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

Download 1: Syllabus

Download 2: Lecture Notes 1

Download 3: Lecture Notes 2

Download 4: Exercises (No need to hand in)

Download 5: Homework Assignment One (Due Date: Jan 23)

Download 6: Lecture Notes 3

Download 7: Lecture Notes 4

Download 8: Homework Assignment Two (Due Date: Feb. 3) (Revised)

Download 9: Lecture Notes 5

Download 10: Solutions to Homework Assignment One.

Download 11: Solutions to Homework Assignment Two.

Download 12: Homework Assignment Three (Due Date: Feb. 25)

Download 13: Lecture Notes 6

Download 14: Lecture Notes 7

Download 15: Lecture Notes 8

Download 16: Lecture Notes 9

Download 17: Solutions to Homework Assignment Three.

Download 18: New Problems Set (no need to hand in. For solutions please ask me.)

Download 19: One Example on Fully Nonlinear First Order

Download 20: Solution to Midterm

Download 21: Homework Assignment Four (Due Date: March 18)

Download 22: Lecture Notes 10

Download 23: Lecture Notes 11

Download 24: Lecture Notes 12

Download 25: Lecture Notes 13

Download 26: Homework Assignment Five (Due Date: March 27)

Download 27: Solutions to Homework Assignment Four.

Download 28: New Problems Set (no need to hand in. For solutions please ask me.)

Download 29: Homework Assignment Six (Due Date: April 8)

Download 30: Lecture Notes 14

Download 31: Solutions to Homework Assignment Five.

Download 32: Homework Assignment Seven (Due Date: 5:30pm of April 17)

Download 33: List of Formulas and Theorems for MATH400

Download 34: Solutions to Homework Assignment Six.

Download 35: Solutions to Homework Assignment Seven.

Download 36: Midterm Test Problems

Download 37: Final Exam Problems

Download 38: Solutions to Final Exam

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.

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