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Math 340 Numerical Analysis Instructor

Lecture Hours

Dr. C. H. Lee

MWF 11:00-11:50 MH-452

Office MH 182 E

Text Book

Office Hours MWF 10AM-11AM Phone 657-278-2726 E-mail [email protected]

URL newton.fullerton.edu

Exam Dates Exam 1 Chapters 1-3

Friday Sept. 30

Exam 2 Chapters 1-5

Friday Nov. 04

Final Exam Comprehensive

Wed. Dec. 14

Grade Distribution Homework

15%

Numerical Analysis 10th Edition by Richard L. Burden, J. Douglas Faires & Annette M. Burden

Course Description Math 340 is a first course in numerical analysis. The purpose of Math 340 is to introduce some of the many methods for solving scientific problems on a modern computer. In this course we focus on approximate numerical solutions of nonlinear equations and linear systems, ordinary differential equations, methods of interpolation, numerical differentiation and integration, and iterative techniques for solving large systems of equations and eigenproblems.

Grade Scale 93%-100%

A

90%-92.9%

A-

87%-89.9%

B+

83%-86.9%

B

80%-82.9%

B-

Quizzes

15%

CAP

5%

Exam 1

20%

77%-79.9%

C+

Exam 2

20%

70%-76.9%

C

Final Exam

25%

60%-69.9%

D

Total

100%

0%-59.9%

F

Important Remarks Withdrawal deadlines: Tue-Sep 07, 2016 Drop without a “w” Fri-Sept 30, 2016 Drop without documentation Fri-Nov 11, 2016 Proper Documentation required Class Attendance & Participation (CAP): Make every effort to be in class on time. Perfect attendance and actively participating in class will earn you 100 CAP points. You are allowed to have one absence. Each absence thereafter will cost you 5 points. Being tardy or leaving class early twice is equivalent to one absence. Electronics Devices: Using personal electronic devices (PED) in class can distract instruction and learning. No PEDs such as cell phones and tablets are allowed in class. Ten CAP points will be deducted for texting or using PEDs in class. Academic Dishonesty: Students who violate university standards of academic integrity are subject to disciplinary sanctions, including failure in the course and suspension from the university. Since dishonesty in any form harms the individual, other students and the university, policies on academic integrity are strictly enforced. Academic dishonesty violations include, but are not limited to, copying from another student’s homework, term paper, or exam, possessing or using unauthorized materials during the exam, or allowing another student to copy your work.

Homework: Homework assigned in the current week is due on Friday of the following week. Homework must be carried step by step. Solutions alone are not acceptable. Computer assignments: Computer programing assignment must be typed up as a Word document with both the code and the results and/or figures, as needed. Assignments & Exams: To guarantee your work are graded and returned promptly , NO late assignments will be accepted. No make-up exam except in very special circumstances. (call in advance & documentation required). Emergency situations: Know your nearest emergency exit. In the event of a fire or an emergency, take all your personal belongings, leave the building using the nearest stairs, go to the lawn areas on Nutwood Avenue, and stick with class. Do not use the elevators. If an earthquake happens, you need to Drop, Cover and Hold On. No evacuation is needed. Anyone who may have difficulty evacuating the building, please see the instructor. In general: It’s recommended that you read ahead and be familiar with new material, terms and concepts before the lecture. Spend twelve hours o more a week for this course outside of class. Collaboration are welcome, but ALL work must be turned in individually. Finally, make good use of instructor’s office hours.

Course Materials MATHEMATICAL PRELIMINARIES AND ERROR ANALYSIS. Review of Calculus. Round-off Errors and Computer Arithmetic. Algorithms and Convergence. Numerical Software and Chapter Summary. SOLUTIONS OF EQUATIONS IN ONE VARIABLE. The Bisection Method. Fixed-Point Iteration. Newton's Method and Its Extensions. Error Analysis for Iterative Methods. Accelerating Convergence. Zeros of Polynomials and Müller's Method. Numerical Software and Chapter Summary. INTERPOLATION AND POLYNOMIAL APPROXIMATION. Interpolation and the Lagrange Polynomial. Data Approximation and Neville's Method. Divided Differences. Hermite Interpolation. Cubic Spline Interpolation. Parametric Curves. Numerical Software and Chapter Summary. NUMERICAL DIFFERENTIATION AND INTEGRATION. Numerical Differentiation. Richardson's Extrapolation. Elements of Numerical Integration. Composite Numerical Integration. Romberg Integration. Adaptive Quadrature Methods. Gaussian Quadrature. Multiple Integrals. Improper Integrals. Numerical Software and Chapter Summary. INITIAL-VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS. The Elementary Theory of Initial-Value Problems. Euler's Method. Higher-Order Taylor Methods. Runge-Kutta Methods. Error Control and the Runge-Kutta-Fehlberg Method. Multistep Methods. Variable Step-Size Multistep Methods. Extrapolation Methods. Higher-Order Equations and Systems of Differential Equations. Stability. Stiff Differential Equations. Numerical Software and Chapter Summary. DIRECT METHODS FOR SOLVING LINEAR SYSTEMS. Linear Systems of Equations. Pivoting Strategies. Linear Algebra and Matrix Inversion. The Determinant of a Matrix. Matrix Factorization. Special Types of Matrices. Numerical Software and Chapter Summary. ITERATIVE TECHNIQUES IN MATRIX ALGEBRA. Norms of Vectors and Matrices. Eigenvalues and Eigenvectors. The Jacobi and Gauss-Siedel Iterative Techniques. Relaxation Techniques for Solving Linear Systems. Error Bounds and Iterative Refinement. The Conjugate Gradient Method. Numerical Software and Chapter Summary.

