MATH400-201 :       Applied Partial Differential Equations   (2nd term 2013/2014)
Lecture   I: Tuesday 9:30am--11:00am, Math Annex 1100.
Lecture II: Thursday 9:30am--11:00am, Math Annex 1100.
Office Hours: Every Monday, Wednesday, Friday, 4pm-5pm, LSK 303D.
Downloads For MATH400
Updates For MATH 400
Jan. 7: Method of Characteristics. Four Examples.
Jan. 9: Method of Characteristics. More Examples including blow-ups. Method of Change of Variables.
Jan. 14: General solutions using method of change of variables. Example in which the data curve coincides precisely with characteristics. Condition on initial condition. Up to page 1.23 of lecture note one.
Jan. 16: Quasilinear 1st Order PDE. Traffic Flow Model. Characteristics Meet. Breaking Time. up to page 2.9 of lecture note two.
Jan. 21: Shock. Rankine-Hugoniot Condition. Examples of Shock curves. Finished Lecture Note Two.
Jan. 23: Fully nonlinear first order PDEs. Eikonal Equation. Finished Lecture Note Three.
Jan. 28: Eikonal Equation. Derivation of Wave Equation and Diffusion Equation. Finished up to 1.3 of Lecture Note Four.
Jan. 30: Initial and Boundary Conditions. Types of Second Order PDE. Finished up to 1.6 of Lecture Note Four.
Feb. 4: Classification of 2nd order linear PDEs using the change of variables. General solutions of wave equation, d'Alembert's formula. Three examples
Feb. 6: Principle of Causality. Domain of Influence/Dependence. Wave Equation with Sources. Well-posedness of Wave Equation.
Feb. 11, Feb. 13: Reflection of Waves. Solution Formula for Diffusion Equation. Up to lecture note 7.
Feb. 25: Diffusion with source. well-posedness. Reflection. Up to Lecture note 8.
March 4: Midterm
March 6: Method of Separation of Variables. Cases of negative eigenvalues. Lecture Note 9.
March 11: Lecture Note 9. Periodic Boundary Conditions.
March 13: Lecture Note 10. Finished up to Example 2.
March 18: Lecture 10 and Lecture 11: up to the method of separation of variables to inhomogeneous heat equation.
March 20: Lecture 11 and the beginning of Lecture 12 (uniqueness).
March 25: Solving Laplace equation in rectangles and cubes. Lecture 12.
March 27: Laplace operator in polar coordinate. Solve Poisson equation in a disk. Poisson formula. Lecture 13.
April 1: Solve Poisson equation in a wedge, an annulus, and exterior of a disk. Maximum Principle.
April 3: Laplace with inhomogeneous source. existence and uniqueness in unbounded domains. Heat equation in a disk--introduction of Bessel function.
April 8: Bessel function of order zero and Bessel function of order $n$. Finished Lecture Note 14. Have a nice final exam
April 23: Final Exam.
Announcements For MATH 400
Office Hours: Every Monday, Wednesday, Friday, 4pm-5pm, LSK 303D. Starting Date: Jan. 8
Homework Two has been revised on Jan. 24.
Midterm Examination Date: March 4 (Tuesday) in class.
Coverage of Midterm Examination: up to Lecture Note 8.
Last homework assignment (HW#7) will be handed out on April 8th.
There will still be office hours on April 11, April 14 and April 16. Same time and same location.
Last Office Hour on Tuesday (April 22). Same time and same location. You can collect your last homework.