Math/CS 467/667

467/667 NUMERICAL METHODS II (3+0) 3 credits

Instructor  Course Section                     Time              Room
------------------------------------------------------------------------
Eric Olson  Math 467/667 Numerical Methods I   TR 10:30-11:45am  DMS106

Course Information

Instructor:

Eric Olson

email:

ejolson at unr dot edu

Office:

Tuesday and Thursday 12 noon DMS 238 and by appointment.

Homepage:

http://fractal.math.unr.edu/~ejolson/467/

Required Texts:

Justin Solomon, Numerical Algorithms: Methods for Computer Vision, Machine Learning and Graphics, CRC Press, 2015.

Supplemental Texts on Numerical Methods:

David Kincaid and Ward Cheney, Numerical Analysis: Mathematics of Scientific Computing, 3rd Revised Edition, Pure and Applied Undergraduate Texts, American Mathematical Society, 2002.

Richard Burden, Douglas Faires and Annette Burden, Numerical Analysis, 10th Edition, Brooks Cole, 2015.

Joe Hoffman and Steven Frankel, Numerical Methods for Engineers and Scientists, Second Edition, CRC Press, 2001.

Classic Texts on Numerical Methods:

Kendall Atkinson, An Introduction to Numerical Analysis, Second Edition, Wiley, 1989.

Richard Hamming, Numerical Methods for Scientists and Engineers, Second Edition, Dover, 1986.

Eugene Isaacson, Analysis of Numerical Methods, Revised Edition, Dover Books on Mathematics, 1993.

Supplemental Texts on Computer Programming:

JTC1/SC22/WG14, C99 Programming Standard, ISO/IEC, 2007.

Simon Long, Learn to Code with C, MagPi, 2017.

Richard Smedley, Conquer the Command Line, MagPi, 2016.

Classic Texts on Computer Programming:

Brian Kernighan, Dennis Ritchie, C Programming Language, 2nd Edition, Prentice Hall, 1988.

Brian Kernighan, Rob Pike, Unix Programming Environment, Pretice-Hall Software Series, 1984.

Student Learning Outcomes

1. Students will be able to use Taylor and Runge-Kutta methods to solve initial value problems for ordinary differential equations.
2. Students will be able to use the shooting and finite difference methods to solve boundary value problems for ordinary differential equations.
3. Students will be able to use numerical techniques to solve elliptic, parabolic and hyperbolic partial differential equations.

Announcements

[20-May-2018] Solutions to Project 2

[14-May-2018] Sample Final Exam

[15-May-2018] Final Exam and Project 2

[13-May-2018] Solution to Exam 2

[12-May-2018] Solution of Programming Project 1

[07-May-2018] Convergence of Euler's Method

[03-May-2018] Exam 2

[18-Mar-2018] Programming Project 1

[13-Mar-2018] Homework 1 Solutions

[11-Mar-2018] Lecture Notes on Gauss Quadrature

[26-Feb-2018] Lecture Notes on Taylor's Theorem

Extra Credit

1. Consider the finite difference approximation of the derivative
   f'(x) ≈ (f(x+h)-f(x-h))/(2h)

   Find conditions on f which guarantee there exists a value m>0 such that

   m h² ≤ |f'(x)-(f(x+h)-f(x-h))/(2h)|

   for all h sufficiently small. Give an explicit estimate for m.

2. Find the constant K for the trapezoid method such that
   |∫_a^b f(x)dx-rintavg(n,a,b,f)| ≤ K h² where h=(b-a)/n

   that is better than the one given in class.

Sample Code

• [25-Jan-2018] Color the complex plane.
• [30-Jan-2018] Basin of Attraction for Newton's Method.
• [01-Feb-2018] First order approximation of derivative.
• [06-Feb-2018] Complex variable technique to avoid loss of precision.
• [08-Feb-2018] Second order approximation of derivative.
• [13-Feb-2018] Richardson extrapolation for derivative and Riemann sums.
• [15-Feb-2018] Preliminary files and convergence of trapezoid method.
• [20-Feb-2018] Newton-Cotes Formula in Maple.
• [22-Feb-2018] Adaptive 2-3 quadrature (integration) and parallel version.
• [27-Feb-2018] Orthogonal Polynomials
• [01-Mar-2018] Gaussian Quadrature
• [27-Mar-2018] Taylor Second Order Method
• [05-Apr-2018] Adaptive Taylor ODE Solver (incomplete)
• [10-Apr-2018] Adaptive Taylor ODE Solver
• [12-Apr-2018] Adaptive Taylor ODE Solver Version 2
• [17-Apr-2018] Adaptive Taylor ODE Solver Version 3
• [19-Apr-2018] RK4 ODE Solver
• [24-Apr-2018] Writing a Report using LaTeX
• [26-Apr-2018] Heat Equation (incomplete)
• [01-May-2018] Heat Equation
• [08-May-2018] Linear Stability Domain for RK2

Programming Assignments

• Programming project 1 due April 26, 2018 (solution).
• Programming project 2 is due at the Final Exam on May 15.

Homework Assignments

• Homework 1: Exercises 14.1, 14.2, 14.4(a), 14.5, 14.6(a-f), 14.10, 14.11
• Homework 2: Programming Project 2 counts as Homework 2.

Grading

     2 Exams                   50 points each
     1 Final Exam             100 points
     2 Homework Assignments    20 points each
     2 Programming Projects    20 points each
     In-class Lab Work         60 points
    ------------------------------------------
                              340 points total

    Grade        Minimum Percentage
      A                 90 %
      B                 80 %
      C                 70 %
      D                 60 %

Final Exam

The final exam is scheduled for

• Tuesday, May 15 from 9:50-11:50am in DMS106.

Equal Opportunity Statement

Academic Conduct

The following is new university policy: Surreptitious or covert video-taping of class or unauthorized audio recording of class is prohibited by law and by Board of Regents policy. This class may be videotaped or audio recorded only with the written permission of the instructor. In order to accommodate students with disabilities, some students may be given permission to record class lectures and discussions. Therefore, students should understand that their comments during class may be recorded.