Physics 315
Computational Physics
Brad Hinaus
B207 Science
bhinaus@uwsp.edu
346-4872
Lecture: TT 2-3 A106 Science
Lab: W 10-1 pm B112/A104 Science
Office Hours MW :1-2pm
F
9-11am
Walk UP if Door Open
Text Book from Text Rental: Computational Physics by Nicholas Giordano
What is Computational Physics?
Computational Physics is a branch of physics which uses computers to solve physics
problems. Physicists use the computer to simulate complex physics situations. These
simulations can be used to model experimental data to determine the physics that explains
the data or to determine what happens under other experimental conditions. The
computer can also be used in a pure numerical sense to compute an integral or a
derivative. In any case the focus of computational physics is to gain in insight into the
physics involved in a scenario through the use of a computer not on writing elegant
compact code.
Programming Software
In this course we are going to learn how to write computer simulations in Fortran 77.
There are numerous reasons why we are using FORTRAN. 1.) The syntax (how
commands are typed) is relatively straightforward. 2.) The compiler we are going to use
is free and you can put it on your home computer. 3.) According to those knowledgeable
in the field, once you understand FORTRAN, it’s not too hard to learn C then C++. We
will also use Microsoft Excel quite often. We will use it spreadsheet functions for quick
calculations and use its graphing routines for visualization. During class you will receive
a copy of the FORTRAN compiler on a CD so you may install it on your own computer.
We will also use GNUPLOT for plotting. It is relatively easy to use for 2D and 3D
plotting
Learning Outcomes
When you finish this course you should be able to do the following. See Appendix for
more detail
 Demonstrate an understanding of physics principles and concepts both through
written and oral communication.
 Solve physics problems that use differential equations, integration, or stochastic
methods by using a computer.
 Program using a high level programming language.
 Model the physics in various complex systems using a computer.
Grading
You will be graded on the following: homework, papers (lab report and project reports)
group projects, presentations, exams and an individual final project
The final course grades will be weighted as follows
Final Individual Project
Exams
Papers and Presentations
Homework/In Class Work
20%
40%
20%
20%
Exams, Homework, and In Class Work will receive numerical scores. Paper,
presentations, and the final project will be given numerical scores out of 100 in 5 point
increments.
The following table shows the ranges of percentage points for final grades.
Letter Range
A
AB+
B
BC+
C
CD
F
Percentage
93-100
90-92.9
87-89.9
83-86.9
80-82.9
77-79.9
73-76.9
70-72.9
60-69.9
0-59.9
Contents of the Course
Section 1
 Physics: One/Two/Three Dimensional Motion and Newton’s Laws. Writing
Newton’s Second Law as a differential equation.
 Programming: Excel
 Numerical.: Solving Differential Equations w/ Euler Method
 Communication: Writing Papers, Writing Introduction and Method and
Measurements, Giving a Presentation
Section 2
 Programming: Basics of Fortran, Simple Programs
 Numerical: Root Findings, Summations, Max/Mins.
 Communication: Rewriting a Previous Report
Section 3
 Physics: Pendulum, Faraday’s Law, Random Systems, Monte Carlo Simulations,
1-D Icing Models
 Programming: Intrinsic Functions, User Defined Functions and Subroutines
 Numerical: Methods for ODE, Integration, Random Numbers, Numerical Recipes
 Writing: Writing to an Audience, Analysis and Discussion
Section 4
 Physics: Quantum Mechanics, Solving Schrödinger’s Equation, Individual
Capstone Projects
 Numerical: Boundary Value Problems and User Choice (Something interesting,
something new, both in physics and computation)
My Teaching Philosophy
I think the college classroom should reflect basketball practice. Mentally picture what
basketball practice looks like. What do you see? Its active, people are moving around
and doing things. Players don’t spend 100% of their time watching their coach draw
diagrams on the chalkboard then go on the floor and walk through the plays. The ball
players spend a good portion of their time working on the skills themselves. That is what
I want us to do, work on our skill during class with each other. Will we eliminate the
lecture? No, but I hope to reduce the amount of time in that mode so we can practice and
ask questions. (If basketball doesn’t work for you, substitute learning a musical
instrument)
Additional References:



