APM346  Fall 2016 


Lecturer Jonathan Korman Office: PG307A email: jkorman at math dot toronto dot edu Office Hours: Tue 34pm and by appointment Lecture L0101 Wed 24 pm in KP 108 Thr 1011am in LM 162 Tutorials (Krishan) T0101: Thr 1213 in BA 1200 T0301: Wed 1617 in MP134 
Teaching
Assistants
Krishan Rajaratnam Office: BA 6283 email: kr dot rajaratnam at mail dot utoronto dot ca Office Hours: Mon 11am1pm (every week) Tristan Milne Office: BA 6283 email: tristan dot milne at mail dot utoronto dot ca Office Hours: Fri 12pm (on Oct 14, 28: 11am12pm). 
#  Week of ...  
Fall Semester:  
1  Sept 1415  Course information, review of ODEs, introduction to PDEs (degree, linear/nonlinear, homogeneous/nonhomogeneous), Principle of superposition, auxiliary conditions, wellposed problems. 
2  Sept 2122  1st order linear equations: method of characteristics, types of 2nd order equations, change of coordinates. 
3  Sept 2829  Heat equation. Separations of variables: Heat equation with frozen ends, Heat equation with insulated ends. 
4  Oct 56  Heat equation. Examples. Qualitative properties: maximum principle, uniqueness and stability of solutions, nonhomogeneous problems. 
5  Oct 1213  Fourier Series. Fouries sine and cosine series. Pointwise convergence. Infinite series solutions. 
6  Oct 1920  Fourier Series. Termbyterm differentiation and integration. Heat equation with heat source: series solutions. Laplace equation. 
7  Oct 2627  Midterm. Laplace equation. 
8  Nov 23  Laplace equation on the disk, qualitative properties: Mean Value property,maximum principle, uniqueness of solutions for BVP, stability,sovability condition. Wave equation. Midterm grades+solutions posted. 
9  Nov 910  Wave equation on finite interval (separation of variables), formula in terms of initial data, wave eq on line (characteristics), D'Alembert formula, qualitative properties: causality, conservation of energy, uniqueness of solutions. 
10  Nov 1617  Wave eq on half line: reflection. Fourier Transform. 
11  Nov 2324  Fourier Transform. Heat equation on line. 
12  Nov 30Dec 1  Method of characteristics for quasilinear equations. Weak solutions. Traffic at stop light. 
HW 1 
due Sept 28, Sept 29 
HW2 
due Oct 12, Oct 13 
HW 3 
due Nov 2, Nov 3 
HW 4 
due Nov 16, Nov 17 
HW 5 
due Nov 30, Dec 1 