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.

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

Grading Policy:

There will be homework assignments about every couple of weeks during the semester, including both analytic work and computer projects 50% that may include some class participation;  One midterm: 15%; Final exam 35%. Up to 3% extra credits for active class participation and extra good projects.

Computer Language:

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

Text:

Numerical Mathematics, by Quarteroni, Sacco, and Saleri, Springer 2000. 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  
 5  B  7  8  9 10 11   2  3  4  5  6  7  8   2  3  4  5  6  7  8  
12 13 14 15 16 17 18   9 10 11  W 13 14 15   9  B  R  E  A  K 15  
19  H 21 22 23 24 25  16 17 18 19 20 21 22  16 17 18 19 20 21 22  
26 27 28 29 30 31     23 24 25 26 27 28     23 24 25 26 27 28 29  
                                            30 31                 

       April                  May                             
Su Mo Tu We Th Fr Sa  Su Mo Tu We Th Fr Sa    
       1  2  3  4  5               1  2  3     
 6  7  8  9 10 11 12   4  5  6  7  8  9 10     
13 14 15 16 17 18 19  11 12 13 14 15   
20 21  L 23 24 25 26    
27 28 29 30              

H: Holiday  L: Last day of instruction; W: Wellness Day