MA501 Advanced Mathematics for Engineers and Scientists I: PDE

Instructor: Zhilin Li, SAS 3148, 515-321, https://zhilin.math.ncsu.edu/TEACHING/MA501/index.html

Office Hours: T:10:30-11:20am, TH: 2:30-3:20pm, or by appointment

Course description: Linear partial differential equations and solution techniques including analytic techniques, separation of variables and resulting Sturm-Liouville problems; series solutions, Fourier series and analysis, and special functions. Some applications to engineering and science will also be covered.

Due to the corona virus pandemic, public health measures have been implemented across campus. Students should stay current with these practices and expectations through the Protect the Pack website (https://www.ncsu.edu/coronavirus/). Face masks are optional. Consideration and understanding for wearing or not wearing masks are both appreciated.

Classes Notes will be available on Google drive and/or Moodle. Classes recording can be accessed through NCSU Panopto.

Text Book: An Introduction to Partial Differential Equations, Zhilin Li and Larry Norris, World Scientific Publisher , e-book option should be available

A good reference: Partial Differential Equations with Fourier Series and Boundary Value Problems by Nakhle Asmar, 2nd edition

Prerequisite: MA 141-242, calculus sequence; MA341 Ordinary differential equations.

Grading:

Homework: 20% including some class practice. Homework will be done (1) in written; (2) using WebWork accessible from Moodle.
Two tests: 50 %
Final Exam: 30 %
Class attendance: in-person or virtually through Panopto. Class attendance will be self-reporting through Moodle (during the class time).
Extra credits can be earned through class participation, or form a study group for some extra projects.

Material

Test 1: September 29 Test 2: November 10 Final: 3:30-6:00pm, December 8.

HW

Maple files:

Fourier_x_LtoL.mws Fourier_Sawtooth_LtoL.mws Fourier_sinxhalf_LtoL.mws

Maple file for Fourier Series: Fourier(-LtoL) Fourier(0to2L)

Maple file for 1D Wave equation with animation:: Wave_sep_10 Wave_sep_xcos

Maple file for 1D Heat Equation with animation: Heat_sep_ex1

Maple file for 2D Laplace Equation: laplace_mws

Bessel function_order 0 of first kind.

Vibration of a circular membrane (radially symmetric): Derivation and animation,

Handouts:

ODE_Review Orth_Func_ Sturm_Liouv Commonly used differential form in polar and spherical coordinates.

Calendar

        July                 August              September        
Su Mo Tu We Th Fr Sa  Su Mo Tu We Th Fr Sa  Su Mo Tu We Th Fr Sa  
                1  2      1  2  3  4  5  6               1  2  3  
 3  4  5  6  7  8  9   7  8  9 10 11 12 13   4  5  6  7  8  9 10  
10 11 12 13 14 15 16  14 15 16 17 18 19 20  11 12 13 14 15 16 17  
17 18 19 20 21 22 23  21  B 23 24 25 26 27  18 19 20 21 22 23 24  
24 25 26 27 28 29 30  28 29 30 31           25 26 27 28 T1 30     
31                                                                

      October               November              December        
Su Mo Tu We Th Fr Sa  Su Mo Tu We Th Fr Sa  Su Mo Tu We Th Fr Sa  
                   1         1  2  3  4  5               1  2  3  
 2  3  4  5  6  7  8   6  7  8  9 T2 11 12   4  L  6  7  F  9 10  
 9  V  V 12 13 14 15  13 14 15 16 17 18 19  11 12 13 14 15 16 17  
16 17 18 19 20 21 22  20 21 22  H  H  H 26  18 19 20 21 22 23 24  
23 24 25 26 27 28 29  27 28 29 30           25 26 27 28 29 30 31  
30 31                                                                    


H: Holiday;  V: Vacation (No class);  L: Last day of instruction. T: Mid-term tests