PROGRAMMING LANGUAGE—MATLAB You are required to use MATLAB for your homework assignments.

MATLAB is available for free to all CSUF students. You are responsible for downloading MATLAB. Please visit the following link for instructions: http:// itwebstg.fullerton.edu/it/students/ matlab_students.asp

MATLAB is also available during school hours in the Math Department's computer lab MH 47.

If you need help getting started with MATLAB, the MathWorks offers free online video tutorials www.mathworks.com/academia/student_center/ tutorials

Students with Special Needs On the CSUF campus, the office of Disable Student Services (DDS) has been delegated the authority to certify disabilities and to prescribe specific accommodation for students with documental disabilities. DSS provides support services for students with mobility limitations, learning disabilities, hearing or visual impairments, and other disabilities. Counselors are available to help students plan a CSUF experience to meet their individual needs. If you feel you require such support services, contact the Office of Disable Students Services, located in UH 101, at (657) 2783117; or: (657) 278 – 3112.

Learning Goals a. To understand and appreciate the various ways in which numerical analysis is used to solve problems in engineering and the physical sciences. b. To demonstrate knowledge of basic numerical methods and their limitations. c. To understand the source, propagation, magnitude, and rate of growth of errors, and to demonstrate knowledge of methods for detecting, estimating, and controlling errors. d. To utilize computer algorithms for numerical solutions and explain the overall process (and the particular steps) of a numerical method. e. To demonstrate a sense of mastery and confidence in the ability to solve problems that require numerical solutions. Note: These goals are achieved through the course work, including homework, classroom activities, projects, and exams.

Course Schedule

Math 340 — Numerical Analysis — CSUF — Fall 2016 — Prof. Charles H. Lee

Week of

Monday

Wednesday

Friday

8/22/16

8/26/16

Orientation Introduction to Matlab

Introduction to Matlab

Review of Calculus

8/29/16

9/2/16

Round-Off Errors & Computer Arithmetic

Algorithms & Convergence

Bisection Method

9/5/16

9/9/16

Labor Day

Fixed-Point Iteration

Newton’s Method & Its Extensions

9/12/16

9/16/16

Error Analysis for Iterative Methods

Accelerating Convergence

Zeros of Polynomials & Muller’s Method

9/19/16

9/23/16

Interpolation & Lagrange Polynomial

Data Approximation & Neville’s Method

Divided Differences

9/26/16

9/30/16

Hermite Interpolation

Review

Exam 1

10/3/16

10/7/16

Cubic Spline Interpolation

Numerical Differentiation

Richardson’s Interpolation

10/10/16

10/14/16

Elements of Numerical Integration

Composite Numerical Integration

Romberg Integration

10/17/16

10/21/16

Adaptive Quadrature Methods

Gaussian Quadrature

Initial-Value Problems

10/24/16

10/28/16

Euler’s Method

Higher-Order Taylor Methods

Runge-Kutta Methods

10/31/16

11/4/16

Error-Control & The RungeKutta-Fehlberg Method

Review

Exam 2

11/7/16

11/11/16

Linear Systems of Equations

Pivoting Strategies

Linear Algebra & Matrix Inversion

11/14/16

11/18/16

Determinant of a Matrix

Matrix Factorization

Special Types of Matrices

11/21/16

11/25/16

Happy Thanksgiving

Happy Thanksgiving

Happy Thanksgiving

11/28/16

12/2/16

Norms of Vectors and Matrices

Eigenvalues & Eigenvectors

The Jacobi and GaussSeidel Iterative Techniques

12/5/16

12/9/16

Relaxation Techniques for Solving Linear Systems

Error Bounds & Iterative Refinements

Review

12/12/16

12/16/16

Comprehensive Final Exam 12:00-1:50 p.m.