Math 381 - Introduction to Partial Differential Equations
Sevak Mkrtchyan
456 Herman Brown Hall
e-mail: (first name).(last name)@rice.edu
Phone: x5319

Course Description

General theories for solving linear and quasi-linear partial differential equations. The heat equation with various boundary conditions. The wave equation. Boundary value problems: Fourier series, Bessel functions, Legendre polynomials. We will mostly cover chapters 8 and 9 of the textbook, but also other needed material on the way.

Lectures

MWF 1:00-1:50 in HZ212

Office Hours:

M 3-4, W 3-3:30, Th 1:30-2:00 (456 Herman Brown Hall)
Teaching Assistant: Jon Fickenscher - Office hours: TuTh 12:30-1:30 in HB 48

Textbook

Advanced Calculus for Applications, Second Edition, by Francis B. Hildebrand

Grades

Your grade in the class will be based on the following weights:
25% - Homework
20% - Midterm 1: Friday, September 25
20% - Midterm 2: Friday, November 13
35% - Final Exam

Homework

Homeworks will be put up here and are due on Fridays (or on Wednesday in the two weeks with midterm exams on Friday) in class at the beginning of the class. Late homework will not be accepted under any circumstances. Your lowest homework grade will be dropped before computing your homework average. You are welcome to work together with other students on your homeworks, but your write-up must be your own, and you should write on your homework the names of any other students you worked with.

This is a schedule for topics covered in class each day and homework assigned for that day. This part of the website will be updated regularly.

Date
 Sections
 Topic
 Homework
 Due
Mon, August 24
 8.1 Definitions of PDE's and example. 8.1: 1a,c,2 Sept 4
Wed, August 26
 8.2 The Quasi-Linear Equation of 1st order - general theory 8.2: 5d,6 Sept 4
Fri, August 28
 8.2-8.3 Examples 8.3: 8,9,14a,d Sept 4
Mon, August 31 8.3-8.5 Initial conditions. Special linear equations with constant coefficients: generic situation. 8.3: 11, 17; 8.5: 23 a,c,f Sept 14
Wed, September 2
 8.5, 2.1-2.2 Special linear equations with constant coefficients: repeated roots. Introduction to the Laplace transform. 8.5: 32, 33, 34 Sept 14
Fri, September 4
 2.2-2.3 Some properties of the Laplace transform. L(f') in terms of L(f). Solve ODE using Laplace transforms. f'=-af. 2.2: 3a,d Sept 14
Mon, September 7
 no class
 Labor Day
Wed, September 9
 2.3 Properties of the Laplace transform continued. Solve a PDE using Laplace transforms.
Fri, September 11
 2.9 The Gamma function 2.8: 41a; 2.9: 51, 54, 56, 57, 59b Sept 21
Mon, September 14
 4.8 Bessel Functions of the first type. Solve Bessel's equation for p=1/2. Sept 21
Wed, September 16
 4.8 Bessel Functions of the second type.
Fri, September 18
 4.9,4.10 Asymptotics of Bessel functions. Differential equations satisfied by them.
Mon, September 21
 4.12 Legendre functions
Wed, September 23
 5.10 Fourier sine series 5.10: 49,51 Oct 5
Fri, September 25
 1st Midterm Exam
 In-class Midterm Exam
Mon, September 28
 5.10 Fourier cosine series
Wed, September 30
 5.11 Complete Fourier series 5.11: 62,64,65 Oct 5
Fri, October 2
 Solve the midterm problems 5.11: 57 Oct 14
Mon, October 5
 9.1, 9.2 Heat Flow 9.1: 5,7 Oct 14
Wed, October 7
 9.3 Steady state temperature distribution in a rectangular plate 9.3: 14,15,16,21,22,23 Oct 14
Fri, October 9
 9.4 Steady state temperature distribution in an annulus (Registrar drop deadline)
 9.4: 27,28,29 Oct 26
Mon, October 12 no class
 Midterm Recess
Wed, October 14
 9.4, 9.5 Steady state distribution in a disk and the complement of a disk, Poisson's Integral 9.5: 33,34 Oct 26
Fri, October 16
 9.7 Steady state distribution in a rectangular parallelepiped 9.7: 42 Oct 26
Mon, October 19
 9.7 Steady state distribution in a rectangular parallelepiped
Wed, October 21
 9.6 Axisymmetrical temperature distribution in a solid sphere
Fri, October 23
 5.14 Legendre Series 4.12: 59,60 Nov 9
Mon, October 26
 5.14, 9.6 Legendre Series 9.6: 36,37,38,39 Nov 9
Wed, October 28
 9.8 Ideal fluid flow about a sphere
Fri, October 30
 9.8 Ideal fluid flow about a sphere
Mon, November 2
 9.8 Ideal fluid flow about a sphere
Wed, November 4
 9.9 The wave equation: circular membrane.
Fri, November 6
 9.9 The wave equation: derivation.
Mon, November 9
 5.6 Orthogonality of characteristic functions
Wed, November 11
 5.13 Fourier-Bessel Series 2.3: 13,14 Dec 4
Fri, November 13 9.10 Heat flow: derivation of heat equation in a rod. Take home midterm exam due Nov 23.
Mon, November 16
 9.10 Heat flow in a rod.
Wed, November 18
 9.11 Duhamel's integral
Fri, November 20
 5.15 The Fourier Integral 5.15: 88,89a,91,93 Dec 4
Mon, November 23
 9.14 Examples using Fourier Integrals. Problem from midterm.
Wed, November 25
 9.14 Examples using Fourier Integrals. Problem from midterm.
Fri, November 27
 no class
 Thanksgiving break
Mon, November 30
 9.14-15 Examples using Fourier Integrals. Laplace transform method.
Wed, December 2
Fri, December 4
 Review
Wed, December 9 to
Wed, December 16
 Final exam period
 The exact date and time of the final will be posted as soon as the Registrar tells us. 

It is the policy of the mathematics department that no final may be given early to accommodate student travel plans.

Exams

There will be two in-class midterm exams and one comprehensive final exam. It is the policy of the mathematics department that no final may be given early to accommodate student travel plans. We will not know when the final in this course will be scheduled for some time. Therefore, if you should make plans for travel before the end of the final exam period, and it turns out that the final for this course is after your scheduled departure date, you will have to choose between keeping your plans and receiving a zero for the final, or incurring the cost for changing your plans and taking the final at its scheduled time. Thanks for your understanding.

Disability Support

If you have a documented disability that will impact your work in this class, please contact me to discuss your needs. Additionally, you will need to register with the Disability Support Services Office in the Allen Center.