# What To Expect on Final Exam

The final exam will cover topics discussed since the midterm.

Final exam questions will be drawn primarily from the following sections of the reading:

• In Heath ch. 7, Interpolation: sections 7.1.3-4, 7.2.6, 7.3.0 (by that I mean the portions of 7.3 before 7.3.1).
• In Heath ch. 8, Integration & Differentiation: sections 8.1.1, 8.2.1, 8.2.4, 8.7.1.
• In Heath ch. 9, IVP: 9.1, 9.2, 9.3.2, 9.4.
• In Heath ch. 10, BVP: 10.1-5.
• In Heath ch. 11, PDE & iterative methods: 11.1.1, 11.3, 11.5.2-3, 11.5.5-7, 11.6. (You might be asked about the computational complexity for some of the iterative methods given information about the eigenvalues and sparseness of the matrices).
• In Burrus, the following chapters/sections: 1, 2.1-4, (also figures 2.11, 2.12, 2.16), 3.1-2, 5.0-1 (pages 50-51), 5.5, 5.7, 6.1 (defn. of moment). Note that you can skip the rest of chapter 6 entirely. Make sure you know the definitions of: scaling function, wavelet function, nested function space, analysis, synthesis, wavelet transform, refinement equation, scaling coefficient (h), wavelet coefficient (h1), vanishing moment, compact support.
• In Bern-Plassmann paper, 1.2, 4.1, 4.4, 4.5. The theoretical results discussed in this paper but not discussed in lecture will not be tested on.
For each of the bullet items above, there will be roughly one question, except two or three questions on chapter 11, and two or three on wavelets. You are also urged to review the lecture notes, of course.

Exam questions will stress conceptual understanding primarily. Knowing the definitions of key concepts and the strengths and weaknesses of various methods is more important, to me, than memorizing formulas. When and if detailed, advanced formulas are needed for a problem (e.g. defn. of a Fourier Transform, wavelet refinement equation, convergence rate of conjugate gradients, formulas for conjugate gradients), they will be provided. You are, however, expected to have memorized more elementary formulas and facts, e.g. the basic formula for function representation using basis functions, Euler's method, Taylor series, computational cost of Gaussian elimination, moment formula, ...

Exam will be closed book, closed notes, no computer. Calculators will not be needed.

15-859B, Introduction to Scientific Computing
Paul Heckbert, 9 Dec. 2000, minor revision 10 Dec.