welcome to physics 331user.physics.unc.edu/~drut/public_html_unc/assets/lecture01.pdf · welcome to...

Welcome to Physics 331:Introduction to Numerical Techniques in Physics

Instructor: Joaquín Drut

Lecture 1

Logistics…

Phys 331

Introduction to Numerical Techniques in Physics

Spring 2016

Course information

Instructor: Joaquín E. Drut.

Email: drut at email.unc.edu.

Office: Phillips 296

Where and When:

Class: Phillips 265 - Mo-We-Fr, 12:20pm-1:10pm

Mo-We : Lectures

Fr : Review / Q&A session / Exams (see below)

Lab 1: Phillips 265 - Mo, 5:45pm-7:45pm

TAs: Ryan Tanner (rjtanner .at. physics.unc.edu)

Philip Wulfken (wulfken .at. email.unc.edu)

Lab 2: Phillips 265 - We, 4:40pm-6:40pm

TAs: Ryan Tanner (rjtanner .at. physics.unc.edu) Andrew Loheac (loheac .at. live.unc.edu)

Office hours: By appointment only.

To obtain an appointment, email me directly. Your subject heading must begin with Phys331.

Website: http://user.physics.unc.edu/~drut/public_html_UNC/physics-331.html

Bibliography: - A. Gilat & V. Subramaniam, Numerical Methods for Engineers and Scientists. - Press, Teukolsky, Vetterling, Flannery, Numerical recipes in C (2nd Edition, 1992). - M.L. Boas, Mathematical Methods in the Physical Sciences.

Software: MATLAB

Midterm 1: Friday, February 12th (in class).

Midterm 2: Friday, March 11th (in class).

Final Exam: Saturday, April 30th, 12pm, Phillips 265

How to get MATLAB

https://software.sites.unc.edu/software/matlab/

Follow this link:

Or use our instructions here:http://user.physics.unc.edu/~drut/public_html_UNC/assets/matlabinstructions.pdf

https://software.sites.unc.edu/software/matlab/

http://user.physics.unc.edu/~drut/public_html_UNC/assets/matlabinstructions.pdf

Important dates

Also in the syllabus:IntroductionSpecific objectives

Grading

Numerical techniquesProgramming techniques

Homework

Attendance policy

- There will be a lab this week.- The homework assignment is posted on our website.- The due date will always be on the first page of the assignment.- The homework will always be turned in via Sakai. - Turn in a PDF file for written part (scan or picture OK) - More instructions for programming assignment next time

Why numerical techniques?

Why are you here?

Many (in fact most) problems do not have a closed-form analytic solution

For example...


For example...

In classical mechanics

Anharmonic motion of a pendulum at large amplitudes

The three-body problem

The n-body problem for any n > 2

-1.5 -1.0 -0.5 0.5 1.0 1.5x

-1.0

-0.5

0.5

1.0

p


For example...





-5 -4 -3 -2 -1 1 2x

-1.0-0.5

0.51.0p


For example...






For example...

In electromagnetism

this looks “simple”, but...

What if... ... the geometry is complicated (it usually is!) ... the response functions depend on the field (they usually do!)


For example...

In quantum mechanics

Schroedinger equation (single particle) in most potentials


http://phys.org/news/2009-04-quantum-few-body-physics.html

http://phys.org/news/2009-04-quantum-few-body-physics.html


For example...

In quantum field theory

Pretty much any interacting theory in 2D and 3D

http://www.lattice-qcd.org/


Some solutions require repetitive tasks

For example...

Systems of linear equations

Root-finding

Integration

12.4x+ 37y + 238.45z = 20

1.6x+ 123y + 19.1z = 1

3.4x+ e

6.2y + 7.65z = ⇡

Image source: wikimedia commons


Some solutions require repetitive tasks

Sometimes the question we have can be answered without a full analytic solution

For example...

Collective phenomena

Thermo- and hydrodynamics

Lorentz-contracted ionsbefore collision

Quark-gluon plasma (QGP)

Physical results Predictions

Calculations

Physical results Predictions

Theories

Fully numerical(Semi-) Analytic

What you will get from this course (hopefully)

Physics problem

Mathematical representation

Numerical solution on a computer

Hopefully we agree on what problem we are interested in solving!

What are the equations that define the problem?What are the variables? What constitutes a solution?What is the mathematical language?

What algorithm are we going to use?What programming language?What kind of computer?

Mathematics reviewChapter 2 in Gilat and Subramaniam.If any of this sounds daunting or too foreign, you may want to: a) consider taking this course another time; b) read chapter 2 now as fast as you can.

CalculusFunctions

Domain, Range

Limit

Continuity

Differentiation

Intermediate value theorem

Chain rule, mean-value theorem

Integration

Fundamental theorem of calculus

Riemann sum, mean-value theorem

Taylor series

Linear algebraVectors

Definition in 3d and arbitrary dimension

Addition and subtraction

Multiplication by scalar

Transposition

Scalar product and orthogonality

Linear dependence and independence

Triangle inequality

Linear algebraMatrices

Definition and relationship with vectors

Addition and subtraction

Multiplication by scalar

Transposition

Matrix-matrix multiplication

Special matrices: square, diagonal, triangular, identity, symmetric

Inverse of a matrix

General properties of operations: associativity, commutativity (or lack thereof), etc.

Determinants and norms

Differential equationsLinear vs. non-linear

Homogeneous vs. inhomogeneous

Order

Analytic solutions

Multivariable calculusFunctions of more than one variable

Partial derivatives

Chain rule

Taylor series expansion

Next time:

Reading:

Introduction - Chapter 1

Sources of error

First steps in MATLAB

Number representation

welcome to physics 331user.physics.unc.edu/~drut/public_html_unc/assets/lecture01.pdf · welcome to...

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