MATH 3311: Introduction to Numerical Methods

 

Course Outline- Fall 2014

 

1.      Instructor

Name: Mo Mu

Contact Details: mamu@ust.hk, Rm3436, x7446, http://www.math.ust.hk/~mamu

Office Hours: Thursday 12:00-13:00

 

2.      Teaching Assistant

Name: Taylor, Michael

Contact Details: mtaylor@ust.hk

 

3.      Meeting Time and Venue

Lectures:

Date/Time: Mon and Wed (10:30--11:20)

Venue:

Tutorials:

T1A    Mon from 6:00pm to 6:50pm

 

4.      Course Description

Credit Points: 2

Corequisite(s): MATH 2010 OR MATH 2011 OR MATH 2021 OR MATH 2023 OR MATH 3043

Exclusion: MATH 3312, MECH 4740, PHYS 3142

Brief Information/synopsis:

Computer arithmetic, solution of nonlinear equations, interpolation and approximation, numerical differentiation and integration, solution of differential equations, and matrix computation 

5.      Intended Learning Outcomes

Upon successful completion of this course, students should be able to:

No.

ILOs

1

Develop an understanding of the core ideas and concepts of Numerical Methods.

2

Be able to recognize the power of abstraction and generalization, and to carry out investigative mathematical work with independent judgment.

3

Be able to apply rigorous, analytic, highly numerate approach to analyze and solve problems using Numerical Methods.

4

Be able to communicate problem solutions using correct mathematical terminology and good English.

 

6.      Assessment Scheme

Option A: Homework: 10%; Computer Projects 30%, Midterm Exams: 25 %; Final Exam: 35 %

Option B: Computer Projects 30%; Midterm Exams: 30 %; Final Exam: 40 %

 

Total Marks = max{Option A, Option B}

Final grades are determined based on the curve of total marks following the general guidelines of the University.

 

Homework: The TA will announce the due dates and collect the homework assignments and projects, as well as provide the solution keys in the due time.

 

Midterm Test:

Time:10:30-11:20, Wed, Oct 15. (Week 7)

Venue:

Form:

1.      Closed books and notes. No formula sheets are provided.

2.      Calculators approved by Hong Kong Examinations and Assessment Authority (香港考試及評核局) are allowed.

3.      Use 5-(significant) digit rounding arithmetic (see the exact definition in the textbook) in major steps of calculations.

Marks: 100

Topics to be tested in the midterm examination:

Root Finding (Chapter 2)

·         Bisection method (2.1)

·         Fixed-point iteration (2.2)

·         Newton's method, Secant method (2.3)

Interpolation (Chapter 3)

·         Interpolation and the Lagrange (interpolating) polynomial (3.1)

·         Divided differences and Newton's interpolatory divided-difference formula (3.2)

Final Examination:

Time: 12:30-13:30 (60 minutes), Dec. 12, 2014, Room 3008

Form:

1.      Closed books and notes. No formula sheets are provided.

2.      Calculators approved by Hong Kong Examinations and Assessment Authority (香港考試及評核局) are allowed.

3.      Use 5-(significant) digit rounding arithmetic (see the exact definition in the textbook) in major steps of calculations.

Marks: 100

Topics to be tested:

All materials taught in the whole semester will be tested, although including those already tested in the midterm test, however with focus on those not tested in the midterm test.

7.      Student Learning Resources

Text(s): Textbook:

Numerical Analysis (9th Ed), by Burden, R.L. and Faires J. D., Thomson Brooks/Cole.

 

8.      Teaching and Learning Activities

Scheduled activities: 2 hrs (lecture)

 

9.      Course Topics (tentative):

 

 

Mathematical Preliminaries (Chapter 1)

Root Finding (Chapter 2)

Interpolation (Chapter 3)

Numerical Differentiation and Integration (Chapter 4)

Solution of Ordinary Differential Equations (Chapter 5)

Solving Linear Systems (Chapters 6 & 7)

Other topics: Eigenvalue and eigenvector computation, Least squares data fitting, FFT, etc. (tentative)

Hope you enjoy this course. Thank you very much!

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