Computational Physics: Problem Solving with Computers by Rubin H. Landua
and Manuel J. Paez. Internet Site: http://www.physics.orst.edu/~rubin/CPbook/
An Introduction to Computer Simulation Methods: Applications to Physical
Systems by Harvey Gould and Jan Tobochnik
Numerical Recipes in Fortran 77: The Art of Scientific Computing can be found
on the internet at: http://lib-www.lanl.gov/numerical/bookfpdf.html
Appendix A
Spring 2012
Learning Outcomes
1. Numerically Solve Different Types of Physics Problems Using Multiple
Techniques
a. Ordinary Differential Equations
i. Types of Differential Equations
1. 1st Order Differential Equation
2. 2nd Order Differential Equations
3. Differential Equations which need to be written in
Component Form
4. Coupled Differential Equations
ii. Techniques for Solutions of Ordinary Differential Equations
1. Euler Methods
2. Euler Cauchy Method
3. Euler Richardson Method
4. Verlet Method
5. 2nd Order Runge-Kutta
6. 4th Order Runge-Kutta
iii. Types of Problems using Differential Equation
1. Initial Value
2. Boundary Value
iv. Final Project
b. Integrals
i. Techniques for Solving
1. Endpoint Rule
2. Trapezoid Rule
3. Simpson’s Rule
4. Monte Carlo
ii. Dealing with Singularities (Divergences)
c. Stochastic (Random) Processes
i. Uniform Random Number Generators
ii. Small Sample vs. Large Sample
iii. Generating Non Uniform Distributions
1. Transformation Method
2. Rejection Method
iv. Monte Carlo Simulations
2. Understand the Fundamentals of a Programming Languages
a. Useful Features on Microsoft Excel
i. Absolute Reference vs. Relative Reference
ii. Variable Naming
iii. Graphing
b. Fortran
i. Understand the Structure of a Program by
1. Developing Flow Charts or Algorithms
ii. Correctly use the Syntax of the Programming Language (Fortran)
1. Columns
2. Continuation
3. Comment Lines
4. Type Declaration
5. Arithmetic
6. Integer Division
7. Real Division
8. Do Loop
9. If Statements
10. Implicit Function calls
11. Explicit Function calls
12. Subroutines
13. Type change (i.e. changing an integer number to a real
value)
14. Arrays
iii. Synthesize the Algorithm and Syntax To write a Program
iv. Ensure that programs are running correctly
1. working from known answers
2. working in limits
3. conceptual justifications (not always fool proof)
4. use of different methods/routines
v. Debug any incorrectly running program
3. Effective Communication
a. Write Clearly and Concisely to Communicate the Physics, Methods and
Results of a Project
i. An effective paper will
1. Be written to the appropriate audience
2. Briefly Summarize the entire paper
3. Describe the basics physics of the problem
4. Explain the appropriate numerical technique being used
5. Interpret and analyze the data
6. Present the results in an understandable format i.e.
descriptions, tables or graphs
7. Justify the results are correct by using a conceptual
explanation, limiting cases analysis, analytic solution,
solution by multiple numerical techniques, etc.
8. Estimate limits of the solution
9. Convey an understanding of the broader application of the
solution
ii. Papers will include the following Sections
1. Title
2. Introduction/Abstract
3. Methods and Measurement Section
4. Results Analysis and Discussion
5. Conclusion
iii. Critique the Writing of Peers
1. Offer Constructive Feedback on Points of Excellence and
Points of Improvement
b. Oral Presentations
i. An effective talk will have the same elements as an effective paper
ii. Presenters will be
1. Comfortable
2. Confident
3. Professional
Appendix B Schedule until It Changes
Wk Week
Topics
Tues Lecture
Wed Lab
Thurs Lecture

1
2
1/23
1/30
Euler’s Method
with 1-D ODE’s
Euler’s Method
with 2-D ODE’s
Write a Paper
Peer Review
Intro
3
4
5
6
2/6
2/13
2/20
2/27
3-D ODE with
constrained
motion
No Lecture
Practice Problems
Approx. to deriv
Solve a few probs
with Euler method
Time Steps
Analytic Solutions
•Intro to Newton’s
Laws in 2-D
•Writing Newton’s
Laws in Differential
form
•Writing NL in
component form.
•Practice Problems
Project
Project
Fortran/Exam
•Columns
•Type Declaration
•Math
•Assignment
•Statement
•Basic Structure
Fortran
Structures
•Loops and
• If Statements
Paper Pencil Problems

Intro/ Physics 101
Problems



Drag Problem/NonLinear Spring
Translate from Phys
101 to Differential
Form
Fundamental Theorem
of Calc.
Euler’s Method
Initial Values
Coupled Differential
Equations
How to Write a Paper
Components
What’s in each Comp.
Example from AJP
Hand in Drag Paper
Project Handout
•Magnus Force •Baseball
•Coriolis Force
•Electron Microscope
•Magnus Force Golf with a
side breeze
Project
Good Talk Bad Talk
Presentations and
Papers from Project
Reflective Essays
Exam
Basic Problems
Interactive
•Loops and Play
Computer
Practice Loops
Play computer
Redneck Jumping
Write Intro and
Methods Section
•Simple numerical
problems i.e. Root
finding, max and mins
•Work on Pendulum
Analysis
7
3/5
Practice Fortran
•Intrinsic Functions
•Counting number of
occurrences
8
3/12
Alternative
Solutions to
ODE/Integration
Array’s
9
10
11
3/26
4/2
4/9
Integration
Function Calls
Random
Subroutines
Examples of Monte
Carlo
Flux Computation and
Paper
Nuclear Decay
Diffusion or 1-D Ising
or Fractal
12
4/16
Boundary Value
Problems
Analytic Solutions
Quantum Wells
Exam
13
14
15
4/23
4/30
5/7
Final Projects
Final Projects
Final Projects
Final Projects
Final Projects
Final Projects
Final Projects
Final Projects
Final Projects
Random
Swinging Pendulum
Analysis - Presentations
Make Up Time
Exam
No Name
Net Force
Spring 2012 Comp
In front of the University Center there was a crane that lifted material into the air when it
was being remodeled. Let’s say the crane is lifting a box and the box is not on the ground.
a.) Draw the two main vertical forces acting on the box. Label each force with what
exerts the force and what feels the force.
Box
b.) The box is moving upward but begins to slow down as it approaches one of the floors
where it is needed. As this happens, which of the two forces on the box is bigger, or are
they the same. Explain your reasoning.
Thinking In Extremes or in Baby Steps
Jars
Monte Hall Problem