Python for Scientific Computing and Artificial Intelligence

Cover....1

Half Title....2

Series Page....3

Title Page....4

Copyright Page....5

Dedication....6

Contents....8

Foreword....14

Preface....16

SECTION I: An Introduction to Python....22

CHAPTER 1: The IDLE Integrated Development Learning Environment....24

1.1. INTRODUCTION....25

1.1.1. Tutorial One: Using Python as a Powerful Calculator (30 Minutes)....26

1.1.2. Tutorial Two: Lists (20 Minutes)....28

1.2. SIMPLE PROGRAMMING IN PYTHON....29

1.2.1. Tutorial Three: Defining Functions (30 Minutes)....30

1.2.2. Tutorial Four: For and While Loops (20 Minutes)....32

1.2.3. Tutorial Five: If, elif, else constructs (10 Minutes)....32

1.3. THE TURTLE MODULE AND FRACTALS....32

CHAPTER 2: Anaconda, Spyder and the Libraries NumPy, Matplotlib and SymPy....42

2.1. A TUTORIAL INTRODUCTION TO NUMPY....44

2.1.1. Tutorial One: An Introduction to NumPy and Arrays (30 Minutes)....44

2.2. A TUTORIAL INTRODUCTION TO MATPLOTLIB....46

2.2.1. Tutorial Two: Simple Plots using the Spyder Editor Window (30 minutes)....46

2.3. A TUTORIAL INTRODUCTION TO SYMPY....49

2.3.1. Tutorial Three: An Introduction to SymPy (30 Minutes)....49

CHAPTER 3: Jupyter Notebooks and Google Colab....54

3.1. JUPYTER NOTEBOOKS, CELLS, CODE AND MARKDOWN....54

3.2. ANIMATIONS AND INTERACTIVE PLOTS....58

3.3. GOOGLE COLAB AND GITHUB....62

CHAPTER 4: Python for AS-Level (High School) Mathematics....66

4.1. AS-LEVEL MATHEMATICS (PART 1)....67

4.2. AS-LEVEL MATHEMATICS (PART 2)....71

CHAPTER 5: Python for A-Level (High School) Mathematics....82

5.1. A-LEVEL MATHEMATICS (PART 1)....83

5.2. A-LEVEL MATHEMATICS (PART 2)....89

SECTION II: Python for Scientific Computing....100

CHAPTER 6: Biology....102

6.1. A SIMPLE POPULATION MODEL....102

6.2. A PREDATOR-PREY MODEL....105

6.3. A SIMPLE EPIDEMIC MODEL....108

6.4. HYSTERESIS IN SINGLE FIBER MUSCLE....110

CHAPTER 7: Chemistry....116

7.1. BALANCING CHEMICAL-REACTION EQUATIONS....116

7.2. CHEMICAL KINETICS....118

7.3. THE BELOUSOV-ZHABOTINSKI REACTION....120

7.4. COMMON-ION EFFECT IN SOLUBILITY....122

CHAPTER 8: Data Science....128

8.1. INTRODUCTION TO PANDAS....128

8.2. LINEAR PROGRAMMING....131

8.3. K-MEANS CLUSTERING....136

8.4. DECISION TREES....140

CHAPTER 9: Economics....146

9.1. THE COBB-DOUGLAS QUANTITY OF PRODUCTION MODEL....147

9.2. THE SOLOW-SWAN MODEL OF ECONOMIC GROWTH....149

9.3. MODERN PORTFOLIO THEORY (MPT)....151

9.4. THE BLACK-SCHOLES MODEL....154

CHAPTER 10: Engineering....160

10.1. LINEAR ELECTRICAL CIRCUITS AND THE MEMRISTOR....160

10.2. CHUA'S NONLINEAR ELECTRICAL CIRCUIT....163

10.3. COUPLED OSCILLATORS: MASS-SPRING MECHANICAL SYSTEMS....165

10.4. PERIODICALLY FORCED MECHANICAL SYSTEMS....167

CHAPTER 11: Fractals and Multifractals....174

11.1. PLOTTING FRACTALS WITH MATPLOTLIB....174

11.2. BOX-COUNTING BINARY IMAGES....179

11.3. THE MULTIFRACTAL CANTOR SET....181

11.4. THE MANDELBROT SET....183

CHAPTER 12: Image Processing....188

12.1. IMAGE PROCESSING, ARRAYS AND MATRICES....189

12.2. COLOR IMAGES....190

12.3. STATISTICAL ANALYSIS ON AN IMAGE....191

12.4. IMAGE PROCESSING ON MEDICAL IMAGES....193

CHAPTER 13: Numerical Methods for Ordinary and Partial Differential Equations....198

