BA201 Engineering Mathematics 2

RESTRICTED BA201 Engineering Mathematics 2

POLYTECHNICS
MINISTRY OF HIGHER EDUCATION MALAYSIA
DEPARTMENT OF MATHEMATICS, SCIENCE AND COMPUTER

COURSE : BA201 ENGINEERING MATHEMATICS 2

INSTRUCTIONAL DURATION : 15 WEEKS

CREDIT(S) :2

PRE REQUISITE(S) : BA101 ENGINEERING MATHEMATICS 1

SYNOPSIS

ENGINEEERING MATHEMATICS 2 provides exposure to students regarding complex
numbers which explains real and imaginary numbers. This course also emphasizes on
calculus and its applications.

COURSE LEARNING OUTCOME (CLO)

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

1. Explain basic operations on complex numbers stated in various forms using
algebraic operations or by constructing Argand’s diagrams. (C2)

2. Apply various differentiation techniques to determine the derivatives of
algebraic, trigonometric, logarithmic, exponential and parametric functions up
to the second order including solving real life optimization and kinematic
problems. (C3, P1)

3. Use suitable integration methods in solving related problems to determine the
definite and indefinite integrals of algebraic, trigonometric, reciprocal and
exponential functions. (C3, A1)

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SUMMARY (30 LECTURE : 15 TUTORIAL)

RTA

1.0 COMPLEX NUMBERS ( 06 : 03 )

This topic discusses the difference between real numbers and

imaginary numbers. Basic operation on complex numbers is also

explained. This topic also shows the representation of complex
numbers in the form of Argand’s diagrams, polar and exponential.

Basic operation in polar form is also discussed.

2.0 DIFFERENTIATION ( 06 : 03 )

This topic includes first order differentiation and various

differentiation techniques. It includes differentiation of algebraic,

trigonometric, logarithmic and exponential functions. Differential

concept is also applied in parametric equation functions.

3.0 APPLICATION OF DIFFERENTIATION ( 06 : 03 )

This topic explains application of differentiation in calculating

gradient of curve. This topic also expounds the application of

differentiation to find stationary points as well as sketching its graph.

Differentiation is applied to solve kinematical and real problems.

4.0 INTEGRATION ( 06 : 03 )

This topic shows that integration is the inverse of differentiation.

Integration for algebraic, trigonometric, exponential and reciprocal

functions are discussed. This topic also explains the substitution

method.

5.0 APPLICATION OF INTEGRATION ( 06 : 03 )

This topic builds an understanding of the integration applications in

calculating the areas and the volumes of bounded region. Integration

is also applied to solve kinematical problems.

RTA – Recommended Time Allocation

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SYLLABUS

1.0 COMPLEX NUMBERS

1.1 Understand complex numbers in Cartesian form (z = a + ib).
1.1.1 Recognise that i stands for √-1 .
1.1.2 Recognise that all complex numbers are in the form
(real part) + i (imaginary part) .

1.2 Do algebraic operations on complex numbers.
1.2.1 Perform addition and subtraction.
1.2.2 Perform multiplication.
1.2.3 Introduce conjugate of complex number.
1.2.4 Perform division.
1.2.5 Apply the conditions of equality of two complex numbers to solve
problems.

1.3 Understand graphical representation of complex numbers through
Argand’s diagrams.
1.3.1 Draw Argand Diagrams to represent complex numbers.
1.3.2 Perform addition.
1.3.3 Perform subtraction.
1.3.4 Obtain modulus and argument of the resultant complex
numbers.

1.4 Explain complex numbers in other forms.

1.4.1 Convert Cartesian form to polar form ( z  r or

z  rcos  j sin  ) and vice versa.

1.4.2 Convert Cartesian form to exponential form and vice versa.
1.4.3 Solve multiplication and division in polar form.
1.4.4 Solve complex numbers problems in various forms.

2.0 DIFFERENTIATION

2.1 Understand the differentiation rules.
2.1.1 Identify basic differentiation formulae.
2.1.2 Apply the different techniques of differentiation:
a. Chain rule.
b. Product rule.
c. Quotient rule.

2.1.3 Use various differentiation techniques to solve problems.

2.2 Apply the differentiation formula for trigonometric, logarithmic and
exponential functions.
2.2.1 Apply the formula to solve related problems.
2.2.2 Use various differentiation techniques to solve problems.

