79

2.7.1 Objects and Classes

80

2.7.2 Inheritance

84

2.8 Project Task: Dimensions of a Shaft

86

2.9 Tasks

88

3 Numerical Calculations Using NumPy

91

3.1 NumPy Functions

91

3.1.1 Creating One-Dimensional Arrays Using arange() and linspace()

91

3.1.2 Creating Two-Dimensional Arrays Using array()

94

3.1.3 Slicing

96

3.1.4 Mathematical NumPy Functions

97

3.1.5 Statistical NumPy Functions

99

3.2 Vectors

101

3.2.1 Addition of Vectors

101

3.2.2 Scalar Product

103

3.2.3 Cross Product

105

3.2.4 Triple Product

107

3.2.5 Dyadic Product

108

3.3 Matrix Multiplication

109

3.3.1 Chain Shape with B Parameters

113

3.3.2 Usage Example: Calculating the Energy of a Rotating Rigid Body in Space

114

3.4 Linear Systems of Equations

116

3.4.1 Systems of Equations with Real Coefficients

116

3.4.2 Systems of Equations with Complex Coefficients

118

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

4.1.1 Basic Structure of a Function Plot

125

4.1.2 Gridlines

132

4.1.3 Labels

134

4.1.4 Line Styles

137

4.1.5 Designing Axes

138

4.1.6 Coloring Areas

144

4.1.7 Subplots

147

4.1.8 Parameter Representation

154

4.1.9 Changing Function Parameters Interactively

158

4.1.10 Contour Plots

163

4.2 3D Function Plots

166

4.2.1 Helical Line

166

4.2.2 Circular Ring

168

4.2.3 Combining a 3D Plot with a Contour Plot

169

4.3 Vectors

171

4.3.1 Vector Addition

171

4.3.2 Vector Field

173

4.4 Displaying Figures, Lines, and Arrows

174

4.4.1 Rectangles

174

4.4.2 Circles and Lines

176

4.4.3 Arrows

178

4.4.4 Polygons

179

4.4.5 Usage Example: A Metal Rod in a Magnetic Field

181

4.5 Animations

182

4.5.1 A Simple Animation: Shifting a Sine Function

183

4.5.2 Animated Oblique Throw

186

4.5.3 Animated Planetary Orbit

188

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

5.1.1 Addition

211

5.1.2 Multiplication of Terms

212

5.1.3 Multiplication of Linear Factors

213

5.1.4 Division

214

5.1.5 Exponentiation

215

5.1.6 Usage Example: Analyzing an Electrical Power Transmission System

216

5.2 Multiplying Matrixes

217

5.2.1 Calculation Rule

217

5.2.2 Transmission Function of a Catenary Circuit

218

5.3 Equations

220

5.3.1 Linear Systems of Equations

221

5.3.2 Nonlinear Systems of Equations

223

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

5.8.1 Limits of Sequences

234

5.8.2 Limits of Functions

236

5.8.3 Differential Quotient

237

5.9 Differentiation

238

5.9.1 Usage Example: Curve Sketching

239

5.10 Integrations

240

5.10.1 Indefinite Integral

241

5.10.2 Definite Integral

242

5.10.3 Usage Example: Stored Electrical Energy

243

5.11 Differential Equations

245

5.11.1 Linear First-Order Differential Equations

246

5.11.2 General Solution of a Second-Order Differential Equation

250

5.11.3 Special Solution of a Second-Order Differential Equation

252

5.12 Laplace Transform

254

5.12.1 Solving Differential Equations

255

5.12.2 Analyzing Networks with Transmission Functions

259

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

5.14.1 Second Moment of Area

265

5.14.2 Equation of the Bending Line

267

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

6.4.1 Methods of Numerical Differentiation

286

6.4.2 Drawing a Tangent Slope

287

6.4.3 Derivative of a Sine Function

289

6.4.4 Usage Example: Free Fall

291

6.5 Numerical Integration

293

6.5.1 Methods of Numerical Integration

293

6.5.2 Definite Integral

295

6.5.3 Integrating a Constant

296

6.5.4 Usage Example: Free Fall

298

6.5.5 Improper Integral

300

6.5.6 Calculating Arc Lengths

302

6.5.7 Volume and Surfaces of Rotating Bodies

303

6.5.8 Double Integrals

305

6.5.9 Triple Integrals

306

6.6 Solving Differential Equations Numerically

307

6.6.1 Numerical Solution of Differential Equations

307

