NORTH CAROLINA STATE UNIVERSITY

DEPARTMENT OF MATHEMATICS

 

Link to On Line Materials

 

MA401: Applied Differential Equations II

Semester:  Spring, 2020

Course:  MA401

Sections: 001, 002 (L.K. Norris)

Office hours:  MWF 10:00 – 11:00 am

TEXTBOOK:

 

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

 

GRADING:

(plus-minus grading)

 

(0) Test #0: 10% - Review Material in section 1.4

 

(1) Test #1:  20% - Wednesday, February 19

 

(2) Test #2:  20% - Friday, April 10

 

(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% - Friday, May 4 from 8 - 11 a.m.

 

COURSE SCHEDULE

 

(Topics covered in each chapter are listed on page 2)

 

1.         January 6 – February 17:  Chapters 1 and 2

2.         Wednesday, January 22: Test #0

3.         Wednesday, February 19:  Test #1

4.         Friday February 21 – Wednesday April 8: Chapters 3 and 4

5.         Friday, April 10:   Test #2

6.         April 13 – April 23:  Parts of chapters 5 and 6

7.         Final Exam: 

                   Friday, May 1, 8-11 a.m. for section 001

                   Monday, May 4, 8-11 a.m. for section 002

 

 

 

 

 

 

 

 

 

 

 

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-Liouville 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