13.1. EULER'S METHOD TO SOLVE IVPS....199

13.2. RUNGE KUTTA METHOD (RK4)....200

13.3. FINITE DIFFERENCE METHOD: THE HEAT EQUATION....202

13.4. FINITE DIFFERENCE METHOD: THE WAVE EQUATION....205

CHAPTER 14: Physics....212

14.1. THE FAST FOURIER TRANSFORM....213

14.2. THE SIMPLE FIBER RING (SFR) RESONATOR....215

14.3. THE JOSEPHSON JUNCTION....217

14.4. MOTION OF PLANETARY BODIES....219

CHAPTER 15: Statistics....224

15.1. LINEAR REGRESSION....224

15.2. MARKOV CHAINS....228

15.3. THE STUDENT T-TEST....231

15.4. MONTE-CARLO SIMULATION....235

SECTION III: Artificial Intelligence....242

CHAPTER 16: Brain Inspired Computing....244

16.1. THE HODGKIN-HUXLEY MODEL....245

16.2. THE BINARY OSCILLATOR HALF-ADDER....248

16.3. THE BINARY OSCILLATOR SET RESET FLIP-FLOP....252

16.4. REAL-WORLD APPLICATIONS AND FUTURE WORK....255

CHAPTER 17: Neural Networks and Neurodynamics....262

17.1. HISTORY AND THEORY OF NEURAL NETWORKS....262

17.2. THE BACKPROPAGATION ALGORITHM....266

17.3. MACHINE LEARNING ON BOSTON HOUSING DATA....268

17.4. NEURODYNAMICS....271

CHAPTER 18: TensorFlow and Keras....276

18.1. ARTIFICIAL INTELLIGENCE....277

18.2. LINEAR REGRESSION IN TENSORFLOW....278

18.3. XOR LOGIC GATE IN TENSORFLOW....280

18.4. BOSTON HOUSING DATA IN TENSORFLOW AND KERAS....282

CHAPTER 19: Recurrent Neural Networks....288

19.1. THE DISCRETE HOPFIELD RNN....288

19.2. THE CONTINUOUS HOPFIELD RNN....291

19.3. LSTM RNN TO PREDICT CHAOTIC TIME SERIES....294

19.4. LSTM RNN TO PREDICT FINANCIAL TIME SERIES....299

CHAPTER 20: Convolutional Neural Networks, TensorBoard and Further Reading....306

20.1. CONVOLVING AND POOLING....306

20.2. CNN ON THE MNIST DATASET....309

20.3. TENSORBOARD....311

20.4. FURTHER READING....313

CHAPTER 21: Answers and Hints to Exercises....320

21.1. SECTION 1 SOLUTIONS....320

21.2. SECTION 2 SOLUTIONS....324

21.3. SECTION 3 SOLUTIONS....327

Index....330

Python for Scientific Computing and Artificial Intelligence is split into 3 parts: in Section 1, the reader is introduced to the Python programming language and shown how Python can aid in the understanding of advanced High School Mathematics. In Section 2, the reader is shown how Python can be used to solve real-world problems from a broad range of scientific disciplines. Finally, in Section 3, the reader is introduced to neural networks and shown how TensorFlow (written in Python) can be used to solve a large array of problems in Artificial Intelligence (AI).

This book was developed from a series of national and international workshops that the author has been delivering for over twenty years. The book is beginner friendly and has a strong practical emphasis on programming and computational modelling.

Features:

• No prior experience of programming is required
• Online GitHub repository available with codes for readers to practice
• Covers applications and examples from biology, chemistry, computer science, data science, electrical and mechanical engineering, economics, mathematics, physics, statistics and binary oscillator computing
• Full solutions to exercises are available as Jupyter notebooks on the Web