Math 222: Partial Differential Equations TR 9:00-10:15 AM in COB 262: Syllabus (PDF) CHANGED: Exam 1 is now February 21, 2017 Discussion Section: Fridays from 10:30 AM - 11:20 AM in COB 274 Office Hours: Wednesdays from 3:30 - 5:00 PM in COB 347 Sections from Texts: Pinchover and Rubinstein, Chapter 1 Shearer and Levy, Chapters 1 and 2 Lecture 1 (01/17): Introduction to PDEs: including well-posedness, and classification (Chapter 1 Pinchover and Rubinstein and Chapters 1-2 Levy and Shearer) HW 1: Due January 26 and Discussion January 27 Levy and Shearer Problem 1.7 matlab example ( movie, 3D plot, 2D projection) Lecture 2 (01/19): Introduction to PDEs: including linear operators and superposition principle, mathematical models, and conditions (Chapter 1 Pinchover and Rubinstein and Chapters 1-2 Levy and Shearer) Lecture 3 (01/24): First order equations: example and quasilinear equations (Chapter 2 Pinchover and Rubinstein and Chapter 3 Levy and Shearer) Linear transport matlab example ( movie, 3D plot) Lecture 4 (01/26): Method of Characteristics: General Theory and Examples (Chapter 2 Pinchover and Rubinstein and Chapter 3 Levy and Shearer) General initial curve matlab example ( movie, 3D plot, 2D projection) HW 2: CHANGED: Due February 14 and Discussion February 17 Lecture 5 (01/31): Method of Characteristics: General Theory, Theorem of existence and uniqueness, and Burger's Equation (Chapter 2 Pinchover and Rubinstein and Chapter 3 Levy and Shearer) Lecture 6 (02/02): Derivation of Burger's Equation as a model of traffic flow and using Method of Characteristics to solve (Chapter 2 Pinchover and Rubinstein and Section 2.4 and Chapter 3 Levy and Shearer) Lecture 7 (02/07): Burger's equation: time at which characteristics cross and weak solutions (Section 2.7 Pinchover and Rubinstein and end of Chapter 3 and Chapter 13 Levy and Shearer) Burger's Equation matlab example ( movie, 3D plot, 2D projection) Lecture 8 (02/09): NO CLASS Lecture 9 (02/14): Burger's Equation: Riemann Problem (Section 2.7 Pinchover and Rubinstein and end of Chapter 3 and Chapter 13 Levy and Shearer) HW 3: Due February 28 and Discussion March 3 Lecture 10 (02/16): Review and Introduction to second order linear equations (Chapter 3 Pinchover and Rubinstein and Section 2.2 Levy and Shearer) Lecture 11 (02/21): Exam 1 Lecture 12 (02/23): Introduction to second order linear equations (Chapter 3 Pinchover and Rubinstein and Section 2.2 Levy and Shearer) Lecture 13 (02/28): Introduction to wave equation and derivation (Chapter 4 Pinchover and Rubinstein and Chapter 4 Levy and Shearer) Lecture 14 (03/02): Wave equation: General solution, Cauchy problem, d'Alembert's formula, and characteristics(Chapter 4 Pinchover and Rubinstein and Chapter 4 Levy and Shearer) HW 4: Due March 16 and Discussion March 17 HW 5: Due April 13 and Discussion April 14 HW 6: Due April 27 and Discussion April 28 Final Project Presentations Tuesday, May 9, 2016 3:00 PM in COB 262 |