MATH5351
Mathematical Methods in Science and Engineering I
Lectures: Monday
18:3021:20, Rm 5504, Lift 2526
Office Hour: Monday 16:0017:00, or by appointment
Announcements:
Lectures 23&24 (Nov. 27) 
Calculus of variations, HamiltonJacobi
equations 

Lectures 21&22 (Nov. 20) 
Stability analysis,
perturbation solutions, energy estimates 
Textbook 5.4, 6.5.2 
Homework 5 (part II) Due Nov. 27 
Lectures 19&20 (Nov. 13) 
Weakly nonlinear
approximations, nondimensionalization, Diffusion
process, similarity methods 
Textbook 4.5, 5.1, 5.2, 5.3 
Homework 5 (part I) Due Nov. 27 
Lectures 17&18 (Nov. 6) 
An example, wavefront expansions 
Textbook 4.3, 4.4, 2.4 

Lectures 15&16 (Oct. 30) 
Method of characteristics
for hyperbolic systems, jump conditions 
Textbook 4.2, 4.3 
Homework 4 (part II) Due Nov. 6 
Lectures 13&14 (Oct. 23) 
Weak solutions, equal area
principle, examples of hyperbolic systems, small amplitude approximation 
Textbook 3.5, 3.6, 4.1 
Homework 4 (part I) Due Nov. 6 
Lectures 11&12 (Oct. 16) 
Rarefaction fan solutions,
entropy conditions, Shock formation 
Textbook 3.2, 3.3 
Homework 3 (part II) Due Oct. 23 
Lectures 9&10 (Oct. 9) 
General first order
equations, Discontinuous solutions, jump conditions, shock solutions 
Textbook 2.5, 3.1, 3.2 
Homework 3 (part I) Due Oct. 23 
Lectures 7&8 (Sep.25) 
Method of characteristics:
linear first order PDEs, a simple nonlinear PDE, nonhomogeneous PDEs 
Textbook 2.1, 2.2, 2.3 
Homework 2 (part II) Due Oct. 9 
Lectures 5&6 (Sep.18) 
Traveling wave solutions,
Plane wave solutions, dispersion relation, Fourier transform method, ColeHopf transformation 
Textbook 1.5 
Homework 2 (part I) Due Oct. 9 
Lectures 3&4 (Sep.11) 
Conservation laws,
Constitutive equations, initial and boundary value problems, wellposedness 
Textbook 1.2, 1,3, 1.4 
Homework 1 (part II) Due Sep. 18 
Lectures 1&2 (Sep. 4) 
PDE, Order, Solution,
Linear and Nonlinear PDEs, Fundamental types of PDEs 
Textbook 1.1 
Homework 1 (part I) Due Sep. 18 