# 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:**

- To use Matlab, go to the University’s oit software download page https://oit.nd.edu/services/software/software-downloads/matlab/ to get a copy to install on your computer. Here is a Matlab user guide: Interactive Matlab Course, you may also find this introduction-to-matlab useful, and here is a cheatsheet

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

Section 1.1 Review of Calculus

**Week 2:**

- Monday (09/02): Section 1.2 HW(due on 09/11): Section 1.2: 19(a,b), 20[for numbers given in 19(a,b)]
- Wednesday (09/04): Section 1.2

HW(due on 09/11): Section 1.2: 3(b), 4(a), 6(c), 14(a, b, d[find relative error obtained from 14(b)]) - Friday (09/06): Section 1.2, Section 1.3

Section 1.3 Algorithms and Convergence

HW(due on 09/11): Section 1.2: 16(b), 21, 25(a), 26

Section 1.2 Round-off Errors and Computer Arithmetic

Decimal-Binary-Convertion (one page)

**Week 3:**

- Monday (09/09): Section 1.3

HW(due on 09/18): Section 1.3: 6(b), 7(b), 11 - Wednesday (09/11): Section 2.1

HW(due on 09/18): Section 2.1: 1, 11(a,b), 14[find approximation correct to within 0.01] - Friday (09/13): Section 2.2

HW(due on 09/18): Section 2.2: 1(d), 4(a)[only compute p1, p2, p3, p4], 10[Replace 10^-4 by 10^-3 in the problem statement. Hence, for the fixed pt algorithm, stopping criterion is |p_n-p_n-1|<10^-3.]

Section 1.3 Algorithms and Convergence

Pseudo_Code_Summary

Section 2.1 The Bisection Method

**Matlab code (PDF format):** *The .m files are also sent out via google group (for technical reasons, I can not upload .m files in this page)*

Matlab: bisection demo

Matlab: bisection demo (full)

**First Computer Project (due on Wed Oct 2):** ComputerProject1

Section 2.2 Fixed-Point Iteration

**Matlab code (PDF format):**

Matlab: fixed-pt demo

**Week 4:**

- Monday (09/16): Section 2.2, Section 2.3

HW(due on 09/27): Section 2.3: 1, 6(a) - Wednesday (09/18): Section 2.3, Section 2.4

HW(due on 09/27): Section 2.3: 4(a), 30 - Friday (09/20): Section 2.4

HW(due on 09/27): Section 2.4: 10[hint: write f(x)=(x-p)^m q(x)], 14

Section 2.3 Newton’s Methods and its Extensions

**Matlab code (PDF format):**

Matlab: (another) fixed-pt iter. demo

Matlab: newton demo

Section 2.4 Error Analysis for Iterative Methods

**Matlab code (PDF format):**

Matlab: secant method demo

**Matlab code (PDF format):**

Matlab: Newton’s method demo2

Matlab: modified Newton’s method demo2

**Week 5:**

- Friday (09/27): Section 2.5

HW5(due on 10/09): Section 2.5: 4,6

Section 2.5 Accelerating Convergence

**Matlab code (PDF format):**

Matlab: Steffensen’s method

**Week 6:**

- Monday (09/30): Section 3.1

HW5(due on 10/09): Section 3.1: 2(d),9, 23 - Wednesday (10/02): Section 3.1

HW5(due on 10/09): NO HW TODAY - Friday (10/04): Section 3.3

HW5(due on 10/09): Section 3.3: 7(a), 14, 16

Section 3.1 Interpolation and Lagrange Polynomial

**Second Computer Project (due on Wed Nov 6):** ComputerProject2

Section 3.3: Divided Differences

**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] - 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 3.4: Hermite Interpolation

Section 3.5: Cubic Spline Interpolation

**Week 8:**

- Monday (10/14): Section 3.5

HW7(due on 11/01): Section 3.5: 4(c),6(c) - Wednesday (10/16): Section 3.5

HW7(due on 11/01): Section 3.5: 21(a),(c)[Use Theorem 3.13 to estimate max|f(x)-s(x)| only] - Friday (10/18): Section 4.1

HW7(due on 11/01): Section 4.1: 2(b),4(b), 6(c), 8(c), 10(a)

Thomas Algorithm for Tridiagonal Linear System

Section 4.1 Numerical Differentiation

**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:**

- Monday (11/04): Section 4.3

HW8(due on 11/13): Section 4.3: 19, 22, 23. - Wednesday (11/06): Section 4.4

HW8(due on 11/13): Section 4.4: 1(a,c), 3[for 1(a,c)], 13(a,b). - Friday (11/08): Section 4.7

HW8(due on 11/13): Section 4.7: 1(a,c).

Section 4.4 Composite Numerical Integration

**Third Computer Project (due on Wed Nov 20, please start early!!!):** ComputerProject3

Section 4.7 Gaussian Quadrature

**Week 12:**

- Monday (11/11): Section 4.7, Section 5.1

Section 5.1 The Elementary Theory of Initial Value Problems/Section 5.2 Euler’s Method

HW9(due on 11/25): Section 5.1: 1(a), 2(a), 3(a). - Wednesday (11/13): Section 5.2, Section 5.3

Section 5.3 High-order Taylor Methods

HW9(due on 11/25): Section 5.2: 1(a), 3(a). - Friday (11/15): Section 5.3.

HW9(due on 11/25): Section 5.3: 1(a), 10(a), Discussion problem 1.

Some mathematicians we met in class:

Brook Taylor (1685-1731)

Leonhard Euler (1707-1783)

**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]. - Friday (11/22): Section 5.6 (interactive MATLAB session)

**Last Computer Project (due on Wed Dec 11, please start early!!!):** ComputerProject4

**Week 14:**

- Monday (11/25): Section 5.10

Section 5.10: Zero-Stability

**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.

- 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]**

- Friday (12/06): Section 6.2

HW11(due on 12/11): Section 6.2: 20 [do 10(c)]

Section 5.11: Stiff Differential Equations

Section 6.1: Linear System of Equations

Section 6.2: Pivoting Strategies

**Week 16:**

- Monday (12/09): Section 7.3

Section 7.3: Jacobi and Gauss-Siedel Iterative methods