1. Computational Physics F33SC2
Numerical methods in physics

2. Outline Module content Module organization Why C?
Compiling, linking and executing
The Salford compiler
The components of a C program

3. Module Aims and Objectives
teach the programming language C
use it to investigate a range of numerical methods that are widely used to solve physics problems.
Objectives: at the end of the module a student should be able to:
formulate a physical problem in a manner suitable for computational solution
choose appropriate numerical algorithms for the solution of a problem
construct a working, structured program in C that includes standard numerical procedures to solve a physical problem
assess the accuracy and reliability of their solutions to problems

4. Module Syllabus C-Programming: Introduction to Numerical Methods:
Introduction to the C language.
Conversion from MATLAB to C.
Use of the C compiler.
Introduction to Numerical Methods:
Data analysis and curve fitting.
Numerical integration.
Ordinary differential equations.
Stochastic Techniques:
Random numbers, non-uniform distributions, testing distributions.
Monte-Carlo integration, precision of results.
Random walks and Markov chains.
Boundary Value Problems and Linear Algebra:
Shooting and matching methods.
Eigenvalues and eigenfunctions.
Applications to quantum mechanics

5. Module Organization One lecture per week Two lab sessions per week
See module web page:
One lecture per week
Wednesdays 9.00 in C5
Introduces new concepts
Two lab sessions per week
Thursdays – and – 16.00
Hands-on session with computers
You put the ideas into practice by working through example sheets and writing programs
Ask for clarification and help from demonstrators

6. Assessment 20% Class test 30% Assignment 1: 50% Assignment 2:
10.00 – on 8 March in B11
Write some simple programs
30% Assignment 1:
Given out 22 March, (the last Wed before Easter break)
Write some longer piece of code to solve a simple problem
Deadline 25 April (first Wed after Easter break)
50% Assignment 2:
Given out 2 May
Write more code to solve a more extended problem
Deadline 17 May

7. Timetable 31/1/07 Introduction to C Programming
07/2/07 Further C Programming
14/2/07 Data analysis and curve fitting
21/2/07 Numerical integration
28/2/07 Ordinary Differential Equations
08/3/07 Class Test 10am B11
14/3/07 Stochastic Methods 1
21/3/07 Stochastic Methods 2
25/4/07 Boundary Value Problems; Linear Algebra
02/5/07 Linear Algebra 2; boundary value problems
10/5/07 Workshop for 2nd assignment

9. Why C? The C language is: small powerful portable
fewer keywords than Pascal
powerful
control structures and data types allow the user to program almost anything
portable
C compilers are available for most computers
once compiled you can share exe files, and your friend then doesn’t even need a C compiler to run them
terse but with a powerful set of operators
Modular
allowing the user to build up libraries of functions
generally efficient
popular

10. C was written specifically to write the Unix operating system
MS-Dos is also written in C
Matlab is written in C
Both C++ and Java are based on C. Everything you learn here can be applied later to programming in these languages

11. Why not C? C will let you do almost anything C is very low-level
C can be complicated

13. Progaming in C C is a compiled programming language
You need 5 steps to get going
Plan your program
Type in your code
Compile it to create an ‘object module’
Link it with other library modules
Run it

14. Developing a program Programmer’s plan Keyboard Source Code Compile
User functions
Object Code
Library Code
Link
Executable Program

15. Enter the code
Create source code containing a list of C commands written in proper syntax
Use any text editor to enter the code and save the c code with the extension ‘.c’
Use a program development environment such as the Salford Plato environment

16. Salford C Compiler

17. Compiling Compile the c code
The compiler reads the C commands and translates them into machine code that gives individual instructions for the computer microprocessors
Save the resulting object code to disc
Object files make it possible to compile a program module by module, hence saving time.

18. Linking/Building Executing
The linker takes the obj file and links it together with
other object files you tell it to link to
and with library function object code, such as the sine function
The result is an executable file (.exe or .com)
This step is called Building on the Salford C compiler
Executing
Running the executable file will make the computer do whatever you asked it to do

19. Developing a program Programmer’s plan Keyboard Source Code Compile
User functions
Object Code
Library Code
Link
Executable Program

20. Developing a program Programmer’s plan Keyboard Source Code DEBUG
Editor
User functions
Object Code
Library Code
DEBUG
Link
Executable Program
Verify and Check, DEBUG

21. Salford C compiler
Access this through the NAL as Plato3 under the ‘Compilers & Development tools’ menu
Copies of the compiler can also be obtained from Dr Hawker

22. Compiling linking and executing in Salford
To compile
Build > Compile (control + F7)
To link
Build > Build (control + shift + b)
To execute
Build > Start Run (control + F5)

23. Points to note
Keep source code, as this will allow you to modify programs
Give your programs sensible names so you know what they do
Put comments in the code to explain what they do and how they do it
C++ compilers will also compile C code

24. Components of a C program
1: /* Program to calculate the product of two numbers */
2: # include <stdio.h>
3: int a,b,c;
4: int main() /**************************************/
5: { /* Get the first number */
6: printf ("Enter a number between 1 and 100: ");
7: scanf ("%d", &a);
8: /* Get a second number */
9: printf ("Enter a number between 1 and 100: ");
10: scanf ("%d", &b);
11: /*Calculate the product */
12: c = a*b;
13: printf("%d times %d = %d \n", a, b, c);
14: return 0;
15: }

25. Line numbers Text of the program Not part of the code
They are just to help identify lines now
Text of the program
It is case sensitive – like Matlab
The variable A is different to a.

26. main (lines 4-15) main(){} is the only obligtory statement
Generally the main body of the code lies within the braces {}
Generally statements enclosed by braces are called a ‘block’
Blocks can actually be used anywhere a statement is used

27. include (line 2)
Instructs the C compiler to add lines from the included file during compilation
Several header files are provided with the compiler
They have extension *.h
You never need to modify them

28. Variable definitions (line 3)
A variable is a name assigned to a data storage location
A variable must be defined before it is used (different to Matlab)
Various types of data are stored (int, float)
This informs compiler of variable’s name and data type
In this case 3 variables are defined: the integers a, b and c

29. Program statements The actual instructions to do the calculations
Generally written one per line
ALWAYS END WITH A SEMICOLON

30. printf() A library function Displays information on screen
Lines of text (lines 7 & 10)
Values of variables (line 14)

31. scanf() Another library function
Reads data from keyboard and assigns it to a program variable

32. Assignment statements
Similar to Matlab
The statement
a = b*c;
calculates the value of b times c and stores the result in the location of variable a

33. return()
At line 14 it simply returns the value 0 to the operating system as the program ends.
This is good style, but the line can be left out.
Has more important use in functions

34. Comments (lines 1, 5 etc)
Any part of the program that starts with /* and ends with */ is called a comment
A comment is just information for a human being, the compiler will ignore it
In Salford C you can also start a comment with // provided there is nothing else after it on the line
If you use this your program will no longer be portable

35. Style C Programs can be made to be very short indeed
This can make for rapid programming, but can also make it hard to read the program again later
A reasonable number of useful comments will help
A good layout will also help
Indentation of code is essential to make a C program easy to follow

36. In the lab session Download the program from the website
Compile, link (build) and run it
Deliberately put in some errors to the text and repeat compiling etc
Change it so that it accept and multiplies three numbers
Change it so that it accepts and multiplies one of the numbers as a float
Follow the worksheet to write other programs

37. for loops Can set up loops to repeat sections of code
for (count = 1 ; count <=3 ; count=count+1) {
printf("%d \n", count); }

38. /* program to read 10 numbers from a file data.dat */
/* and calculate the product */
include <stdio.h>
int a,b,c,n;
int main() /**************************************/ {
FILE *fin ;
fin = fopen("data.dat", "r") ;
for ( n=1 ; n<=10 ; n=n+1)
fscanf(fin,"%d %d",&a,&b) ;
c = a*b;
printf("%d * %d = %d \n", a,b,c); }
fclose(fin) ;
return 0;