This page gives an approximate schedule of topics covered in lecture and related homework problems. Relevant sections in reference material in red.

M Aug 19 Class Business Pelesko 1.2; 
         The Pendulum (large oscillations)
W  21    The pendulum (cont.).
         Exercise 1
F  23    Math, demons, and dimensions.  
         Barenblatt, Dimensional Analysis Ch. 1-2;
         Lin and Segel Ch. 6 
M  26    Short Class: Correction of Dimensional Argument from 
         last class (for which I sincerely apologize).
         Comment:  Be careful when comparing the notation from 
         Pelesko's notes to the one I am using (which is from a 
         book of Barenblatt).  We use Pi to mean different things.
         Exercise (for class discussion):  How does the fundamental 
         frequency of a drum scale with the diameter of the drum?
         i.e., if frequence mu = k d^p, what is p?
         Here is a handout on nondimensionalizing a system 
         which hopefully gets the notation correct.
         Exercise: Some cookbooks say that a roast should be cooked 
         x minutes per pound; others say x_1 minutes per pound for 
         small roasts and x_2 minutes per pound for large roasts. 
         Discuss.
W  28    Approximation. Pelesko 1.3,2.1
F  30    Approximation (cont.)
M Sept 2 Holiday
W   4    Perturbation. Lin and Segel 2.2,7.1
         Exercise: Find the first two terms in a regular perturbation 
         expansion of the solution of u' + 2xu - eps u^2 for eps small.
F   6    Regular Perturbation (cont.)
         Homework 1 due (Pelesko's Assignment 1)
M   9    Regular Perturbation for the Pendulum
         Exercise: Find approximations for each of the roots of 
         eps^2 x^3 + x^2 + 2x + eps = 0 by rescaling to obtain an 
         appropriate regular perturbation problem.
W  11    Singular Perturbation and Asymptotics
         Exercise: Approximate u=u(x,eps) near eps = 0 if 
         x^2 + eps x - eps u + eps sin(u) = 0.
F  13    Singular Perturbation and Asymptotics (cont.)
M  16    Scaling Problems (first assignment)    
W  18    (cont.)
F  20    Guest Lecture: Peter Mucha, Numerical cost.
M  23    The Heat Equation Pelesko Ch. 8; Lin and Segel 4.1
W  25    Large Roots of x = tanx
F  27    Classification of Linear PDE
         Steady State Heat Equation; The Maximum Principle
M  30    The Maximum Principle and Uniqueness for Parabolic Eqns.
W   2    Limits and Asymptotics; homework
F   4    Variational Principle for Laplace's Equation
M   7    Project Prepresentation 
         Homework Assignment 2 due
W   9    Christal Gordon: Modeling neurons
F  11    Variational Principle for Laplace's Equation (cont.)
M  14    break
W  16    Guest Lecture: Peter Mucha 
F  18    Derivation of the Heat Equation
M  21    Heat Equation (cont.)
W  23    Homework Problems from Assignment 3 (heat equation)
         Problem: If a partially filled cylindrical tank with length 3 
         meters and radius 1.5 meters rotates in outer space at angular 
         velocity omega_1, at what velocity omega_2 should a (smaller) 
         system (with length dimensions alpha times the large ones) be 
         rotated so that the behavior in the large tank can be predicted.  
         We assume here that all other parameters, materials, etc. are 
         the same or appropriately scaled.
F  25    The Wave Equation
M  28    Wave Equation (cont.)
W  30    Equilibrium Capillary Surfaces
F Nov 1  Equilibrium Capillary Surfaces (cont.)
         Homework Assignment 3 due
M   4    Some Geometry
W   6    Some more Geometry
F   8    Calculation of Curvature Matrix for a Surface
M  11    Curvature Matrix (cont.)
W  13    Geometric interpretation of capillary equation
F  15    Rigidly Rotating Liquids; 6.2 Scale Models
M  18    Fluid Dynamics, the equation of continuity
W  20    Euler's identity and the equations of motion part 1
F  22    The equations of motion part 2
M  25    Group presentation of Henry Won and Messam Naqvi,
         Propellor Thrust: dependence on shape
W  27    Group presentation: steady flow around a sphere
         (Alan Michaels, Katharina Baamann, Cornelius Ejimofor, Alec Muller)
F  29    holiday
M Dec 2  Assignment 4 Problem 2.
W   4    Presentation: Nick Borer, Airfoil Pressure and Drag
         Chaotic Group Presentation. 
         Manas Bajaj, Tao Tran,...
F   6    Group Presentation: Battery, Motor, and Propellor Modeling
         (Mark Birney, Caleb Branscome, Travis Danner, Tom Ender, 
          Andrew Frits, Holger Pfaender, Colin Pouchet, Jenni Ritchie, 
          Eric Upton, Marie White)
         Presentation: Ed Greco, The saddle trap
M   9    Homework Assignment 4 due
W  11    Project Presentations, 2:50-5:40
Th 12    Project Presentations, 2:50-5:40
         Christal Gordon, Modeling Neurons