e01 : First Midterm

exam date	description	ready?	info
Wed 02/06 09:30AM	First Midterm	true	e01

The midterm exam will be in class on Wednesday, February 6 from 9:30am to 10:45am.

Rules

Phones off! You may use notes or written materials, but no electronic devices of any kind. You won’t need to do any complicated numerical calculations, and if we ask you for Python code we won’t mark it off for exact syntax or details of argument lists.

Use a dark pen (preferred) or soft pencil, and write your answers legibly within the boxes provided.

Syllabus

The exam covers:

• Assigned readings: NCM sections 2.1-2.6, 5.1, 5.2, 5.5 (but not 2.9 or 1.7), Templates sections on Jacobi and conjugate gradient.

• My slides from lecture 1 (temperature problem) and lecture 5 (CG, only up to “Vector and Matrix Primitives”).

• All the problems on homeworks h01 through h04.

• All the topics covered in lecture through Jan 30 (lect07):

  • Numpy arrays, indexing, and matrix/vector arithmetic
  • The temperature problem
  • Residual, relative residual norm
  • Solving triangular systems
  • LU factorization with and without partial pivoting
  • Cholesky factorization of SPD matrices
  • Jacobi and conjugate gradient (but not their theory)
  • QR factorization
  • Least squares data fitting

  • 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

Sample problems

• Steven will answer questions about the sample problems in section on Tuesday before the exam, but you will have to work them yourself before section in order to be prepared!

• 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. The following homework problems are in the format of exam problems as they stand:

  • h01 problems 1 through 7
  • h02 problems 1, 3, 4, and 5
  • h03 problems 1, 2, 3, and 6
  • h04 problems 3 (though we wouldn’t ask for correct syntax) and 4

• Here are some other sample problems.