# Semester 2 2015/16

SSCE 1993 – ENGINEERING MATHEMATICS 2

 Department & Faculty : Dept. of Mathematical Sciences, Faculty of Science Page : 1 of 2 Subject & Code: ENGINEERING MATHEMATICS (SSCE 1993) Total Lecture Hours: 42 hours Semester: Semester 2 Academic Session: 2015/16
 Lecturers Section No Tel No Room No E-mail No of Students Assoc Prof Dr. Munira Ismail (P) 70, 71, 62 34272 C22-441 muniraismail@utm.my 26, 48, 59 Tn Hj Zakaria Dollah 47, 48, 49 34300 C13-331 zakariad@utm.my 54, 45, 37 Dr Rashidah Ahmad 18 34351 C10-335 rashidahahmad@utm.my 32 Dr Faridah Mustapha 17, 19 34271 C22-432 faridahmustapha@utm.my 28, 27 Dr Fuaada Mohd Siam 15, 16, 20 34244 C22- 424 fuaada@utm.my 27, 28, 33 Dr Zaiton Mat Isa 50, 63, 64 34223 C22-440 zaitonmi@utm.my 49, 35, 49 TOTAL ALL 577 Prof Dr Mohd Nor Mohamad SPACE Tn Hj Hamisan Rahmat SPACE

Synopsis :

This course is about multivariable calculus of real and vector-valued functions. The basic theory of partial derivatives and multiple integrals of real functions with their applications are discussed. This theory is extended to vector valued functions to describe motion in space, directional derivatives, gradient, divergence and curl, line integrals, surface integrals and volume integral. Related theorems, namely Green’s Theorem, Stokes’ Theorem and Gauss’ Divergence Theorem and their applications are discussed.

Objectives:

On completing the course, students should be able to:

1. express functions of two and three variables using graphical representations.
2. apply partial derivatives on problems involving rate of change, estimations, relative and absolute extrema.
3. solve double and triple integrals in various coordinate systems involving area, volume, centre of mass and moment.
4. Discriminate express directional derivatives, tangent, normal vectors, divergence and curl of vector-valued functions using del operator.
5. solve line and surface integrals, and apply related theorems to engineering problems (chemical/civil/electrical/mechanical).

Main References:

1. Glyn James (2004). Advanced Modern Engineering Mathematics. 3rd Edition. Prentice Hall.

Textbook:

1.      Maslan Osman & Yusof Yaacob, 2008. Multivariable and Vector Calculus, UTM Press.

(Dr Yusof mobile number: 019 705 7884 )

2.      Yudariah, Roselainy & Sabariah. Multivariable Calculus for Indpt. Learners, 2nd Ed.09. Pearson Edu Pb.

(Dr Yudariah mobile number: 019 760 9600)

3.     Abd Wahid Md Raji & Ismail Kamis & Mohd Nor Mohamad Nor & Ong Chee Tiong, 2013. Advanced Calculus for Science and Engineering Students, Dept of Mathematical Science, Faculty of Science, UTM.

Teaching Methodology :

Lectures and tutorials

Attendance Policy:

1.   All students are required to attend a minimum of 80% of lecture and tutorial classes during this course. All absences from class, including absences due to illness, or other official activities, are counted as official absences.

3. A doctor’s certificate will be required to apply for any re-evaluations that you may have missed.

Weekly Schedule

##### Week
Lecture Topics Notes
1

14-18/2/16

Functions of several variables: Domain and range, level curves

2

21-25/2/16

Common surfaces; level surfaces
3

28/2-3/3/16

Partial derivatives: Rate of change; the chain rule; increments and tiotal differential, implicit differentiations
4

6-10/3/16

Extrema of multivariable functions – relative and absolute
5

13-17/3/16

Double integrals: Integrals in rectangular coordinates; iterated integrals and Fubini’s Theorem; changing the order of integration
6

20-24/3/16

Double integrals in polar coordinates; Application of double integral: Area, volume, mass, centre of mass, and moments Birthday of His Majesty Sultan Johor 23/3/16
7

27-31/3/16

Triple integrals: Triple integral in rectangular coordinates, Triple integral in cylindrical coordinates; Triple integral in spherical coordinates Test 1(15%)

(30/3/15)

3-9/4/16

MID SEMESTER BREAK (1 WEEK) Break
8

10-14/4/16

Applications of the triple integral: Mass, centre of mass, and moments
9

17-21/4/16

Vector-valued functions : Graphs of vector functions, differentiation and integration of vectors; velocity, acceleration, vector tangent and vector normal
10

24-28/4/16

Scalar and vector fields; Del operator, gradient; directional derivatives; divergence and curl
11

1-5/5/16

Vector Calculus: Line Integrals – line integrals in scalar and vector fields; path independence, potential functions and conservative fields Labour Day

(1/5/16)

Wesak Day

(3/5/15)

12

8-12/5/16

Green’s Theorem, Surfaces integrals of scalar and vector fields Test 2(15%)

(4/5/16)

13

15-19/5/16

#### Stokes’ Theorem

14

22-26/5/16

Gauss’ Divergence Theorem

 ASSESSMENT Tests Content Date Test I (15%) 1 hour 15 min Lectures: Weeks 1-5 30/3/2016 Test II (15%) I hr 30 mins Lectures: Weeks 6-9 4/5/2016 Quiz/Assignmt(20%) To be determined To be determined To be determined Final Examination (50%) 3 hours Lectures: Weeks 1-15 To be determined