Quiz 2 Review
Quiz 2 will be in the DMS106 computer lab. The first part of the exam
will be without computers; the second part you will use a computer. Do
not type or use the mouse until the first part of the quiz has been
collected. This review sheet has been prepared to help focus your
studying. The exact exam will have fewer and possibly
some different questions.
Review Topics
- State Taylor's theorem with remainder for
a scalar function in one variable.
- Find the 2-norm of a matrix A in terms of the eigenvalues
of the matrix B=A†A. Note that the
definition of the matrix 2-norm in the book on page 3 is
incorrect.
What the book defined is, in fact, the Frobenius matrix norm.
- State the RK4 tableau from memory.
- Translate an RK tableau into code.
- Explain in 2 to 3 paragraphs what the shooting
method is and how it can be used to solve a 2-point
boundary value problem.
- Show that the Gaussian quadrature formula on n+1 points
is exact for polynomials of degree 2n+1.
- Use the finite difference method to solve a 2-point
boundary value problem.
- State the Thomas algorithm for solving Ax=b where A
is a tridiagonal matrix.
Tue Oct 14 14:55:35 PDT 2014