Preface

 

PART I. BASICS

Introduction

Software Basics

Errors & Uncertainties

Monte Carlo Simulations

Differentiation & Integration

Trial-and-Error Searching & Data Fitting

Matrix Computing and N-D Searching

Differential Equations & Nonlinear Oscillations

 

PART II. DATA SCIENCE

Fourier Analyses

Wavelet & Principal Components Analysis

Neural Networks & Machine Learning

Quantum Computing

 

PART III. APPLICATIONS

ODE Applications; Eigenvalues, Scattering, Trajectories

Fractals & Statistical Growth Models

Nonlinear Population Dynamics

Nonlinear Dynamics of Continuous Systems

Thermodynamics Simulations & Fenyman Path Integrals

Molecular Dynamics Simulations

General Relativity

Integral Equations

 

PART IV. PDE APPLICATIONS

PDE Review, Electrostatics & Relaxation

Heat Flow & Leapfrogging

String & Membrane Waves

Quantum Wave Packets & EM Waves

Shock & Soliton Waves

Fluid Hydrodynamics

Finite Element Electrostatics

 

Appendices

Index