Introduction to Computational Physics for Undergraduates

1 The Linux/Unix Operating System

1.1 Introduction

1.2 Files and Directories

1.2.1 Pathnames and Working Directories

1.2.2 Filenames

1.3 Overview of Unix/Linux Commands

1.3.1 Executables and Paths

1.3.2 Special Files

1.4 Basic Commands

1.4.1 Getting Help and Information

1.4.2 Communicating With Other Computers

1.4.3 Creating, Manipulating and Viewing Files and Directories

1.5 More on the C-Shell

1.5.1 Shell Variables

1.5.2 Environment Variables

1.5.3 C-shell Pattern Matching

1.5.4 Using the C-shell History and Event Mechanisms

1.5.5 Standard Input, Standard Output and Standard Error

1.5.6 Redirecting Input and Output

1.5.7 Pipelines

1.5.8 Usage of Quotes

2 Text Editors

2.1 Vi

2.2 Emacs

3 The Fortran 90 Programming Language

3.1 Introduction

3.1.1 Early Development

3.1.2 Standardization

3.1.3 Fortran 90

3.1.4 Strengths and Weaknesses

3.2 Compilers

3.2.1 File Extensions and Compiling Commands

3.3 Program Layout

3.4 Variable Declaration

3.4.1 Naming Conventions

3.4.2 Data Types

3.5 Basic Expressions

3.5.1 Arithmetic Operators and Expressions

3.5.2 Relational Operators

3.5.3 Logical Expressions

3.6 Input and Output

3.6.1 The READ Statement

3.6.2 The WRITE Statement

3.6.3 The FORMAT Specification

3.6.4 File Input and Output (I/O)

3.7 Control Structures

3.7.1 IF-Blocks

3.7.2 DO Loops

3.7.3 Nested Loops

3.8 Modular Programming

3.8.1 Intrinsic Functions

3.8.2 Intrinsic Subroutines

3.8.3 External Functions

3.8.4 External Subroutines

3.8.5 Program Units

3.8.6 Internal Procedures

3.8.7 External Procedures

3.8.8 Modules

3.9 Arrays

3.9.1 Declaration of Arrays

3.9.2 Vectors

3.9.3 Using Arrays

3.9.4 Array Operations

3.9.5 Elemental Functions

3.9.6 The WHERE Statement

3.9.7 FORALL (Fortran 95)

3.9.8 Array Intrinsic Functions

3.9.9 Allocatable Arrays

3.9.10 Pointers

4 Numerical Techniques

4.1 Curve Fitting–Method of Least Squares

4.1.1 The Linear Least-Squares Approximation

4.1.2 The Quadratic Least-Squares Approximation

4.2 Numerical Differentiation

4.3 Numerical Integration

4.3.1 The Trapezoidal rule

4.3.2 Simpson’s Rule

4.4 Matrix Operations

4.5 Finding Roots

4.6 Solving Ordinary Differential Equations

4.6.1 The Euler Method

4.6.2 The Midpoint Method

4.6.3 The Runge-Kutta Method

4.6.4 Boundary Value Problems

5 Problem Solving Methodologies

5.1 General Guidelines

5.2 Projectile Motion Example

6 Worksheet Assignments

6.1 Coding a Mathematical Expression

6.2 Comparing two Functions

6.3 Bessel Functions of the First Kind

6.4 Logical IF Statements

6.5 Lead Concentration in Humans (Data Analytics)

6.6 Nested Do Loops and Double Summations

6.7 Ionic Crystals

6.8 Least Squares Fit

6.9 Numerical Derivatives

6.10 Numerical Integration

6.11 Finding Roots of a non-linear equation

6.12 Ordinary Differential Equations

6.13 Projectile in a Viscous Medium

6.14 Damped Harmonic Oscillator

6.15 RLC Circuit

7 Homework Assignments

7.1 Fresnel Coefficients

7.2 Earth Atmosphere Model

7.3 Magnetic Permeability

7.4 Maxwell-Boltzmann Distribution

7.5 Kinetic Friction

7.6 Compton Scattering

7.7 Radioactive Decay

7.8 Halley’s Comet

7.9 Rocket Equation

7.10 Hydrostatic Equilibrium and Relativistic Stars

7.11 Massive Stars

7.12 Isothermal Gas Spheres

7.13 Proton in Constant Electric and Magnetic Fields

7.14 Square Voltage Pulse applied to a RC Circuit

7.15 Mutual Inductance of Two Coils

A Summary of Fortran Features

B Plotting using Python

C Fortran 90 Sample Program Illustrating Good Programming