Applied Mathematics 3:        MATH 3076 and MATH 3976 (Advanced)

 

Information & Course Outline 2015

 

Lecturer:        Dr David Ivers             Contact:          Room: Carslaw 623

Phone: 9351 3561

Email: david@maths.usyd.edu.au

Consultation:              Tuesday 1-2 pm  Carslaw 623, or by appointment or by chance.

 

Structure and Teaching Methods:

Lectures (three per week):      Tue 3-4  Carslaw 375  Wed  3-4  Carslaw 375   Thu 3-4  Carslaw 375

Computer Labs (one per week beginning week 2):

Tues 4-5  Carslaw 705/6          Wed  2-3  Carslaw 729/30       Thurs 2-3 Carslaw 705/6

 

Objectives: The broad aim of this course is to give students knowledge and hands-on experience in the use of computers in the mathematics-based sciences.  MATH3076 Mathematical Computing and MATH3976 Mathematical Computing (Advanced) both consist of two distinct Parts, each worth 50% of the course and lasting approximately 6–7 weeks. Specific objectives are to develop  logical thinking, and the ability to formulate problems mathematically and to solve problems computationally using the following:

 

Part 1              Introduction to Fortran90 Programming, Weeks 1–7

Main Topics of Part 1:

1)         Introduction / Overview          

2)         Basics & Perspective

3)         Programming

4)         Variables & Formats

5)         Processing Control Statements

6)         Reading/Writing Data Files

7)         Functions, Subroutines & Modules

Expected Outcomes of Part 1:

Upon successful completion of Part 1 you should be able to:

I.                    write and run Fortran 90/95 programs using features 3)–7);

II.                 solve problems by writing and running a Fortran 90/95 program.

 

Part 2              Numerical Methods, Weeks 7–13

Main Topics of Part 2:

1)           Mathematical Background

2)           Computer Arithmetic & Errors

3)           Root-Finding

4)           Linear Algebraic Systems

5)           Non-Linear Systems

6)           Quadrature (Integration)

7)           Ordinary Differential Equations — Initial Value Problems, Boundary Value Problems

Expected Outcomes of Part 2:

Upon successful completion of Part 2 you should be able to:

I.   solve numerically problems in standard form from topics 3)–7), by writing a Fortran 90/95 program using library routines or your own routines;

II.   understand the methods, their speed and error behaviour, and the implementation in Fortran 90/95 of the simpler methods. Routines for the more difficult methods are supplied and treated as grey (cf. black) boxes;
III.  be able to convert a range of problems to one of standard form from the topics 3)–7) above.

 

Assessment: is based on participation, assignments and a single examination, as described below. Independent work on the assignments and course exercises, as opposed to excessive collaboration or copying, will help in the exam. For final grades students must demonstrate: complete mastery of the material in the course to achieve an HD;  excellent knowledge and understanding to achieve a D; a well-developed knowledge and understanding to achieve a CR; and essential knowledge and understanding to achieve a P.

MATH 3076:        Marks                MATH 3976:        Marks      Due Dates (provisional)

Assignment FP1           5                   Assignment FPA1        5          5pm Thursday  week 4

Assignment FP2           4                   Assignment FPA2        4          5pm Thursday  week 5

Assignment FP3           6                   Assignment FPA3        6          5pm Thursday  week 7

Assignment NM1         7                   Assignment NM1A      7          5pm Thursday  week 10

Assignment NM2         8                   Assignment NM2A      8          5pm Thursday  week 13

Participation              10                   Participation              10          (maximum of 1 mark per week & 5 per part)

Exam                         60                   Exam                         60

Total                       100                                                   100

 

Participation: This is a laboratory based course, and to fulfil the course requirements you are required to participate in the laboratory practice sessions. An automatic computer record will be kept (including time outside scheduled tutorials) of the effort that you put in on the computer laboratories aspect of the course. The participation mark is allocated at the rate of 0.5% per hour participated in the computer laboratories including time outside scheduled tutorials, based on actual active login periods, and 0.25% per lecture. Excessive idle time does not count, nor does any time where you have just left your computer without logging out. A maximum of 1% is allocated each week, and a maximum of 5% for each part of the course. Thus, time may be missed due to illness or whatever, and 10% still obtained. You must sign off your name in lectures. Applications for special consideration should not be necessary unless you are absent from classes and cannot  for an extended.

 

Examination: The exam has two parts: the first part, on Fortan, will include questions on programming principles  and concepts, including Fortran syntax. Anyone who has completed the Fortran assignment and exercises reasonably independently can expect to do well. The second part, on numerical methods, will not involve Fortran. Further exam details will be given towards the end of the course.

 

Assignments: Assignments are not optional.  Assignment dates are provisional and  may vary.

 

Some degree of collaboration between students is helpful and not discouraged. However in order to increase your own ability you should attempt to do the questions primarily via your own skills plus some assistance from the tutor. The assignments are for learning not tests; seek help if necessary from the lecturer. This course assesses you on individual work, as opposed to group work. Excessive collaboration should be avoided, and may lead to lower examination marks and consequently reduced assignment marks as described above. Direct copying is improper conduct. Copiers, and those who allow their work to be copied, will be penalized by marks reduction, possibly total loss of marks. Extreme cases of misconduct will be reported to the University Registrar.

 

Assignments should be submitted by the advertised due time. Unless there are medical, misadventure or other extraordinary circumstances, late submissions attract a penalty at the rate of 10% per day applied pro rata (e.g. 5% for half a day late). Exception: weekends, including long-weekends if any, each count 10% only.

 

Printed Material:

Part 1:  Lecture Notes (about $20 from KopyStop):

MATH3076/3976 Mathematical Computing  Part 1

Fortran90/95 Course Notes 2014

                                  Fortuts (about $15 from KopyStop): optional purchase.

Part 2:  Lecture Notes (about $20 week 7 from KopyStop):

MATH3076/3976 Mathematical Computing Part 2

Numerical Methods Lecture Notes 2014

 

Web Material:            Lab and assignment sheets will be available on the course web page, accessible from the Senior Mathematics web-page:

                                    http://www.maths.usyd.edu.au:8000/u/UG/SM/

 

Online handouts:         Assignments NM1, NM1A, NM2, NM2A only.

 

Course Messages:       Read the course messages regularly on the course web page.