MATH5351 Mathematical Methods in Science and Engineering I

 

 

Lectures: Monday  18:30-21:20, Rm 5504, Lift 25-26

 

Office Hour: Monday 16:00-17:00, or by appointment

 

Textbook:  An introduction to nonlinear partial differential equations, J. David Logan, John Wiley & Sons, 2nd edition, 2008.

 

Syllabus

Academic Integrity

 

Announcements:

 

                     

Lectures 23&24 (Nov. 27)

Calculus of variations, Hamilton-Jacobi 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, Cole-Hopf 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, well-posedness

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