e03 : Final Exam

exam date	description	ready?	info
Wed 03/20 08:00AM	Final Exam	true	e03

The final exam will be in our regular classroom on Wednesday, March 20 from 8:00am to 11:00am.

Rules

Phones off! You may use any books, notes, or written materials, but no electronic devices of any kind. You won’t need to do any complicated numerical calculations.

Use a dark pen (preferred) or soft, dark pencil, and write your answers legibly within the boxes provided. If your handwriting is too faint for the scanner to pick up, it’s likely that you will not get credit for your answer.

Syllabus

The final exam covers everything we’ve done in the course. The format and content of the final will be very similar to that of the midterms. The final will be longer than a midterm, but I don’t expect it to take the full 3 hours.

You can review the sample problems from the first and second midterms (and also the problems from the midterms themselves).

As usual, we won’t ask you to do any coding on the exam (more than one line), but the exam may ask questions related to any of the homework problems.

• Assigned readings:
  • [NCM]https://www.mathworks.com/moler/index_ncm.html Sections 1.7, 2.1-2.6, 2.9, 5.1, 5.2, 5.5, 7.1-7.5, 7.9, 10.1, 10.2, 10.5, 11.1-11.3.
  • Templates: Sections on [Jacobi]http://www.netlib.org/linalg/html_templates/node12.html and [conjugate gradient]http://www.netlib.org/linalg/html_templates/node20.html.
  • [The $25,000,000,000 Eigenvector]https://github.com/ucsb-cs111/w19-lecture-files/blob/master/02.11/25_Billion_Eigenvector_Original.pdf: All of Section 1, All of Section 2, Section 3 through 3.1, Section 4 first two paragraphs.
• All the problems on homeworks h01 through h08.
• All the topics covered in lecture, below.

Topics from lecture covered on final exam

• Numpy arrays, indexing, and matrix/vector arithmetic
• The temperature problem
• IEEE standard 64-bit floating-point arithmetic
• Interesting matrices:
  • Identity matrix
  • Singular and nonsingular matrices
  • Permutation matrices (and permutation vectors)
  • Triangular and unit triangular matrices
  • Symmetric positive definite (SPD) matrices
  • Orthogonal matrices
• Numerical linear algebra:
  • Solving Ax = b by LU factorization with partial pivoting
  • Solving Ax = b by Cholesky factorization
  • Solving Ax = b by conjugate gradient
  • Solving Ax = b by QR factorization
  • Data fitting with least squares
  • Solving triangular systems
  • Residual vector, relative residual norm
  • Matrix condition number
• Graphs, matrices, and eigenvalues:
  • The numpy/scipy eigenvalue/eigenvector routines linalg.eig() and linalg.eigh()
  • Graphs and their adjacency matrices and Laplacian matrices
  • The PageRank algorithm
• ODEs:
  • The scipy ODE routine integrate.solve_ivp()
  • Standard form of an ODE
  • Systems of ODEs
  • ODEs with higher derivatives
  • The Lotka-Volterra equations
  • The harmonic oscillator
  • Euler’s algorithm (forward Euler)
  • The backward Euler algorithm
  • Stiff ODEs
• PDEs (short answer only, no computation):
  • Poisson equation (the temperature problem)
  • Diffusion equation (time-dependent temperature)
  • Wave equation
• Neural nets (short answer only, no theory or computation)

Regrade requests

The deadline for regrade requests (via GradeScope) for the final exam is 11:59pm Thursday, March 21.