Math 151A : Applied Numerical Methods.

Math 151 : Applied Numerical Methods.

MWF 11:00 AM @ MS 5117

• INSTRUCTORS INFO:
  
  NAME: Jinsun Sohn
  
  EMAIL: jinsunks at math.ucla.edu
  
  OFFICE: MS 7310
  
  OFFICE PHONE: (310)825-8531
  
  OFFICE HOUR: Wed 1-3 PM and by appointment
  

• TA INFO:
  
  NAME: MARSHAK, CHARLES
  
  EMAIL: cmarshak at gmail dot com
  
  OFFICE: MS 6153
  
  OFFICE HOUR: TBA
  

PIC Lab

The PIC Lab is located on the 2nd floor of Boelter Hall and is open for your convenience. The lab is staffed by undergraduate lab assistants who can help you with computer issues. They are not there to help your assignments (if you need help, talk to TA). All machines are equipped with the software(C++, java, Maple, Matlab....) necessary to complete and submit your homework.

Location: Boelter Hall 2817

HOUR: Monday-Thursday 9:00-6:00, Friday 9:00-5:00, Sunday 1:00-5:00

Lab Website: www.pic.ucla.edu/piclab

Class info

• Required Text
  
  R. Burden and J. Faires, Numerical Analysis, 9th Ed., Brooks/Cole
  


• Grading
  
  Your final score will be calculated as follows:
  
  20% homework + 30% midterm + 50% final exam
  
  
  All the scores during the quarter will be recorded in the MyUCLA grading program.
  
  


• Homework
  
  The assignments will be announced in class or posted on the course website HW and in CCLE every Friday night. There are some theoretical problems and computational problems which require some programing languages or mathematical software(like matlab).
  Homework will be collected in class before the start of the Friday lecture and will be returned in the Thursday discussion section the following week.
  
  Late homework will not be accepted under any circumstance.
  Your one lowest homework score will automatically be dropped in calculation your final grade.
  
• Exams
  
  There will be one midterm(11/5) and one final(12/11).
  
  No make-up exam will be given.
  


• Calculator and written materials:
  You may use whatever resources you wish to do the homework, incluidng calculators, textbooks, TA, etc.., although for the each exams and by the end of the course you should be able to do all the homework questions without any assistance.
  

• Schedule
  

Week	Lecture	Subject	reading
Week0	Lecture1 (9/28)	General course overview, Background for programming projects.	1.1
Week1	Lecture2 (10/1)	Computer representation of numbers. Limitations imposed by floating point representation.	1.2
	Lecture3 (10/3)	Errors in floating point arithmetic computations	1.2
	Lecture4 (10/5)	Introduction to the solution of nonlinear equations.The bisection method.	2.1
Week2	Lecture5 (10/8)	Convergence estimates for the bisection method. Errors and residuals.	2.1
	Lecture6 (10/10)	The fixed point iteration1	2.2
	Lecture7 (10/12)	The fixed point iteration2	2.3
Week3	Lecture8 (10/15)	The Newton-Raphson method.	2.3
	Lecture9 (10/17)	The secant method. The method of false position. Rates of convergence.	2.3, 2.4
	Lecture10 (10/19)	Error analysis for Newton-Raphson and the secant method.	2.4
Week 4	Lecture11 (10/22)	Multiple roots of a function. Comparison of iterative methods. Global convergence properties.	2.4
	Lecture12 (10/24)	Polynomial Interpolation. Method of undetermined coefficients. (Vandermonde matrix.)	3.1
	Lecture13 (10/26)	Newton Divided differences.	3.3
Week5	Lecture14 (10/29)	Lagrange Interpolation Formula. Interpolant existence and uniqueness.	3.1
	Lecture15 (10/31)	Polynomial interpolation error estimates. (Error estimate for equispaced nodes*.)	3.1, 3.2
	Lecture16 (11/2)	Runge phenomenon. Neville's method.	3.2
Week6	Lecture17 (11/5)	Midterm
	Lecture18 (11/7)	Numerical differentiation.	4.1
	Lecture19 (11/9)	Error estimates for numerical differentiation formula. Asymptotic error expansions for numerical differentiation.	4.1
Week7	Lecture20 (11/12)	Veterans Day holiday
	Lecture21 (11/14)	Richardson extrapolation	4.2
	Lecture22 (11/16)	Numerical integration. Newton-Cotes formulas.	4.3
Week8	Lecture23 (11/19)	Composite integration formulas. Numerical integration error estimates. (Aitken estimation of rates of convergence.)	4.3, 4.4
	Lecture24 (11/21)	Composite integration formulas.Gauss quadrature.	4.4, 4.7
	Lecture25 (11/23)	Thanksgiving holiday
Week9	Lecture26 (11/26)	Gauss quadrature., derivation of 2 and 3 point formulas. Error estimates.	4.7
	Lecture27 (11/28)	Solving linear systems of equations. Review of Gaussian elimination.	6.1, 6.5
	Lecture28 (11/30)	Equivalence of Gaussian elimination and LU factorization.	6.5
Week10	Lecture29 (12/3)	Construction of the LU factorization. Pivoting. Use of the LU factorization.Operation counts for Gaussian elimination (LU factorization).	6.2, 6.6
	Lecture30 (12/5)	(Special type of matrices. Band solvers, Choleski factorization.)	6.6
	Lecture31 (12/7)	Review
Final	12/11 (Thesday)	8:00AM-11:00AM at TBA