MA780: Numerical Analysis II

Spring Semester, 2020, MW 3:00-4:15pm, SAS 1218

Instructor:  Dr. Zhilin Li, SAS 3148, Tel: 919-515-3210
     Office Hours: M: 10:00-11:00am, TH: 2:00-2:50pm, or by appointment
E-mail:  <zhilin at math.ncsu.edu>

Objectives and significance:

This course is continuation of MA580 (numerical analysis with focus on linear algebra) and is one of subjects of the qualifying exams for Ph.D candidates in Mathematics. The focuses of this course are various numerical methods and analysis for problems including: approximation and interpolation,  numerical differentiation and integration, numerical solution of initial value problems for ordinary differential equations,  fast Fourier transform, and numerical solution of non-linear equations of one or several variables.

This course is designed for students in applied mathematics, engineering, and other disciplines to learn basic techniques in numerical analysis and applications. While theoretical foundations will be described, emphasis will also be placed on algorithm design and implementation. We will also explore available software packages in this field.

Prerequisites:
Calculus I-III, some background  in linear algebra, numerical analysis, and MA580; and some programming experience (Matlab, recommended, Python, Fortran, C, C++, ...)

Grading Policy:

There will be homework (may include in-class work) about every couple of weeks during the semester, including both analytic work and computer projects 40%.  One midterm: 30%; Final exam 30% (can be take-home), (+ or -) 3% class participation may be applied.

Class Rules: A good learning environment is essential to the success of a class.  Constant talking, cell phone use, reading irrelevant materials,  late arrival and early departure are discouraged and may be penalized by your class participation grade and attendance record.  Students with excess absences (more than 3 excusable or non-excusable) are required to make-up the classes by writing and final grade may be prorated accordingly to the percentage of class that are missed. 

Computer Language:

Matlab will be used the most for instructional purposes. The students are welcome to use any other language including Matlab, Python, Fortran, C, C++ .

Text:

Numerical Mathematics, by Quarteroni, Sacco, Springer 2007, available at https://www.academia.edu/2827050. Most of numerical analysis books can be used as references.

Calendar:

      January               February               March          
Su Mo Tu We Th Fr Sa  Su Mo Tu We Th Fr Sa  Su Mo Tu We Th Fr Sa  
          1  2  3  4                     1   1  2  3  4  5  6  7  
 5  6  7  8  9 10 11   2  3  4  5  6  7  8   8  B  R  E  A  K 14
12 13 14 15 16 17 18   9 10 11 12 13 14 15  15 16 17 18 19 20 21  
19  H 21 22 23 24 25  16 17 18 19 20 21 22  22 23 24 25 26 27 28  
26 27 28 29 30 31     23 24 25 26 27 28 29  29 30 31              
                                                                  

       April                  May                             
Su Mo Tu We Th Fr Sa  Su Mo Tu We Th Fr Sa    
          1  2  3  4                  1  2        
 5  6  7  8  9 10 11   3  4  5  6  7  8  9     
12 13 14 15 16 17 18  10 11 12 13 14 15 16    
19 20 21 22  L 24 25    
26 27 28 29 30
H: Holiday;    F: Final Exam;   L: Last day of instruction;

Disability services:

Reasonable accommodations will be made for students with verifiable disabilities.  In order to take advantage of available accomodations, students must register with Disability Services for Students at 1900 Student Health Center, Campus Box 7509, 515-7653.  For more information on NC State's policy on working with students with disabilities, please see the Academic Accommodations for Students with Disabilities Regulation (REG02.20.1)