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