2.3 Understand parametric equation.
2.3.1 Use chain rule to find derivative of parametric equation for
algebraic expressions.

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2.4 Describe second order differentiation
2.4.1 Perform second order differentiation by using various
differentiation techniques for algebraic expressions.

3.0 APPLICATION OF DIFFERENTIATION

3.1 Understand the applications of differentiation.
3.1.1 Use differentiation to find the gradient of a curve.
3.1.2 Find turning points/stationary points.
3.1.3 Determine maximum, minimum and point of inflexion.
3.1.4 Sketch the graph of a curve.

3.2 Perform application of differentiation in real problems.
3.2.1 Calculate rates of change.
3.2.2 Solve optimization problems.

3.3 Solve kinematic problems.
3.3.1 Find the instantaneous velocity of a particle.
3.3.2 Calculate the instantaneous acceleration of a particle.
3.3.3 Calculate total displacement.

4.0 INTEGRATION

4.1 Understand the basic integration rules.
4.1.1 Express integration as the inverse of differentiation.
4.1.2 Perform indefinite integrals of algebraic functions.
4.1.3 Evaluate definite integrals using the properties of definite
integrals.

4.2 Do integration for other functions .
4.2.1 Evaluate integrals of :
a. trigonometric functions.
b. exponential functions.
c. reciprocal functions.

4.3 Learn integration through substitution method.
4.3.1 Evaluate integrals involving :
a. trigonometric basic identities.
b. double-angle formulae.
c. exponential function.
d. reciprocal functions.

5.0 APPLICATION OF INTEGRATION

5.1 Apply integration to find the area of bounded region.
5.1.1 Sketch the graph.
5.1.2 Identify the boundaries of the bounded region.
5.1.3 Calculate the area :
a. under a curve.
b. bounded by a straight line and a curve.
c. bounded between two curves.

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5.2 Apply integration to find the volume of bounded region.
5.2.1 Sketch the graph.
5.2.2 Identify the boundaries of the bounded region.
5.2.3 Construct the object generated when the bounded region is
revolved along x-axis or y-axis.
5.2.4 Calculate the volume :
a. under a curve.
b. between a curve and a straight line.

5.3 Interpret kinematic problems.
5.3.1 Find the distance from a given situation.
5.3.2 Find the velocity from a given situation.

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ASSESSMENT

The course assessment is carried out in two sections:

i. Coursework (CA)
Coursework is continuous assessment that measures knowledge,
technical skills and soft skills.

ii. Final Examination (FE)
Final examination is carried out at the end of the semester.

The percentage ratio of FE to CA should follow the guideline stated in the
Arahan-Arahan Peperiksaan dan Kaedah Penilaian which is approved by the
Lembaga Peperiksaan dan Penganugerahan Sijil/ Diploma Politeknik.

ASSESSMENT SPECIFICATION TABLE

CLO ASSESSMENT METHODS FOR COURSEWORK (CA)

CONTEXT CLO 1 Theory Test Quiz Tutorial Exercise Group Discussion
CLO 2
CLO 3 *(2) 30% *(2) 10% *(4) 40% *(2) 20%
√ √ √
Complex Numbers √ √ √ √
√ √ √
Differentiation √ √
Application Of √
Differentiation √
Integration
Application Of
Integration

Remark:

CLO1 : Explain basic operations on complex numbers stated in various forms using
algebraic operations or by constructing Argand’s diagrams. (C2)

CLO2 : Apply various differentiation techniques to determine the derivatives of
algebraic, trigonometric, logarithmic, exponential and parametric functions up
to the second order including solving real life optimization and kinematic
problems. (C3, P1)

CLO3 : Use suitable integration methods in solving related problems to determine the
definite and indefinite integrals of algebraic, trigonometric, reciprocal and
exponential functions. (C3, A1)

*(x) refers to the quantity of assessment

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REFERENCES

Abd Wahid Md Raji et al (2003) Calculus for Science and Engineering Students :
Universiti Teknologi Malaysia & Kolej Universiti Tun Hussein Onn

Amran Hussin et al (2002) Matematik Tulen Pra Universiti . Penerbit Fajar Bakti Sdn.
Bhd.

