MATH/CMPSC 455 (Fall 2011)
Introduction to Numerical
Analysis I, M W F 12:20 pm - 1:10 pm, 112
Engineering
Unit B
Course Brief Description
This course is an introduction to basic and classical numerical
algorithms. We will describe numerical algorithms for floating
point computation, rootfinding, solving linear systems,
interpolation and quadrature. We will also discuss the underlying
mathematical principles and theories of these numerical methods
and their implementations.
Some knowledge of either MATLAB, Octave, Fortran, C, or C++ is
strongly
recommended. MATLAB is used for exposition of algorithms
during the class. You can choose any computer language as a
platform for homework and projects.
Grading Policy
- Homework & Computer projects (50 %);
- Midterm exam (20 %);
- Final exam (30 %).
Homework & Computer projects will be assigned every 2 or 3
sections. The lowest grade will be dropped. Details about midterm
and final exam will be announced later.
Lecture Notes & Slides
0.0 Introduction:
slides
0.1 Evaluating a Polynomial:
Notes &
Slides
0.2 Binary Numbers:
Notes &
Slides
0.3 Floating Point Representation:
Notes
(updated) &
Slides
(updated)
0.4 Loss of Significance:
Notes &
Slides
1.1 Bisection Method:
Notes &
Slides
1.2 Fixed Point Iteration:
Notes &
Slides
1.3 Newton's Method:
Notes &
Slides
1.4 Root Finding without Derivatives:
Notes &
Slides
2.1 Gaussian Elimination:
Notes
&
Slides
2.2 LU factorization:
Notes
&
Slides
2.3 Source of Error:
Notes
2.4 PA=LU:
Notes
&
Slides
2.5 Iterative Method:
Notes &
Slides
2.6 Conjugate Gradient Method:
Notes &
Slides
3.1 Interpolation:
Notes &
Slides
3.2 Interpolation Error:
Notes
&
Slides
3.4 Splines:
Notes
&
Slides
5.2 Numerical Integration: Notes &
Slides
5.3 Romberg Integration:
Notes &
Slides
5.5 Gauss Quadrature:
Notes &
Slides
6 Ordinary Differential Equations:
Notes &
Slides
