Math 5620 - Math 6865: Introduction to Numerical Analysis II

Instructor: Yekaterina Epshteyn

Lectures: MTWF 10:45 - 11:35 am, LCB 323


Office Hours (tentative (not finalized yet), it may be some changes to the office hours at the beginning of the semester)

M 11:45am - 12:45, W 11:45-12:45 pm, or by appointment
Office: LCB 337
E-mail: epshteyn@math.utah.edu


Prerequisites: "C" or better in Math 5610. Basic Matlab programming.


Textbook and References (to supplement lectures with additional material, however attendance of the lectures is important)

Main Textbooks: 

Numerical Analysis - Mathematics of Scientific Computing by D. Kincaid and W. Cheney, 3rd Edition. ISBN: 978-0-8218-4788-6.

Additional References (you are not required to buy these books): 

Randall J. LeVeque, Finite Difference Methods for Ordinary and Partial Differential Equations: Steady-State and Time-Dependent Problems, SIAM

Kendall Atkinson, An Introduction to Numerical Analysis, Wiley

Kendall Atkinson, Elementary Numerical Analysis, Wiley

E. Suli and D. Mayers, An Introduction to Numerical Analysis, Cambridge 2003

The course

Math 5620 - Math 6865 is the second semester (continuation of a Math 5610/6860) of two semester undergraduate/(beginning graduate) - level sequence in numerical analysis. The second semester focuses primary on introduction to numerical methods for solving differential equations. Accuracy, stability, and efficiency of the algorithms will be studied from both theoretical and computational standpoint.

Graduate Students:  You can take this class as a graduate level class (Math 6865). The lectures are the same for everyone but there may be extra problems for PhD students.

Homework

Homework will be assigned (probably once in two weeks or so)  and collected due on Tuesdays in class (late homework will not be accepted), and will include theoretical analysis and computational assignments.

The computational part should be done using MATLAB, software produced by The MathWorks. The Matlab language provides extensive library of mathematical and scientific function calls entirely built-in. Matlab is available on Unix and Windows. The full set of manuals is on the web in html format. The "Getting Started" manual is a good place to begin and is available in Adobe PDF format.

Students may consult one another and discuss homework problems, however the assignments you turn in must represent your own work

5620 - 6865 Tentative Topics (brief overview of some topics - will be updated/adjusted based on the course progress):

Chapter 6: Approximating Functions: Polynomial interpolation; Divided differences; Error in polynomial interpolation; Best Approximations: Chebyshev Theory.

Chapter 7: Numerical Integration: The Trapezoidal and Simpson rules; Error formulas; Gaussian numerical integration

Chapter 8: Numerical Solution of Ordinary Differential Equations: Taylor-Series methods, Runge-Kutta methods, Linear Multistep Methods for initial value problems of ordinary differential equations (ODEs). Shooting methods, Finite Differences for boundary value problems of ODEs.

Chapter 9: Numerical Solution of Partial Differential Equations:

Parabolic Problems (heat equation example, solution properties, boundary conditions; Implicit methods);

Advection Equation and Hyperbolic Systems (Method of Characteristics, solution properties, boundary conditions; Upwind Methods; The Lax-Wendroff Method);

Elliptic Problems (solution properties, boundary conditions; Finite Difference Approximations).

ADA Statement

The Americans with Disabilities Act requires that reasonable accommodations be provided for students with physical, sensory, cognitive, systemic, learning and psychiatric disabilities. Please contact me at the beginning of the semester to discuss any such accommodations for the course.


Grading: Homework 65%, one Midterm Written Exam 15% - February 28 2014, and one Final Written Exam - 20%, April 28 2014


 


Homework due dates will be announced and posted


 


  • Homework 1 

  • Homework 2 

  • Homework 3 

  • Homework 4 
  • For a vague idea of what to expect on the Midterm Exam (February 28, 2014), see below:  

  • Midterm Practice Exam 
  • For a vague idea of what to expect on the Final Exam (April 28, 2014), see below:  

  • Final Practice Exam 
  • Letter Grade Information (More or Less Standard) 
  • Note: Updated topics, assignments, etc. will be posted on class website. Students are responsible for checking it regularly.