Day  Topics  Notes 
13Jan2016 
Section 1.2: Basic concepts and definitions Section 1.3: Mathematical problems Section 1.4: Linear operators 
Please also read section 1.1 
15Jan2016 
Section 1.5: Superposition principle Section 2.2: Classification of firstorder equations Section 2.5: Construction of a firstorder equation 

20Jan2016 
Section 2.4: Geometrical interpretation of a first order equation Section 2.5: Construction of a firstorder equation Section 2.6: Canonical forms of firstorder linear equations 

22Jan2016 
Section 2.6: Canonical forms of firstorder linear equations Section 2.7: Method of separation of variables 

27Jan2016 
Firstorder nonlinear PDEs and shocks 

29Jan2016 
Firstorder nonlinear PDEs and shocks Section 3.1: Classical equations 

3Feb2016 
Section 3.2: Wave equation Section 3.5: Heat (diffusion) equation 

5Feb2016 
Section 3.5: Heat (diffusion) equation (continued) Common boundary conditions Section 4.1: Second order equations in two independent variables Section 4.2: Canonical forms 

10Feb2016 
Section 4.2: Canonical forms Section 4.3: Equations with constant coefficients 

12Feb2016 
Section 4.4: General solutions Section 4.5: Summary and further simplifications Section 5.3: Cauchy problem for the homogeneous wave equation 
D'Alembert solution example 
17Feb2016  No class. Instead go to the Research computing days talks.  
19Feb2016 
Section 5.3: Cauchy problem for the homogeneous wave equation Section 5.4: Initial and boundaryvalue problems 
D'Alembert solution on semiinfinite domains example 
26Feb2016  Section 6.16.7, 6.11: Fourier series  
02Mar2016  Section 6.7, 6.8: Fourier series  Fourier sine series example 
04Mar2016 
Section 6.13: Fourier transform Section 7.17.3: Vibrating string and separation of variables 
Fourier series and transforms in Mathematica 
09Mar2016  Section 7.17.3: Vibrating string and separation of variables  
11Mar2016  Midterm exam  
16Mar2016  Section 7.17.4: Existence and uniqueness of the wave equation  Wave equation demo in Mathematica 
30Mar2016 
Section 7.57.6: Heat conduction problem Section 7.8: Nonhomogeneous problems 
Heat equation demo in Mathematica 
01Apr2016 
Section 7.8: Nonhomogeneous problems 
Example and plot of solution 
06Apr2016  Section 8.18.2: SturmLiouville problems  
13Apr2016  Section 8.108.12: Green's function for SturmLiouville problems  Green's function example 
15Apr2016 
Section 8.12: Constructing the Green's function for a SturmLiouville problem Section 9.1: Boundary value problems: Laplace's and Poisson's equation Section 9.79.8: Solving Poisson's equation on a rectangle 
Green's function example 
20Apr2016  Section 9.7: Solving Poisson's equation on a rectangle  
22Apr2016  Section 12.112.4: Fourier transforms  
27Apr2016 
Section 12.5: Fourier transforms Section 12.6: Fourier sine and cosine transforms Section 12.8: Laplace transforms 
Understanding convolution Heat equation: Fourier transform solution Heat equation: Fourier sine transform solution 
You are also encouraged to check out these suggestions from the Mathematics Department at
Harvey Mudd on
formatting homework assignments in
mathematics.
Due date  Problem set  Notes 
22JAN2016  HW01  
05FEB2016  HW02  Select solutions 
26FEB2016  HW03  Solutions 
9MAR2016  HW04  
18MAR2016  HW05  For plotting help see WaveEquationEx.nb (Mathematica) or PlottingWaveEquation.m (Matlab). Solutions 
08APR2016  HW06  Solutions 
02MAY2016  HW07 (This will count as extra credit)  Solutions 