Information

Welcome to the Methods of Applied Math Winter Quarter Website.

3/9/05

Here is the Variational Calculus Final Exam. It is due on Friday, March 11th at 12:00 pm.

3/9/05

Here is the Complex Variables Final Exam. It is due on Thursday, March 10th at 12:30 pm.

3/8/05

Here is the Partial Differential Equations Final Exam. It is due on Wednseday, March 9th at 12:30 pm.

The Julia Set Mathematica Demo Notebook is posted.

Here is a link to some spherical harmonic functions images and a java script for rolling your own.

We talked about Noether's Theorem in class the other day and its importants in particle physics check out Wikipedia's entry on Noether's theorem and Emmy Noether and its discoverer. Over the quarter you've gotten to know the work of a fair number of dead white guys -- Euler, Cauchy, Lagrange, Laplace, Laguerre, Legendre ... Another mathematician who worked with many of these men on the patterns of nodal lines on a vibrating drum was Sophie Germain -- who used a pseudonym M. L'Blanc to hide her identity as a women (She wisely chose to stick with with the L theme). You should have a look at this page on the history of Sophie Germain. Here are some images of the Chladni figures -- the types of figures she studied.

3/5/05

The schedule for next quarter is now available: Spring Quarter Schedule .
I have also posted the evaluation signup form. All student leaving the program must signup for a conference and bring their self-evaluation and a faculty evaluation with them to the conference. Evaluation conferences for those who are continuing in the program are optional, but if you want personal feedback or if you have credit concerns I recommend that you signup.

2/18/05

Here is the Second Vector Calculus Take Home Test. It is due on Tuesday, Feb 22nd at 1:00 pm.

2/17/05

Here is the Second Complex Variables Take Home Test. It is due on Tuesday, Feb 22nd at 9:30 am.

2/9/05

Here is the Second Partial Differential Equations Take Home Test. It is due on Monday, Feb 14th at 9:30 am.

2/2/05

There were some questions about how to get Mathematica to solve for the eigen values in the equation Tan[x]=-x. I've posted a Root Finding Notebook, that shows how this is done. I've also put it in the handouts section of our CAL space.

1/27/05

Here is the Vector Calculus Take Home Test. It is due on Tuesday, Feb 1st at 1:00 pm.

1/27/05

Here is the Complex Variables Take Home Test. It is due on Tuesday, Feb 1st at 9:30 am.

1/25/05

There are two in-class tests this week. One on Complex Variables Thursday morning and on Vector Calculus on Friday. They will be approximately 45 minute tests. You may bring one page of formulas with you. What follows is a guide for the important topics that you should study for

Complex Variables

  • Complex arithmetic. Know the basic operations and how to convert between in Cartesian and polar form. Use these rules, for example,to find real and imaginary parts of powers and roots of complex nummbers.
  • Representations of complex numbers on the Argand diagram. For example understand the geometric signifance of multiplying and adding complex numbers
  • Loci in the complex plane. Sketch simple complex innequalitites such as |z-1|=3. Know important definitions of regions such as open, bounded, simply connected sets.
  • Complex Functions. Understand the concept of a limit, continuity and differentiability. Know the meaning of terms such as analytic and entire. Find the domain and range of complex functions and use the Cauchy-Riemann conditions to determine analyticity.
  • Mappings of Complex Functions. Find images and preimage of curves in the x-y and u-v planes Use Cauchy-Riemann conditions to determine families of orthogoanl curves .
  • Applications: Applications of complex functions to solving the Laplace equation in physics.

    Vector Calculus

  • Change coordinates from Cartesian to Polar and vice versa in both 2-D and 3-D .
  • Sketch simple graphs and regions in Cylindrical Polar and Spherical Polar coordinates.
  • Calculuate double and triple integrals in other coordinate systems.
  • Calculate simple line integrals of vector and scalar fields.

    1/19/05

    LateX assignment help:

  • Export images to .eps format from Mathematica
  • Make sure images are in the same directory as you LaTeX file
  • Make sure you have Ghostscript installed on your computer
  • When compiling to PDF using TeXnicCenter, use the LaTeX => PS => PDF option. Do not try to covert directly to PDF.

    1/19/05

    Please complete the Partial Differential Equations Take Home Test. It is due on Monday, January 24th.

    1/14/05

    For those of you searching for new ideas for projects I have added two new links to on-line journals on the resources page. You may find these helpful.

    1/11/05

    For today's lab
  • Complete the short Mathematica lab on ploting graphs in polar and spherical coordinates.
  • Work through the tutorials 4,5,6 and 8. (At a later date you should also look at 10) from the online LateX Tutorials that we started last week. Note: Some of the instructions are specific to the home institution of the University of Leeds. Ignore those instructions.
  • Write a short one to two page lab report on Question 3 of the Laboratory Project on Families of Surface on page 699 of Stewart. Your report should contain a title, a short abstract, an introduction, body, conclusion and references. Please change the margins of your page so that there is one inch on each side and on the top and the bottom. You should import at least two images with captions and refer to them in the body of the text. You will use images that you generate in Mathematica for this. You should also incorporate a table in your report.
  • The report is due during next Tuesday's lab (1/18/05). Have fun!

    1/4/05

    For this afternoon's LaTeX workshop you will be working from a set of LateX Tutorials designed by Andrew Roberts at the University of Leeds. Please work through tutorials 2, 7 and 9 and try out the examples in your own LaTeX document. After you are finished the tutorials complete the LaTeX assignment, which is due on Friday.

    12/31/04

    Text book update:

    I have decided to supplement the material on Partial Differential Equations in Riley with the textbook:

  • Partial Differential Equations for Scientists and Engineers
  • by Stanley Farlow
  • Dover Publications , New York (1993)
  • ISBN 0486-67620-X

    The college book store should have it by the end of Week 2. You may be able to get it on-line faster. We will mostly follow Riley for the first two weeks.

    12/20/04

    We will be using a mathematical typsetting language called LaTeX this quarter. You will learn how to use LaTeX during two CAL labs. I have uploaded information about how to download a LaTeX implementation for your compter. Please read the LaTeX Information and download the suggested programs if you want to be able to create LaTeX documents at home.

    11/28/04

    There are a number of things you should read to prepare for the first week of winter quarter.

  • Look at the class texts so you can order your books early.
  • Check the week 1 schedule for meeting times, rooms and the first week's readings. In particular we will be seminaring on the first three chapters of "e: The Story of a Number" on the first day of winer quarter, so please complete the reading by the first day of class and bring a typed paragraph about some question or questions that arise in the reading.
  • Read the documents in the handouts folder. There is new information there about the projects you will be doing this quarter.
  • Signup for an Applications of Mathematical Methods Presentation as soon as possible.