MASTER 1 Syllabus MAT641

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1 MASTER 1 Syllabus MAT641 Numerical Analysis D. Samy MZIOU [College Of Sciences] [Depart. Of Mathematics & Statistics] [Saturday, December 0, 016] Semester 1 [ ]

Course information Instructors DR SAMY MZIOU Credits 4 Prerequisite: E-Mail: CALCULUS, LINEAR ALGEBRA, ODES AND MATLAB PROGRAMMING. mzious@imamu.edu.

2 Course information Instructors DR SAMY MZIOU Credits 4 Prerequisite: CALCULUS, LINEAR ALGEBRA, ODES AND MATLAB PROGRAMMING. mzious@imamu.edu.sa office Phone : (0) Office Location: College of Science, Department of Mathematics & statistics, 1 st floor, Office FR6 Course Website Office Hours: See Time Table Textbook: Introduction to Numerical Analysis Authors: Stoer, Josef, Bulirsch, R. Edition, Springer Numerical Mathematics Authors: Quarteroni, Alfio, Sacco, Riccardo, Saleri, Fausto Edition, Springer Scientific Computing with MATLAB Authors: Quarteroni, Alfio, Saleri, Fausto Edition 4, Springer-Verlag Berlin Heidelberg Course goals: Provide students a good understanding on numerical methods and a critical interpretation on technical mathematical writing including proofs and algorithms. Perform some algorithms and codes in order to deepen programming via MATLAB software. Allow students understanding of the above concepts through study cases and occasional MATLAB-based homework problems. Develop the skills needed for mathematical writing and communications using Latex or word editor. Notice: This course will make extensive use of MATLAB. Students can ask any questions concerning the course only either during lectures or office hours or via the instructor provided above.

3 Chapter 1. Errors and numbers representation. Root finding problems. Linear Systems Detailed Syllabus Topics Floating-point representation, base 10 and base, conversion between two number bases. Significant digits, Rounding and chopping Accuracy and Precision, absolute error and relative error. Taylor theorem and Remainder, Truncation error, Big O and Small o notation Bisection, fixed point iterations, Newton s method. The Brent method, Aitken s method & Muller method Error & convergence analysis. Direct methods; o Pivoting, o LU factorization o Error analysis and conditioning. MIDTERM Iterative methods; o Jacobi, Gauss-Seidel & SOR methods; o Krylov subspaces methods; o Conjugate gradient method, o GMRES o Error & convergence analysis. o Preconditioning Week 4. Ordinary Differential Equations (part1) 5. Ordinary Differential Equations (part) Solution of initial value ODEs Implicit and Explicit Euler schemes, Taylor and Runge - Kutta methods, Local and global error, convergence analysis. Multistep methods, Predictor corrector methods; Implicit Methods and Stiff Equations; Convergence, stability and consistency of these methods. Numerical methods for solving system of first order differential equations Eigenvalue problems. Boundary value problems using the shooting method. FINAL EXAM Other references: 1. Numerical Analysis, R.L. Burden & J.D. Faires, Brooks / Cole...A Friendly Introduction to Numerical Analysis, Brian Bradie, Prentice Hall. Elementary Numerical Analysis (rd Edition), Kendall Atkinson and Weimin Han, Wiley 4. Matrix Computations, G.H. Golub and C.F. Van Loan, Johns Hopkins University Press 5. Solving ODEs with Matlab, L. F. Shampine,I. Gladwell,S. Thompson, Cambridge University Press

4 Grades and Exams Exam Date Exams Grading Midterm Around 9 th week 0 % Homeworks & assignments & mini projects Will be taken account: 0% mathematical accuracy 0%writing All the semester 0 % Attendance 5 % Class participation 5 % Final Exam Around 15 th week 40 % Grading Scale Letter Grade A+ A B+ B C+ C D+ D F Percentage < 60 The Minimum Pass Mark is 60% Read carefully Attendance: Attendance will be taken in the first 5 minutes of the lecture (lectures). If you came late, you should remind me at the end of the first lecture to consider your attendance for the second lecture, otherwise, you will be marked absent for the two lectures. Excuses for absence should first, be submitted to me via an application form within one week after the absent lectures, and secondly, be sent to the absences committee which dispenses the acceptance or the rejection of your demand (Absence from lectures shall not exceed 15%). Every student should be present 10 minutes before the examination hour. Textbook: It is necessary to have your own textbook. The textbook is essential for course comprehension. It is highly recommended to read the chapter relative to the syllabus. You can find all the documents related to the course in the provided student course website. Classroom Participation: It is expected that every student participate actively in the discussion at lectures by asking and answering questions, raising issues, making observations and constructive comments, and doing the exercises during the lectures. No collaboration is allowed among students in any of the individual exams. Students are allowed to discuss with other students the solution of homework assignments. You may not share written work or programs with anyone else. You may not receive help on homework assignments from students who have taken the course in previous years, and you may not 4

5 review homework solutions from previous years. In writing up your homework you are allowed to consult any book, paper, or published material. If you do so, you are required to cite your source(s). Simply copying a proof is not sufficient; you are expected to write it up in your own words, and you must be able to explain it if you are asked to do so. Your proofs may refer to course material and to home works from earlier in the semester. Except for this, all results you use must be proved explicitly. Copying solutions or code, in whole or in part, from other students or any other source without acknowledgment constitutes cheating. Any student found to be cheating in this class will automatically receive an F grade and will also be referred to the Office of Student Conduct. Calculator dependency is a BAD thing. Cheating and Dishonesty: Each student should write and submit his own work either on exams or on exercises and other course material. Any kind of plagiarism or dishonesty throughout the course is considered a serious offence and will be dealt with strictness and no mercy. Ethics: Don t use or leave open your mobile phone throughout lectures. Violating this may result in lowering your grade or expelling from the classroom. Try to be at time at the lectures. Office hours: Students are required to come and see me only at the office hours. No students will be accepted outside the office hours. Personal course involvement: Every personal extra exercises or mini projects relative to the course are authorized resulting in increasing your grade. Applications with MATLAB programming are recommended for projects. Standard Format for Homework Problems (a template will be given): A student's work should be neat, well organized, and easy to follow. Written and mathematical rigor are expected for this course. You are expected to follow this standard format. Points may be deducted for work that does not adhere to this format. Use 1cm x9.5 cm white paper for home works. Staple all pages of an assignment together in the upper left corner with a copy of the provided cover letter. 5

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ME 4495 Computational Heat Transfer and Fluid Flow M,W 4:00 5:15 (Eng 177)

ME 4495 Computational Heat Transfer and Fluid Flow M,W 4:00 5:15 (Eng 177) Professor: Daniel N. Pope, Ph.D. E-mail: dpope@d.umn.edu Office: VKH 113 Phone: 726-6685 Office Hours:, Tues,, Fri 2:00-3:00 (or