Math 309 HW3
Sec 2.6 Taylor Series
- Taylor Series and remainders: 6.1
- Taylor Series for one variable: 6.2
- Taylor Series in two vars: 6.3, 6.4 (typical calculation-type quiz/exam problem)
- Convexity and the Hessian 6.7, 6.8 (typical proof quiz/exam problem)
Sec 2.7 Newton's Method
- 1.
- 2. (Hint: the obvious f(x) = x − 1 / a doesn't work but try inverting each term).
- 3. (Ignore the last sentence, i.e. you don't need to prove that the method converges.)
Chapter 3
You may want to review Gaussian Elimination from you linear algebra course, or refer to Appendix A1 of the text.
- 2.1 (this is a typical midterm question.)
Hints:
- (i), (ii), decide which of the spaces are one dimensional, and do the projection onto that space.
- (iii) both spaces are two dimensional, but you can project onto a two dimensional space if you are given an orthogonal basis for it, by just projecting onto each basis vector.
- (iv) check if one of the equations is redundant.
- 2.2 (typical midterm question)
- 2.5
- 3.1 (typical midterm question). Hints; (i) use gaussian elimination to invert the 3 by 3 matrix. (iv) same hint as before
- 3.2 You can do this in matlab, but be careful with your transposes and inverses.
- 3.3