Preface
Chapter One
Introduction to Computing
Computer Hardware
Supercomputers & Computation Complexity
Computer Software
Brief Overview of Python
Anaconda Python, Notebooks, and Prutor
Applications of Computers
Chapter Two
Integers
Floating Point and Complex Numbers
Python Variables and Logical Variables
Chapter Three
Character & Strings
List
Numpy Arrays
Dictionary
Mutable and Immutable Objects in Python
Chapter Four
Simple Statements
Conditional Flows in Python
Looping in Python
Chapter Five
Functions in Python
Python Namespace and Scope
Recursive Functions
Chapter Six
Good Progamming Practices
Prime Numbers
Searching and Sorting
Chapter Seven
Matplotlib & Field Plots
Miscellaneous Plots
Animation using Python
Chapter Eight
Reading & Writing Text Files in Python
Reading & Writing Numerical Data in Python
Chapter Nine
Error Analysis
Nondimensionalization of Equations
Numerical Methods
Chapter Ten
Lagrange Interpolation
Splines
Chapter Eleven
Newton-Cotes Formulas
Gaussian Quadrature
Python's Quad & Multidimensional Integrals
Chapter Twelve
Computing Numerical Derivatives
Chapter Thirteen
General Overview
Euler Forward Method, Accuracy & Stability
Implicit Schemes
Higher-order Methods
Multistep Method
Solving a System of Equations
Stiff Equations
Chapter Fourteen
Fourier Transform
One-dimensional Discrete Fourier Transforms
Mutlidimensional Fourier Transform
Chapter Fifteen
Solving PDEs Using Spectral Method: Diffusion Equation
Solving Wave, Burgers, and KdV Equations
Spectral Solution of Naiver-Stokes Equation
Spectral Solution of Schrรถdinger Equation
Chapter Sixteen
General Overview & Diffusion Equation Solver
Solving Wave Equation
Burgers and Navier-Stokes Equations
Schrodinger equation
Chapter Seventeen
Root Finders
Chapter Eighteen
Shooting Method
Eigenvalue Calculation
Chapter Nineteen
Solving Laplace Equation
Solving Poisson Equation
Chapter Twenty
Solution of Algebraic Equations
Eigenvalues and Eigenvectors
Chapter Twenty-One
Random numbers
Integration Using Random Numbers
Regression Analysis
Applications in Statmech
Machine Learning
Epilogue
Appendix A: Errors in Lagrange Interopolation
Appendix B: Improving Accuracy Using Richardson Method
References