e02 : Second Midterm

exam date	description	ready?	info
Wed 03/06 09:30AM	Second Midterm	true	e02

The midterm exam will be in class on Wednesday, March 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 1.7, 2.9, 10.1, 10.2, 10.5, 7.1-7.5, 7.9
  • The $25,000,000,000 Eigenvector: All of Section 1 and Section 2, Section 3 through 3.1, Section 4 first two paragraphs.

• All the problems on homeworks h05 through h07.

• All the topics covered in lecture from February 4 (lect08) through February 27 (lect13).

  • Matrix condition number
  • Sensitivity analysis of Ax = b
  • IEEE standard 64-bit floating-point arithmetic
  • The numpy/scipy eigenvalue/eigenvector routines linalg.eig() and linalg.eigh()
  • Graphs and their adjacency matrices and Laplacian matrices
  • The PageRank algorithm
  • Standard form of an ODE
  • The scipy ODE routine integrate.solve_ivp()
  • Systems of ODEs
  • ODEs with higher derivatives
  • Plotting solutions to ODE and phase space plots
  • The Lotka-Volterra equations
  • The harmonic oscillator
  • Euler’s algorithm (forward Euler)
  • The RK23 (or BS23) algorithm
  • The backward Euler algorithm
  • Stiff ODEs

Sample problems

• Here are some 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.

Regrade requests

The deadline for regrade requests (via GradeScope) for this exam is 11:59pm on Monday, March 18.