# MAD 4401 Introduction to Numerical Analysis

### Basic Information

Instructor:  Maia  Martcheva

Office: 469 Little Hall

E-mail: maia@ufl.edu

Course Meetings:  MWF  3:00-3:50 (Period 8)    Lit  219

Office Hours:  W  F  9:35-10:25  (Period 3),   or by appointment

### Exam Schedule:

• Midterm Exam:  March 13, 2019 (in class)
• Final Exam: April   24, 2019 (in class)

Quizzes:  Regular in-class quizzes will be given.

Note 1: You can read more details about the class from the syllabus.

Note 2: This is a class in which programming  is expected. I prefer that you program in MATLAB.  MATLAB code will be given in class and can be found in Canvas.

### Answers to Practice Final Exam:

1. p(x) = (x+1)^2(x-1)^2
2. (a) -1<alpha<1, (b) -2, 3/2,  (c) -2<alpha<3/2
3.  (a) (0,pi/2), (b) many answers possible
4. (a) will not converge, (b) will converge, (c) will converge
5. (a) l21 = 2, l31 = -1 l32 =0, u11 = 2. u12 = 3, u13 = -1, u22 = -2 , u23 = 1, u33 = 3 (b) To solve Ly=b we need 5 MD and 3 AS,  to solve Ux=y we need 5 MD, 3 AS
6. p(x) = a+bx+cx^2 +dx^3,  with  a=0. b= 12, c= -18, d=7
7.  (a) A = -pi^3/6, B = pi^2/2, (b) approx -pi^3/6
8.  (a) 2, (b) 4, (c) 3
9.  (a) n>=4
10.  (a)  L=2, (b) w0=0, w{i+1} = wi+0.25[tie^{3ti}-2wi+0.125(e^{3ti}+tie^{3ti}+4wi)]
11.  a=2/5,  b=4/5
12. (a) proof, (b) O(0.25^n), (c) n> ln pi10^2/ln 4