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
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.
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.
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).
For a vague idea of what to expect on the Midterm Exam (February 28, 2014), see below:
For a vague idea of what to expect on the Final Exam (April 28, 2014), see below:
Note: Updated topics, assignments, etc. will be posted on class website. Students are responsible for checking it regularly.