ACMS 40390-02: Fall 2019 – Numerical Analysis

Course Information

Instructor: Guosheng Fu, gfu@nd.edu 201D Crowley Hall
Office phone number: (574) 631-9291

Class time: M, W, F, 02:00pm-02:50pm
Classroom: 109 Pasquerilla Center
Teaching assistant: TBD

Office hours:
Fu: T 3:00-5:00pm or by appointment and drop-in (when available), 201D Crowley Hall

Textbook: Richard L. Burden and J. Douglas Faires, Numerical Analysis, 10th Edition.

Prerequisites:
(MATH 20750 or MATH 20860 or MATH 30650 or ACMS 20750 or PHYS 20452) and (ACMS 20620 or MATH 20610) and ACMS 20210.

The course requires a certain amount of programming. Matlab is the preferred programming language. However, you may also use other programming language including C, C++, Fortran, Python or Mathematica.

Syllabus is here

Tips about Matlab programming:

Important Dates

First test review Monday, 09/23

in class
First in class test Wednesday, 09/25

in class
Second test review Monday, 10/28

in class
Second in class test Wednesday, 10/30

in class
Final exam TBD

TBD

Week 1:

  • Wednesday (08/28): Section 1.1 HW(due on 09/04): Section 1.1: 2(c), 4(b), 6(c)
  • Section 1.1 Review of Calculus


  • Friday (08/30): Section 1.1 HW(due on 09/04): Section 1.1: 19, 25(b)


Week 2:

Week 3:

Week 4:

Week 5:

Week 6:

Week 7:

  • Monday (10/07): Section 3.4 HW6(due on 10/16): Section 3.4:
    2(a)[Use both Theorem 3.9 and divided difference method to construct Hermite polynomial],4(a), 7[do H3 only]
  • Section 3.4: Hermite Interpolation


  • Wednesday (10/09): Section 3.4
    HW6(due on 10/16): Section 3.4: 10

  • Friday (10/11): Section 3.5
    HW6(due on 10/16): Section 3.5: 11,13
  • Section 3.5: Cubic Spline Interpolation



Week 8:

Week 10:

  • Friday (11/01): Section 4.1, Section 4.3
    HW8(due on 11/13): Section 4.3: 1(a,c), 3[Find error bound and actual error for 1(a,c); hint: for 1(c), antiderivative is x^3 (ln(x)/3-1/9)], 5[repeat 1(a,c) using Simpson’s rule].
  • Section 4.3 Elements of Numerical Integration



Week 11:

Week 12:

Week 13:

  • Monday (11/18): Section 5.4
    Section 5.4 Runge-Kutta Methods
    HW10(due on 12/04): Section 5.4: 2(d), 7[repeat for 2(d)], 15[repeat for 2(d)].

  • Wednesday (11/20): Section 5.6
    Section 5.6 Multistep Methods
    HW10(due on 12/04): Section 5.6: 1(a)[use AB2 and AB3 methods only].
  • Last Computer Project (due on Wed Dec 11, please start early!!!): ComputerProject4


  • Friday (11/22): Section 5.6 (interactive MATLAB session)


Week 14:

Week 15:

  • Monday (12/02): Section 5.11
    HW11(due on 12/11):
    Section 5.10: 5(a) [Hint: for analyzing consistency by local truncation error, do 3rd order Taylor expansion for y_{i-2}, y_{i-1} and y_{i+1} about y_i respectively. In the difference equation, replace the approximate solution by exact values and plug these Taylor expansions into the equation. See what you have after some cancellation.]
    Section 5.11: 10.
  • Section 5.11: Stiff Differential Equations

  • Wednesday (12/04): Section 6.1
    HW11(due on 12/11):
    Solve the linear system Ax=b using the Gaussian elimination with back-substitutions, where
    the unknown vector x=[x_1; x_2; x_3],
    the matrix A = [5, 1, 4; 10, 4, 7; -15, 5, -9]
    and the right hand side b = [19; 39; -32]
  • Section 6.1: Linear System of Equations


  • Friday (12/06): Section 6.2
    HW11(due on 12/11): Section 6.2: 20 [do 10(c)]
  • Section 6.2: Pivoting Strategies


Week 16: