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COURSE OUTLINE

Department of Mathematics, Faculty of Science Page : 1 of 4

Course Code:SSE1693 ENGINEERING MATHEMATICS I

Total Lecture Hours: 42 hours

Semester: FIRSTAcademic Session: 2011/2012

Prepared by:Name: Assoc Prof Dr Ong Chee TiongSignature:

Date: 8 August 2011`

Certified by: (Course Panel Head)Name:Signature:

Date:

Lecturer : ASSOC PROF DR ONG CHEE TIONGRoom No. : C21 - 426Tel. No : 5534082 / 013 7788291e mail : [email protected] or [email protected] : This is a first course in Engineering Mathematics. Contents include

differentiation and integration which focus on trigonometric,hyperbolic and inverse functions, improper integrals, series,vectors, matrices, polar coordinates, and complex numbers. Vectorspaces, eigenvalues and eigenvectors are also introduced.

Learning Outcomes:By the end of the course, students should be able to:

No.Course Learning Outcomes

Students are able to;ProgrammeOutcome(s)

Taxonomiesand

Soft-Skills

AssessmentMethods

CO1 apply limits, derivatives, and integrals to furthertranscendental functions and evaluate improperintegrals

PO1 C4, P3 Q1,T1,F

CO2 express functions as power series and analyzeconvergence of infinite series

PO1 C3, P3 A1,T2,F

CO3 use Taylor series to estimate limits and integrals

CO4 solve problems using vector methods and matrixalgebra

PO1 C3, P1 Q2,T2,F

CO5 analyse and graph polar equations, and solve problemsinvolving polar and parametric equations

PO1 C4, P1 A2, F

CO6 manipulate complex numbers and solve relatedproblems

PO1 C4, P1 F

(T Test ; PR Project ; Q Quiz; A Assignment ; Pr Presentation; F Final Exam)

Note:-PO8 or any PO regarding soft skills will be briefly acknowledge in each COwhile teaching and learning process is in action.
mailto:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]


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COURSE OUTLINE



Total Lecture Hours: 42 HOURS


STUDENT LEARNING TIME (SLT)

Teaching and Learning ActivitiesStudent LearningTime (hours)

1. Face-to-Face Learninga. Lecturer-Centered Learning

i. Lecture 42b. Student-Centered Learning (SCL)

i. Laboratory/Tutorialii. Student-centered learning activities Active

Learning, Project Based Learning

14

2. Self-Directed Learninga. Non-face-to-face learning or student-centered learning

(SCL) such as manual, assignment, module, e-Learning,etc.

12

b. Revision 35c.

Assessment Preparations 10

3. Formal Assessmenta. Continuous Assessment 4b. Final Exam 3

Total (SLT) 120

TEACHING METHODOLOGY

Lecture and Discussion, Assignments, Quizzes, Independent Study


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COURSE OUTLINE





WEEKLY SCHEDULEWeek 112/9/11-18/9/11

: Further Transcendental Functions: Inverse trigonometric functions, hyperbolicfunctions and its inverse in logarithmic form including graph sketching. Solvingequations related to the functions.

Week 219/9/1125/9/11

Differentiation: Differentiation of functions involving inverse trigonometric functions,hyperbolic functions and inverse hyperbolic functions.

Week 3 4

26/9/11-9/10/11

: Integration: Review on integration techniques standard integral table, substitution,

by parts, and partial fractions. Integration of expressions involving inversetrigonometric functions, hyperbolic functions, inverse hyperbolic functions. Using tableof integrals to integrate related functions.

Week 510/10/11-16/10/11

: Improper Integrals: Evaluation of limits including lHopital rule, limits of

indeterminate forms of type 0/0 and /. Improper integrals with infinite limits ofintegration and infinite integrands.

Week 6 717/10/11-30/10/11

: Series: Expansion of finite series, infinite series, power series, and the summations ofr, r2 and r3 .Test of convergence divergence test, ratio test and integral test. Taylorsand Maclaurins series of standard functions including applications to finding limits andapproximating definite integral.

Test 1 : 17 October 2011 , Monday (8.30 pm-10.00pm)

Week 831/10/11- 4/11/11

: Vectors: Vector in space and its operations including dot product, cross product andtriple products. Equation of line and plane. Angle between two lines, intersection oftwo lines,

Week 9MID SEMESTER BREAK (4 DAYS 5/11/11 -9/11/11)

Week 1010/11/11-20/11/11

Vectors: Intersection of two planes. Shortest distance from a point to a line, a point toa plane, and between two skewed lines. Angle between two planes, and angle betweena line and a plane.

Week 11-1221/11/11-

4/12/11

: Matrix Algebra: Minors, cofactors, adjoints, and determinants. Properties ofdeterminants including interchanging rows or columns, multiplying by a scalar.Determinant of triangular matrix and determinant of product of matrices. Solve system

of linear equations using Cramers rule and inverse matrix. Elementary row operations(ERO). Use ERO to obtain inverse matrix and solve system of linear equations usingGauss elimination. Rank of matrix, consistency of linear systems. Eigen value, eigenvector. General vector space: properties, linear combinations, linear independence,spanning and basis.

Test 2 : 30 November 2011 , Wednesday (8.30 pm-10.30pm)

Week 135/12/11-11/12/11

: Polar Coordinates: Point representation in polar coordinates, relationship betweenpolar and Cartesian coordinates. Graph sketching including tests of symmetries.

Week 14-1512/12/11

-25/12/11

: Complex Numbers: Definition of imaginary number and complex number. Algebraicoperations and solving equations involving complex numbers. Modulus and argument.

de Moivres theorem to show some trigonometric identities, to find power and roots ofcomplex numbers. Eulers formula. Function of complex variable such as sin(z),


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COURSE OUTLINE





relationship between circular and hyperbolic functions.

REFERENCES

Course Texts:1. Glynn James, (2010). Modern Engineering Mathematics, Prentice Hall.2. Glynn James, (2004).Advanced Modern Engineering Mathematics, Prentice Hall

Supplementary Texts:.

1.

Abd Wahid Md Raji et.al (2011). Engineering Mathematics I2. Stroud K.A (1996).Advanced Engineering Mathematics; MacMillan Ltd.3. Alan Jeffrey (2002).AdvancedEngineering Mathematics,Academic Press.4. Bradley, G.L and Smith (1998), Calculus, Prentice Hall International Inc.5. Finey, R., Weir, M and Giordano, F. (2001), Thomas Calculus, Addison-Wesley Pub.

GRADING:No Type of Assessment Materials % each % total Date

1 Assignment 2 5 10 W6, W14

2 Quiz 2 2.5 5 W3, W11

2 Test 1 (17 Oct 2011) Weeks 1

4 15 15 W63 Test 2 (30 Nov 2011) Weeks 510 25 25 W12

4 Final Examination 1 50 50 W17-W18

Total 100

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