Finney, R. L. & Thomas, G. B. (1993). Calculus (2nd ed). Addison-Wesley Publishing
Company.

Misiahi & Sullivan (2000). Finite Mathematics: An Applied Approach (8th ed). Ins. New
York: John Wiley & Sons.

Stroud, K. A. (2001). Engineering Mathematics: Programs and Problems (5th ed).
Macmillan Press Ltd.

Yong Zulina Zubairi et al (2006) Mathematics for STPM & Matriculation: Calculus :
Thompson

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MATRIX OF COURSE LEARNING OUTCOMES (CL

Course Learning Outcome (CLO) PLO1 PLO2 PLO3
LD1 LD2 LD3

Explain basic operations on complex numbers √
C2
1 stated in various forms using algebraic
operations or by constructing Argand’s

diagrams. (C2)

Apply various differentiation techniques to

determine the derivatives of algebraic,

2 trigonometric, logarithmic, exponential and
parametric functions up to the second order

including solving real life optimization and

kinematic problems. (C3, P1)

Use suitable integration methods in solving
related problems to determine the definite
3 and indefinite integrals of algebraic,
trigonometric, reciprocal and exponential
functions. (C3, A1)

Total 1

Remark :

LD1 Knowledge
LD 2 Practical Skills
LD 3 Communication Skills
LD 4 Critical Thinking and Problem Solving Skills
LD 5 Social Skills, and Responsibilities
LD 6 Continuous Learning and Information Management Skills
LD 7 Management and Entrepreneurial Skills
LD 8 Professionalism, Ethics and Moral
LD 9 Leadership and Teamwork Skills

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BA201 Engineering Mathematics 2

LO) VS PROGRAMME LEARNING OUTCOMES (PLO)

Compliance to PLO PLO7 PLO8 PLO9 Recommended Assessment
LD7 LD8 LD9 Delivery
PLO4 PLO5 PLO6 Methods
LD4 LD5 LD6

Theory Test, Quiz

√

Lecture, Theory Test, Quiz,

Discussion, Tutorial Exercise,

C3, Q&A, Problem Group Discussion

P1 Solving Activities

√

Theory Test , Tutorial
Exercise, Group

C3, Discussion
A1

2

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DISTRIBUTION OF STUDENT LEARNING TIME
ACCORDING TO COURSE LEARNING - TEACHING ACTIVITY

No. Learning and Teaching Activity SLT
[ 2 hour(s) x 15 week(s) ] 30
FACE TO FACE
1.0 Delivery Method
1.1 Lecture

1.2 Practical [ 0 hour(s) x 15 week(s) ] 0

1.3 Tutorial [ 1 hour(s) x 15 week(s) ] 15

2.0 Coursework Assessment (CA)

2.1 Lecture-hour-assessment 2

- Test [2] 30 min/ Test 1
15 min/ Quiz 0.5
- Quiz [2] 15 min/ Discussion 0.5

- Group Discussion [2] 24 min/ Lab Exe 2

2.2 Practical-hour-assessment [0]
- Practical Exercises

2.3 Tutorial-hour-assessment [4] 0
- Tutorial Exercises

NON-FACE TO FACE

3.0 Coursework Assessment (CA)

- End-of-chapter [0]

4.0 Preparation and Review

4.1 Lecture [ 1 hour(s) x 15 week(s) ] 15

- Preparation before theory class eg: download lesson notes. [√]
[√]
- Review after theory class eg: additional references, discussion group,discussion

4.2 Practical [ 0 hour(s) x 15 week(s) ] 0

- Preparation before practical class/field work /survey eg: review notes, [] 12
[]
- Post practical activity eg: lab report, additional references and discussion session 6
80
4.3 Tutorial [ 0.8 hour(s) x 15 week(s) ] 2
- Preparation for tutorial
[√]

4.4 Assessment [2] [ 2 hour(s) x 2 = 4]
- Preparation for test. [2] [ 1 hour(s) x 2 = 2]
- Preparation for quiz.

Total
Credit = SLT/40

Remark:
1. Suggested time for

Quiz : 10 - 15 minutes
Test (Theory) : 20 - 30 minutes
Test (Practical) : 45 - 60 minutes

2. 40 Notional hours is equivalent to 1 credit
3. Tutorial Exercises are conducted during Tutorial Hours

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