Math 174
Numerical Methods in Science and Engineering
Fall 2006

Course Syllabus

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INSTRUCTOR:   Daniel Reynolds

TEXTBOOK(S):  
  • Cheney and Kincaid, Numerical Mathematics and Computing, 5th Edition, Brooks/Cole--Thompson Learning, ISBN: 0-534-8993-7.
  • (Optional) Cleve Moler, Numerical Computing with Matlab, SIAM Philadelphia, 2004. Available for free at this site.


CATALOG DESCRIPTION:   174. Numerical Methods in Science and Engineering (4)
Floating point arithmetic, linear equations, interpolation, integration, differential equations, nonlinear equations, optimization, least squares. Students may not receive credit for both Math. 174 and Physics 105 or MAE 153 or 154. Students may not receive credit for Math 174 if Math 170 A,B, or C has already been taken. Prerequisites: Math 20D (21D) and Math 20F.


TENTATIVE LECTURE SCHEDULE:
  • Weeks 1-2: Introduction to Numerical Analysis
    • What is numerical analysis?
    • What is an algorithm?
    • Introduction to Matlab
    • Floating-point numbers and arithmetic   [ch 2]
    • Floating-point errors and error propagation   [ch 2]
  • Weeks 2-3: Nonlinear Equations   [ch 3]
    • Bisection method & Regula Falsi
    • Fixed-point iteration
    • Newton Method (& variants)
  • Week 4-5: Linear Systems of Equations   [ch 7-8]
    • What is a matrix?
    • Special Matrices (triangular, tridiagonal)
    • Gaussian elimination
    • Gauss-Jordan Elimination
    • LU Decomposition
    • Ill-Conditioning and Error Propagation
    • Simple Iterative Methods
  • Week 6: Polynomial Interpolation and Curve Fitting   [ch 4]
    • Lagrange Interpolation
    • Neville's Algorithm
    • Chebyshev Interpolation
  • Week 7: Piecewise Polynomial Interpolation   [ch 9]
    • Linear Splines
    • Cubic Splines
  • Week 8:
    • Numerical Differentiation   [ch 4]
    • Numerical Integration: Quadrature rules, Error estimates   [ch 5-6]
  • Week 9: Initial Value Problems   [ch 10-11]
    • Taylor series methods
    • Runge-Kutta methods
    • Systems of ODEs
  • Week 10:
    • Least-squares approximation: Normal Equations   [ch 12]
    • Trigonometric interpolation, Fast Fourier Transform
    • Review

READING:
Reading the sections of the textbook corresponding to the assigned homework exercises is considered to be part of each homework assignment.  It is expected that you have read this material in advance of each lecture.  Furthermore, you are responsible for all of the material in the assigned reading whether it has been presented in the lecture or not.

HOMEWORK:
Homework problems will be assigned on the course homework page, and are due at the beginning of lecture on the posted due date. Assignments will include theoretical as well as computational exercises. Students are free to perform their computational problems in Matlab, C, C++, Java, Fortran, Python, or any other scripting/programming language that they choose; however, instructional support will only be provided for Matlab-based work. As a result, all students should have ACS accounts, with access to the Matlab software for performance of homework exercises. If any student does not believe that they have Matlab access, they should contact the instructor prior to the due-date of the first homework set.

A 25% reduction will be applied to the grade for all homeworks handed in up to 24 hours late (until noon the next day).  A 50% reduction will be applied to the grade for all homeworks handed in up to 72 hours late.  Thereafter, all homeworks will be considered too late, and will receive a zero grade.

EXAMS:
There will be two mid-term exams -- see the main page for dates and material covered.  No notes, books or calculators are allowed during the exams.

It is your responsibility to ensure that you do not have a schedule conflict during the final examination;  you should not enroll in this class if you cannot take the final examination at its scheduled time.  No notes, books or calculators are allowed during the final exam.

There will be no make-up exams for those missed during the scheduled times.

The final examination will be held at the following date, time and place:

Friday, December 8,  8:00 -- 11:00 AM.  Place: TBD


MATLAB:  For those unfamiliar with Matlab, you may find the following references helpful:
  • Yousef Saad's Matlab introduction notes
  • Kermit Sigmon's Matlab Primer (3rd ed.)
  • Hanselman and Littlefield, Mastering Matlab 6, Prentice Hall, 2000.
  • The online Matlab Help Desk provides a good reference for Matlab functions.
  • The "help" command at a Matlab prompt will bring up an extensive list of help topics.
  • For those who do not own the Matlab software, Octave is a free software system that may be installed on any Windows, OS X, or Linux platform, and provides an interface that is nearly identical to Matlab. All homework assignments may be performed in Octave as well.

GRADING:
Your course grade will be based on the following decomposition:
  • 30%  Homeworks (5 assignments, at 6% each)
  • 20%  Mid-term 1
  • 20%  Mid-term 2
  • 30%  Final Exam
Final grades will be assigned based on the following scale.  We may curve the scale to be more lenient, depending on the final grade distribution, though this is at the sole discretion of the instructor.

F D C - C C + B - B B + A - A A +
0-59 60-69 70-72 73-76 77-79 80-82 83-86 87-89 90-92 93-96 97-100

We (the TA and I) will attempt to grade all homeworks and exams fairly the first time.  However, if you would like to debate the assigned grade we reserve the right to re-grade the entire assignment, not only the problems that you feel should have been awarded more points.  Only the course instructor may change grades, i.e. do not ask the TA for re-grades.  Lastly, you have a maximum of one week after the homework or mid-term is returned to request a re-grade.

ACADEMIC DISHONESTY:
Academic dishonesty is considered a serious offense at UCSD.  All homeworks and exams must represent your own individual effort.  Discussions regarding assigned problems is OK, so long as what is turned in represents individual efforts.  Cheating on an exam or assignment results in zero points for that exam/assignment.  This exam may not be dropped in computing the final grades.  In other words, cheating on an exam will result in a drop of at least 2 letter grades in the course (2 for a mid-term, 3 for the final).  Furthermore, we resolve to do everything within our ability to ensure that students caught cheating will face an administrative sanction which may include suspension or expulsion from the university.