MATHEMATICAL METHODS FOR CHEMISTS
NUMERICAL METHODS: FORTRAN & MATHEMATICA

Harold W. Schranz
Research School of Chemistry
ANU, Canberra, ACT 0200
Australia
E-mail: Harold.Schranz@anu.edu.au
WWW: http://rsc.anu.edu.au/HWS/hws.html

June 27, 1997

• Contents
• Introduction to Course Structure
  • A Quick Tour of Fortran
  • A Quick Tour of Fortran Program Libraries
  • A Quick Tour of Mathematica
  • A (Bonus) Quick Tour of the Internet & the WWW
• Introduction to Fortran
  • Introduction
    • Solving Problems Using Computers and High Level Programming Languages
    • Operating Systems and Computer Platforms
  • Use of the FTN90 Fortran Compiler in the Computer Labs
    • Some useful DOS commands
    • Some useful NAG Fortran 90 Compiler commands
  • First Steps
    • From problem to program
    • Basic Fortran statements
  • Structure of a Fortran Program
    • Errors in Programs
    • Design and Testing
    • F90 free form
    • F77 fixed form
    • Programming Exercises
  • The Fortran Programming Language
    • The Fortran Character Set
    • Constants and Variables
    • Names
    • Variable Type Declarations
    • Derived Data Types
    • Kind Type Parameters
    • Arithmetic Expressions
    • Expression Type
    • Assignment Statement
    • Overflow, Underflow and Divide Check Error
    • Exercises
  • Input And Output
    • READ Statement
    • WRITE Statement
    • A Sample Program using I/O Statements
    • Exercises
  • Basic Building Blocks: Program Units
    • Intrinsic Functions and Subroutines
    • External Functions
    • Subroutines
    • Modules
    • Modules and derived data types
    • Modules and explicit procedure interfaces
    • Exercises
  • Control Structures
    • IF Statements
      • Relational and Logical Expressions
    • Logical Variables
      • Logical IF Statement
      • Block IF Statements
      • The CASE construct
    • DO Loop Statement
      • Syntax
    • Exercises
  • Arrays
    • Array Declarations
    • Two and Higher-Dimensional Arrays
    • Arrays with Lower Bounds
    • Array constants and initial values
    • Arrays as Subprogram Parameters
    • Implied Do Loops
    • Using arrays in expressions
• Fortran Library Routines & Applications
  • Introduction
  • Library Routines and Driver Programs
    • Solution of Linear Algebraic Equations
    • Eigenvalues/Matrix Diagonalization
    • Numerical Integration
    • ODE Solvers
    • Random Number Generators
    • Use of Random Number Generators in Monte Carlo Integration
  • Some Details about Arguments to the Fortran Library Routines
    • Solution of Linear Algebraic Equations
    • Eigenvalues/Matrix Diagonalization
    • Numerical Integration
    • ODE Solvers
    • Random Number Generators
    • Exercises
• An Integrated Environment - Mathematica.
  • Introduction
  • Use of the Mathematica Package in the Computer Labs
  • Simple Tour
    • Numerical Calculations
    • Graphics
    • Algebra and Calculus
    • Solving Equations
    • Lists
    • Matrices
    • Transformation Rules and Definition
    • Advanced Topic: Symbolic Computation
    • Programming
    • Mathematica Packages
    • Interfacing with Mathematica
    • Front Ends and Notebooks
  • Applications
    • Eigenvalues and Eigenvectors of a Linear Chain in 1D
    • Solving Differential Equations
    • Laplace Transforms
  • Exercises
  • Further Applications
    • 1D diffusion of particles
  • Mathematic on the Computer Lab PC's
• The Internet & the World Wide Web
  • Introduction
  • What is the Internet?
    • The Internet
    • The Internet and The Matrix
  • How Big is the Internet?
    • Size Estimates
    • Growth of the Internet?
  • Tools for Exploiting the Internet
    • E-mail
    • UseNet (Newsgroups)
    • Telnet
    • FTP & Archie
    • Gopher & Veronica
    • WAIS
    • The World Wide Web
  • Appendix
    • Notes
    • Further Information
    • Postscript
  • Fortran Information on the WWW
  • Symbolic Algebra Information on the WWW
• About this document ...