CE 204: Numerical Analysis and Computer Programming
CE 303: Numerical Analysis for Civil Engineers
Course Objective
To give students necessary background on numerical analysis needed to solve civil engineering problems numerically when their analytical solution is either not available or difficult to obtain. MATLAB programming environment will be introduced and used in this course.
Instructor
Professor Tribikram Kundu – Ph.621-6573, Office: Civil Engineering Building 324D
e-mail: tkundu@email.arizona.edu
Class Hours – MWF 10–10:50, CHVEZ 301
Office Hours – MWF 11-11:50, CE324D
Text Book
Numerical Methods for Engineers and Scientists: An Introduction with Applications using MATLAB, Amos Gilat and Vish Subramaniam, John Wiley, First Edition 2007/2008 [Most but not all topics are covered in the text]
Additional recommended books for students who like supplementary reading
1. Applied Numerical Analysis - Using MATLAB, Laurene V. Fausett, Prentice Hall, 1999 [Good for computer codes but not so good for explanation].
2. Applied Numerical Methods with MATLAB for Engineers and Scientists, Steven C. Chapra, McGraw Hill, 2nd Edition 2007/2008 [Good for explanation but not everything is covered in this book and only a few computer codes are given].
Textbook and recommended other books cannot substitute the class lectures. Therefore, students are strongly advised to attend every lecture.
Software
MATLAB – Some online tutorial help is available at the following websites
However, if you attend the class regularly and follow the lectures then you do not need any outside help.
All registered students can use MATLAB for free. You can download the software from the university website. You have to go to the following website and click
"download for individuals" with an active net id. There you will have the option
to download two files. The zip file contains the software files and txt file
contains the license number. You can run this software as long as you are a student of the University of Arizona. However, if you want to own the software without any time limit so that you can use it beyond your student years then you can purchase MATLAB student version that costs about $100.
Syllabus:
1. Review of the Mathematical Foundation (Chapter 2)
- Physical Meaning of Derivatives and Integrals
- Taylor Series Expansion
- Definition of Matrix and Vector; Matrix Algebra - Summation, Subtraction and Multiplication of Matrices; Transpose, Determinant and Rank of a Matrix
2. Fundamentals of MATLAB programming (Appendix A)
3. Solving System of Linear Equations (Chapter 4)
- Unique and Multiple Solutions, Trivial and Non-Trivial Solutions, No solution
- Direct Methods
- Gauss Elimination method
- Gauss Elimination with Row Pivoting
- Iterative Methods
- Jacobi Method
- Gauss-Seidel Method
4. Roots of Nonlinear Equations (Chapter 3)
- Incremental Search Method
- Bisection Method
- Regula Falsi and Secant Methods
- Newton-Raphson Method
5. Curve Fitting and Interpolation (Chapter 5)
- Polynomial Interpolation – Lagrange and Newton’s Polynomials
- Cubic and Quadratic Spline Interpolation
- Curve Fitting by Function Approximation
- Least Squares Fit
6. Numerical Differentiation (Chapter 6)
- Finite Difference Methods – Forward, Backward and Central Difference formulae
- Derivatives for Noisy Data
7. Numerical Integration (Chapter 7)
- Euler, Mid-Point, Trapezoidal, Simpson and Gaussian Quadrature schemes.
8. Solution of Ordinary Differential Equations: Initial Value Problems (Chapter 8)
- Euler’s explicit method
- Modified Euler’s method, Midpoint method
- Runge-Kutta methods (2nd, 3rd and 4th order methods)
- Modified Euler’s Predictor-Corrector Method
9. Solution of Ordinary Differential Equations: Boundary-Value Problems (Ch 9)
- Shooting Method
- Finite-Difference Method
Home Work
Homework problems will be posted on the web (u.arizona.edu/~tkundu/ungradcourse). Homework is to be done neatly using only one side of a sheet. Homework due date will be announced every time a homework is assigned. The homework will be graded and returned (grading is done by the Grader). Late homework submitted after the cutoff time will not be graded and a grade of zero will be assigned.
Exams
Final Exam will be a comprehensive open book exam on Dec. 16 (Wednesday, 11:00 – 1:00). Times for the two mid term exams will be announced in the class.
Grading Policy:
Grading will be based on Weekly Homework, two mid term tests and a final exam. Final exam will have 34% weight. Remaining 66% weight will be equally split among the two midterms and the homework.
Assignment of the final grade will be based on the following scale
A 90 - 100
B 80 < 90
C 70 < 80
D 60 < 70
E < 60
Reward for submitting homework on time: Students who submit their homework on time will be given the higher grades if their total points are on the borderline between two grades.
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