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Final Exam Study Guide, CPSC 303, Spring 2024

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Examinable Material (Course Coverage) The handout 303: Skills for the Final Exam has a detailed list of skills you should have for each unit below for the final exam. Here is a list of the units we covered, including the corresponding sections in [A&G], and the corresponding sections of the handouts.
  1. Intro to ODE's, Numerical Methods for ODE's:
    1. [A&G]: Sections 2.1 (relative an absolute error), 4.2 (vector and matrix morms), 14.1 (numerical differentiation via Taylor series), 16.1 (initial value ODE's), 16.2 (Euler's method).
    2. CPSC 303: Introduction to ODE's (and Review of Calculus for Numerical Methods), all Sections except material on angular momentum (the part of Section 4 starting in Example 4.4), and Appendices A and B. (For a review of separable ODE's, we recommend Section 2.4 of UBC Math's Calculus Textbooks.)
    3. Rough correspondence to: classes 01_08 to 01_26 and Homework 1-4.
  2. Recurrence Relations (and ODE analogs), Normal and Subnormal Numbers (in Double Precision):
    1. [A&G]: 2.4 (IEEE standard).
    2. CPSC 303: Recurrence Relations and Finite Precision (2020), Sections 1-4, Sections 5.3, 5.4, Appendices A-C (some of this material overlaps with the ODE material). CPSC 303: Normal and Subnormal Numbers in Double Precision (2020).
    3. Rough correspondence to: classes 01_29 to 02_07 and Homework 4-5.
  3. Polynomial Interpolation:
    1. [A&G]: Sections~10.1-10.5, and 10.7 (we covered 10.7 only for Hermite interpolation with two points, needed for splines).
    2. CPSC 303: What the Condition Number Does and Does Not Tell Us (2020). CPSC 303: Remarks on Divided Differences (2024).
    3. Rough correspondence to: classes 02_09 to 03_13 and Homework 6-8.
  4. Splines:
    1. [A&G]: Section 11.3 (formulas for natural splines).
    2. CPSC 303: Energy in Cubic Splines, Power Series as Algorithms, and the Initial Value Problem (2020).
    3. Rough correspondence to: classes 03_18 to 04_03 and Homework 8-9.
  5. The Heat Equation (and relationshiop to splines):
    1. CPSC 303: Adjacency Matrices, Splines, and the Heat Equation (2024).
    2. Rough correspondence to: classes 04_05 to 04_08 and Homework 10.
  6. More topics in ODE's (stiff equations and checking numerical schemes):
    1. Parts of [A&G], Sections 16.2 and 16.3.
    2. Rough correspondence to: classes 04_10 to 04_12 and some practice final questions.
Homework, Midterm Practice, and Midterm You should make sure you can do all problems on the homeworks, and that you understand the solutions, except for the bonus Problem 5 on Homeworks 8 and 9. You should make sure you can do the practice midterm problems; here are some brief solutions. You should make sure you can do the 2024 midterm problems.
Practice Problems for the Final Exam Past the Midterm Here are: a first practice problems for the final exam and solutions, and a second practice problems for the final exam and solutions.

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