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Computational Methods for Physicists and Materials Engineers

AP3114 Course information

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Lecturer(s) and TA(s)

Lecturer:

Dr Jun Fan (course leader) Email: junfan@cityu.edu.hk Tel: 3442-9978 Office: P6712

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Lecturer(s) and TA(s)

Teaching Assistant(s):

Mr Chun CHANTel: 27844045Email: cchan2242-c@my.cityu.edu.hk

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Aims Computational Science concentrates on solving

scientific problem by computers. The use of software packages and programs to

solve problems in Physics and Materials Engineering will be emphasized.

This course also consists of the formulation and analysis of problems, simulations and modelling, mathematical and numerical analysis, visualisation through graphics, and preliminary programming.

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Aims This course provides an introduction to scientific

problem solving using fourth generation programming languages (4GL), e.g. SciLAB, MATLAB or equivalent.

However, no previous programming experience in MATLAB (or any other language) is needed. The emphasis is on problem solving rather than programming.

Scientific problems from Physics and Materials Engineering will be targeted with the aim of providing an introduction to the use of computers in science for students who may need such skills in the pursue of their Major of studies in Applied Physics and Materials Engineering.

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Course Intended Learning Outcomes

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

No CILOs Level of Importance

1 To analyse and formulate the mathematical models for typical problems in Physics and Materials Engineering.

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2 To attain a basic level of competency in 4GL computational tool, e.g. MATLAB or equivalent, including the use of variables, arrays, matrices, and control structures involving logical statements, and to use MATLAB or equivalent interactively as well as writing simple script files and user-defined functions.

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3 To implement basic numerical methods, for example procedures for numerical root finding, integration, and solution of ordinary differential equations; and to apply such techniques to solve the mathematical models of typical problems in Physics and Materials Engineering.

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4 To understand some of the ways in which computation may lead to misleading results, including a model being invalid and numerical errors such as round-off error.

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Teaching and Learning Activities

TLAs Lectures Practical sessions

Total no of hours

CILO 1 3 6 9

CILO 2 3 6 9

CILO 3 4 8 12

CILO 4 3 6 9

Total (hrs) 13 26 39

Suggested lecture/practical sessions mix: 2 hr lecture + 1 hrs practical session

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Grading of Student Achievement

Grading of Student Achievement: Refer to Grading of Courses in the Academic Regulations (Attachment) and to the Explanatory Notes.

The grading is assigned based on students’ performance in assessment tasks/activities.

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Keyword Syllabus

Typical problems in Physics and Materials Engineering: Time-series analysis, Signal-processing, Heat-transfer/diffusion equation, Stress and strain analysis, Harmonic motion, etc.

MATLAB as a Programmable Calculator: Use built-in functions, scalars, and row-vectors. Perform simple arithmetic operations on vectors and matrices. Use 2D graphics to plot built-in functions.

Flow Control : Write simple m-files. Looping constructs (for/while) and conditional execution (if/else). Working with matrices and the logical data type. Using the ‘find’ command. Be able to solve array problems without looping constructs.

User-Defined Functions : Create user-defined functions.

Uniformly Distributed Random Numbers (Optional): Generating and using random numbers. Simulations as an alternative to analytic methods. Statistical accuracy. Using histograms.

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Keyword Syllabus

The Normal Distribution (Optional): Generating normally-distributed random numbers. Convergence of other distributions to the normal distribution.

The Bisection method : Understand the bisection method for numerical root finding for a function of one variable.

The Newton-Raphson method: Understand the Newton-Raphson method for numerical root finding for a function of one variable.

Statistical description and analysis of data: Statistics and moments, Least-square fitting

Fourier Analysis: Fourier Transform and Spectral analysis, Fast Fourier Transform (FFT)

Solving differential equations (an introduction): Solving ordinary differential equations using MATLAB built-in function ‘ode23’ or ‘ode45’, appreciation of numerical solution to partial differential equation using MATLAB.

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Recommended Reading

Reference Book(s):

Essential MATLAB for Scientists and Engineers, 2nd/3rd/4th/5th Edition, by Brian D. Hahn.

WK Syllabus 1 (Aug. 31,2015) Introduction & simple operations2 (Sep. 7, 2015) Matrix, Statistical description and analysis of data

3 (Sep. 14, 2015)Flow control (script files; for/done, if/else)User-defined functions

4 (Sep. 21, 2015) Plots & Random Numbers5 (Sep. 28, 2015) University Holiday6 (Oct. 5, 2015) Solving Non-linear equations I7 (Oct. 12, 2015) Practical Test 1 (Lectures 1-4)8 (Oct. 19, 2015) Solving Non-linear equations II9 (Oct. 26, 2015) More programming examples 10 (Nov. 2, 2015) Solving differential equations I11 (Nov. 9, 2015) Solving differential equations II12 (Nov. 16, 2015) Fourier Analysis13 (Nov. 23, 2015) Project PresentationRevision (Nov. 30, 2015) Practical Test 2 (All lectures)

Tentative Class Schedule

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Assessment Tasks/Activities

Practical Tests: 60% (20% PT1 & 35% PT2 & 5% small tests) Assignments and lab reports: 40% (10% project, 30% homework) 75% lecture attendance rate must be obtained. Marks will be

deducted for students failing to meet the attendance requirement. Homework due: 9 am Monday, to be submitted online to Canvas Homework late policy: 10% off per day

ATs Assignments & lab reports

Practical tests

Total (%)

CILO 1 10 15 25%CILO 2 10 15 25%CILO 3 10 15 25%CILO 4 10 15 25%

Total (%) 40 60 100%

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Course Website

Login to e-Portal/Canvas

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Any Questions?