6.6.2 First-Order Linear Differential Equation

312

6.6.3 Second-Order Linear Differential Equation

315

6.6.4 Nonlinear Second-Order Differential Equation

318

6.6.5 Second-Order Differential Equation System: Coupled Spring-Mass System

322

6.6.6 Nonlinear Second-Order Differential Equation System: Double Pendulum

325

6.7 Discrete Fourier Transform

328

6.7.1 Basic Use of the Fast Fourier Transform Algorithm

329

6.7.2 Frequency Spectra of Non-Sinusoidal Periodic Signals

330

6.7.3 Reconstructing a Noisy Signal

332

6.8 Writing and Reading Sound Files

334

6.8.1 Generating and Saving Signals

334

6.8.2 Reading and Displaying Signals

335

6.9 Signal Processing

337

6.9.1 Frequency Response of a Butterworth Lowpass

337

6.9.2 Frequency Response of a Crossover

339

6.9.3 Filtering Signals

341

6.10 Project Task: Simulation of a Rolling Bearing Damage

342

6.11 Project Task: Predator-Prey Model

345

6.11.1 Exponential Growth

346

6.11.2 Logistic Growth

346

6.11.3 Predator-Prey Relationship for Exponential Growth

346

6.11.4 Predator-Prey Relationship for Logistic Growth

347

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

7.2.1 Cylinder

359

7.2.2 Cuboid

361

7.2.3 Points

363

7.2.4 Lines

364

7.2.5 Sphere

366

7.2.6 Penetration

369

7.2.7 Composite Bodies

370

7.3 Bodies in Motion

371

7.3.1 Vertical Movement

372

7.3.2 Horizontal Movement

373

7.3.3 Movement in Space

374

7.3.4 Composite Motion

377

7.3.5 Rotational Motion

378

7.3.6 Random Motion

383

7.4 Animation of Oscillations

385

7.4.1 Simple Pendulum

385

7.4.2 Spring Pendulum

387

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

8.2.1 Symbolic Method

403

8.3 Calculating with Complex Resistors

403

8.4 Function Plots with Complex Magnitudes

406

8.4.1 Complex Frequency Response of a Series Resonant Circuit

406

8.4.2 Locus Curves

408

8.5 Project Task: Electric Power Transmission System

410

8.5.1 Task

411

8.5.2 Equivalent Circuit Diagram of a Three-Phase Power Line

413

8.6 Tasks

415

9 Statistical Computations

417

9.1 Generating, Saving, and Reading Measurement Values

419

9.1.1 Generating Measurement Values

419

9.1.2 Converting a Measurement Series into a Table

420

9.1.3 Writing Measurement Values to a File

422

9.1.4 Reading Measurement Values from a File

423

9.2 Frequency Distribution

423

9.2.1 Frequency Tables

424

9.2.2 Histograms

425

9.3 Location Parameters

426

9.3.1 Arithmetic Mean

427

9.3.2 Mode, Median, Harmonic Mean, and Geometric Mean

428

9.4 Dispersion Parameters

430

9.5 Normal Distribution

434

9.5.1 Graphical Representation of the Density Function

434

9.5.2 Probability Distribution

435

9.6 Skew

437

9.7 Regression Analysis

439

9.7.1 Computing the Regression Parameters

439

9.7.2 Representing the Scatter Plot and the Regression Line

442

9.8 Project Task: Simulation of a Quality Control Chart

443

9.9 Tasks

448

10 Boolean Algebra

449

10.1 Logical Operations

450

10.1.1 Conjunction

450

10.1.2 Disjunction

451

10.1.3 Negation

452

10.2 Laws of Boolean Algebra

453

10.2.1 Simple Postulates

453

10.2.2 De Morgan’s Laws

454

10.2.3 Distributive Law

455

10.3 Circuit Synthesis

456

10.3.1 Simplifying Logic Functions by Factoring Out

456

10.3.2 Simplification Using the Disjunctive Normal Form

457

10.3.3 Simplification Using the Conjunctive Normal Form

460

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

11.1.1 Labels

467

11.1.2 Textboxes and Command Buttons

468

11.2 The Layout Manager of Tkinter

468

11.2.1 The pack Method

470

11.2.2 The grid Method

472

11.2.3 Summary

474

11.3 Selection with Radio Button

475

11.4 Slider

477

11.5 The Canvas Drawing Area

478

11.5.1 Representing Lines

478

11.5.2 Function Plots

480

11.5.3 Querying Mouse Coordinates

482

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