Objectives and significance:

This course is continuation of MA580 (numerical analysis with the focus on linear algebra) and is one of subjects of the qualifying exams for Ph.D candidates in Mathematics. The focuses of the course are various numerical methods and analysis for non-linear 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 the sciences to learn the 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; 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 55%. Class participation is strongly recommended (5%).  Final exam 40% is May 5,  Monday, 2003 in classroom HA366.
 

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 Methods, by Quarteroni, Sacco, and Saleri, Springer 2000. Most of numerical analysis books can be used as references.

Calendar:

         Jan                    Feb                    Mar
 S  M Tu  W Th  F  S    S  M Tu  W Th  F  S    S  M Tu  W Th  F  S
                                          1                      1
             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 12 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
         Apr                    May                    
 S  M Tu  W Th  F  S    S  M Tu  W Th  F  S    
       1  2  3  4  5                1  L  3    
 6  7  8  9 10 11 12    4  F  6  7  8  9 10    
13 14 15  V  V  V 19   11 12 13 14 15 16 17   
20 21 22 23 24 25 26      
27 28 29 30

H: Holiday;    V: Vacation (No class); L: Last day of instruction;