MATH 505: Introductory Numerical Analysis: Approximation and Differential Equations

• 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

• Python tutorial (https://docs.python.org/3/tutorial/index.html)
• Facts and myths about Python names and values (http://nedbatchelder.com/text/names.html)
• Dive into Python 3 (http://www.diveinto.org/python3/)
• Introduction to Python for Science (https://github.com/djpine/pyman)
• The SciPy lectures (http://scipy­lectures.github.io/)
• The Numpy MedKit (http://mentat.za.net/numpy/numpy_advanced_slides/)
• The Numpy User Guide (http://web.mit.edu/dvp/Public/numpybook.pdf) by Travis Oliphant
• Spyder (https://github.com/spyder­ide/spyder) (a Python IDE, like Matlab)
• An introduction to Numpy and SciPy (http://www.engr.ucsb.edu/~shell/che210d/numpy.pdf)
• 100 Numpy exercises (http://www.loria.fr/~rougier/teaching/numpy.100/index.html)

*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