NORTH CAROLINA STATE UNIVERSITY

DEPARTMENT OF MATHEMATICS

 

MA401: Applied Differential Equations II

Semester:  SS-1, 2019

Course:  MA401.001 (L.K. Norris)

Office hours:  TBA

TEXTBOOK: “Introduction to Applied Partial Differential Equations” by John M. Davis

GRADING:  plus-minus grading

 

(0) Test #0: 10% - Monday, May 20.  Review Material in section 1.4 

(1) Test #1:  20% - Tuesday, May 28. Chapters 1 and 2

(2) Test #2:  20% - Wednesday, June 12. Chapters 3 and 4

(3) Homework:  20% - Composed of take-home problems given throughout the semester. 

A good portion of the work will require you to use Maple.

(4) Final Exam: 30% - Thursday, June 20 from 8 - 11 a.m. Chapters 1-6

 

 

 

May 15

May 16

May 17

May 20

 

Test #0

30 minutes

May 21

May 22

May 23

May 24

May 27 - HOLIDAY

May 28

 

Test #1

 

May 29

May 30

May 31

June 3

June 4

June 5

June 6

June 7

June 10

June 11

 

 

June 12

 

Test #2

 

June 13

June 14

June 17

June 18

 

Last day of classes

June 19

 

Study day

June 20

 

Final Exam

8-11 am

 

COURSE CALENDAR

 

 

Semester Schedule

 

Chapter                     Topics

 

1…………………………….Introduction to PDEs

                        1.1      ODEs vs PDEs

                        1.2      How PDEs Are Born:  Conservation Laws, Fluids and Waves

                        1.3      Boundary Conditions in One Space Dimension

                        1.4      ODE Solution Methods

                                    Test #0

 

2……………………………Fourier’s Method:  Separation of Variables

                        2.1      Linear Algebra Concepts

                        2.2      The General Solution via Eigenfunctions (the heat & wave equations)

                        2.3      The Coefficients via Orthogonality

                        2.4      Consequences of Orthogonality

                        2.5      Robin Boundary Conditions

                                    Test #1

 

3…………………………….Fourier Series Theory

                        3.1      Fourier Sine, Fourier Cosine, and Full Fourier Series 

                        3.3      Error Analysis and Modes of Convergence

                        3.4      Convergence Theorems

                        3.5      Basic L^2 Theory

 

4…………………………….General Orthogonal Series Expansions 

                        4.1      Regular and Periodic Sturm-Liouille Theory

                        4.2      Singular Sturm-Liouville Theory

                        4.3      Orthogonal Expansions:  Special Features

                                    Test #2

 

5…………………………….PDEs in Higher Dimensions

                        5.5      Laplace’s Equation in 2D

                        5.6      The 2D Wave and Heat Equations

 

6…………………………….PDEs in Other Coordinate Systems

                        6.1      Laplace’s Equation in Polar Coordinates

                        6.3      The Wave and Heat Equations in Polar Coordinates

                        6.4      Laplace’s Equation in Cylindrical Coordinates

                        6.5      Laplace’s Equation in Spherical Coordinates

 

Final Exam