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
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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 |
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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