# MATH 505: Introductory Numerical Analysis: Approximation and Differential Equations

**Time and Place:** Tuesday/Thursday 12:30 - 1:45 pm, SMLC 124

**Instructor:** Jehanzeb H. Chaudhry (Zeb),
jehanzeb@unm.edu,
www.math.unm.edu/~jehanzeb

**Office Hours:** Tuesday and Wednesday: 9:30 - 11:00 am (SMLC 310)

**Texts :**
- Numerical Analysis (second edition), Walter Gautschi, available from the Springer standard collection. (Required)
- Numerical Methods in Scientific Computing vol. 1, Dahlquist and Bjork, SIAM. (Recommended)

**Course Description:**
This is an introductory course in numerical analysis. Topics that will be covered
are: Numerical approximation of functions. Interpolation by polynomials, splines and trigonometric
functions. Numerical integration and solution of ordinary differential equations. An introduction
to finite difference and finite element methods, time permitting.

**Syllabus**

** Computation **
You can use either Python, Matlab or C/C++ for the computations.

#### *Python

I find Python along with the libraries numpy,
scipy and matplotlib better than Matlab. Python has a very gentle learning curve, so you should feel at home even if
you've never done any work in Python.

#### *Python and Numpy Help

#### *Matlab

**A simple tutorial (intended for Math 375) ** MATLAB tutorial (PDF)
script with all commands(matlab_tutorial.m)
ApproxExp.m
f1.m
df1.m
MyDeriv.m
my_funky_fcn.m
MTU
MIT
#### *C/C++

C/C++ is like a double shot espresso. If you don't know what it is, its better to steer clear.
**Grading:**

60% Homework

10% Class Participation

30% Project

After the above weighted score has been calculated, letter grades will be assigned according to the following scheme: A, 90 or above, B, 80 or above, C, 70 or above, D, 60 or above, F below 60. However, the instructor reserves the right to “curve” grades to offset unforeseen circumstances. The curving of grades will never decrease a student’s letter grade below that given by the above formula.

**Homeworks:**
The homeworks will have both a computational and theoretical component. Late homeworks will not be accepted.

**Homework 1: ** **Chapter 1 Exercises:** 3, 5, 7ab, 10, 11, 23, 28, 29, 37, 43 ** Chapter 1 Machine Assignments:** 15 **Assigned:** Aug 31 **Due:** Sept 14

**Homework 2: ** **Chapter 2 Exercises:** 2, 4 (skip the p=1 case), 6, 11, 23a, 33, 36 ** Chapter 2 Machine Assignments:** 2 **Assigned:** Sept 14 **Due:** Sept 28

**Homework 3: ** **Chapter 2 Exercises:**37, 41, 52a, 58, 61, 62, 69, 70 ** Chapter 2 Machine Assignments:** 7 , 8 bcd (for part (a), use the MATLAB backslash operator) **Assigned:** Sept 26 **Due:** October 17

**Homework 4: ** **Chapter 3 Exercises:** 4, 5a, 7, 8, 30, 37a ** Chapter 3 Machine Assignments:** 4 (a-d)
**Bonus:** Exercise 9 (Error term in Simpson's rule)
**Assigned:** October 17 **Due:** November 2

Homework 5
**Assigned:** November 2 **Due:** November 16

**Homework 6:** In class quiz on Chapter 5
**Assigned:** November 28 **Due:** December 7

**Projects**
Project Guidelines and Suggestions
Grading Rubric