INTERNATIONAL ISLAMIC UNIVERSITY MALAYSIA
COURSE OUTLINE
Kulliyyah
Centre for Foundation Studies
Department
Department of Mathematics
Programme
Engineering, Physical Science and Information and Communication Technology
Course Title
Mathematics III
Course Code
SEF1134
Status
Core Course
Level
3
Credit hours
4
Contact hours
5
Pre-requisites
Mathematics 1 ( SHE 1114 ) , Mathematics II ( SEF1124 )
Co-requisites
Nil
Instructor(s)
Sis. Nur Azila Mohd Zain
Room no: C205
(ext. 4875 );
Sis. Parveen Kausar Yacob
Room no: A217
(ext. 3483);
Sis. Salbi Dollah
Room no: C205
(ext. 2718 )
Semester offered
Semester I, Semester II, Semester III
Course Synopsis
This course covers topics on limits and continuity; derivatives, applications of
derivatives in graphing; principles of integration and techniques of integration.
Course Objective
The objectives of this course are to:
1.
2.
3.
4.
December 2011
relate the concept of ‘limit’ with the concepts of derivative and integral;
formulate functions and solve problems involving applications of differentiation
in graphing;
apply techniques of differentiation and integration;
develop their understanding of mathematical concepts and applications and
skills to interpret and solve problems so that they have a complete and strong
foundation to pursue their studies in Engineering, ICT and Physical Sciences
programmes.
Learning
outcomes
At the end of this course, students should be able to:
1.
2.
3.
4.
analyze and solve limits problem;
solve derivative using the concept of limit ;
analyze the functions and interpret exact shape of graph using derivatives;
apply techniques of differentiation to solve problems in basic functions,
trigonometric functions, logarithmic and exponential functions and inverse
trigonometric functions;
apply basic techniques of integration and other techniques of integration
(substitutions, by parts, trigonometric substitution and partial fractions) to
evaluate integrals.
5.
Instructional
Strategies
Lectures and tutorials
Course
Assessment
LO
METHOD
%
1,2,3,4,5
Tutorial test
10
1,2,3,4,5
Quizzes
10
1,2
Mid-Semester Examination
20
1,2,3,4,5
End-of-Semester Examination
60
Total
100
Course Outlines /
Contents
Week
Topics
Task /
Assignment
(Anton)
1
CHAPTER 1 : Limits & Continuity
(11/1
1.1 Limits (An Intuitive Approach)
(1.1)
1.2 Techniques Computing of
Limits.(1.2 & 1.3)
pp. 49 – 58
1.3 Continuity (1.5)
1.4 Continuity of Trigonometric
Functions.(1.6)
pp. 90 – 94
pp. 101 –105
-13/1)
2
(16/1
– 20/1)
December 2011
pp. 62 – 78
Important
Dates
3
(23/1 27/ 1)
4
(30/1
– 3/2)
5
(6/2
CHAPTER 2 : Derivative
CNY
(23 & 24 Jan)
2.1 Definition of the derivatives (2.1)
& (2.2)
2.2 Introduction to Techniques of
Differentiation(2.3)
pp. 111 – 129
2.3 The Product and Quotient Rules
(2.4)
2.4 Derivatives of Trigonometric
Functions (2.5)
pp. 142 – 147
pp. 149 – 149
Quiz 1
(30/1 & 1/2)
2.5 The Chain Rule (2.6)
2.6 Implicit Differentiation (2.7)
pp. 153 – 157
pp. 161 – 165
Maulidur Rasul
(5/2)
Thaipusam (7/2)
2.7 Derivatives of Logarithmic and
Exponential Function(6.2) & (6.3)
2.8 Derivatives of Inverse
Trigonometric Functions(6.7)
pp. 421 – 423
pp. 429 – 430
pp. 467
pp. 134 – 139
Tutorial 1
– 10/2)
6
(13/2
– 17/2)
7
(20/2
CHAPTER 3 : The Derivative in
Graphing and Applications
3.1 Analysis of Functions I: Increase,
Decrease and Concavity(3.1)
3.2 Analysis of Functions II: Relative
Extrema, Graphing
Polynomials.(3.2)
pp. 187 –192
pp. 207 –211
(27/2
3.3 Analysis of Functions III: Graphing
Rational Functions.(3.3)
– 2/3)
CHAPTER 4 : Integration
– 24/2)
8
4.1 An Overview of the Area
Problem(4.1)
(5/3
– 11/3)
December 2011
pp. 197 –204
Tutorial 2
Quiz 2
(27/2 & 28/2)
pp. 265 – 270
MIDTERM
9
(12/3
– 16/3)
10
(19/3
– 23/3)
11
(26/3
– 30/3)
12
4.2 The Indefinite Integral (4.2)
4.3 The Definition of Area as a Limit;
Sigma Notation (4.4)
4.4 Definite Integral and RiemannSum(4.5)
pp. 271 – 276
pp. 291- 296
4.5 Fundamental Theorem of
Calculus.(4.6)
4.6 Integration by Substitution (4.3)
4.7 Evaluating Definite Integrals by
Substitution (4.9)
pp. 310 – 311
Tutorial 3
pp. 281 – 286
pp. 337 - 340
Quiz 3
(19/3 & 20/3)
4.8 Integrals involving Logarithmic,
Exponential and Inverse
Trigonometric Functions (6.2),
(6.3), (6.7)& (7.1)
pp. 423 – 424
pp. 430 – 431
pp. 467 – 468
pp. 489
(formula 1-14,
21-23)
pp. 300 - 305
(2/4
CHAPTER 5 : Principles of Integral
Evaluation
– 6/4)
5.1 Integration by Parts (7.2)
pp. 491- 497
5.2 Integrating Trigonometric
Functions (7.3)
5.3 Trigonometric Substitutions (7.4)
pp. 501 – 505
5.4 Integrating Rational Functions by
Partial Fractions (7.5)
pp. 514– 521
13
(9/4
– 13/4)
14
(16/4
–20/4)
December 2011
Tutorial 4
Quiz 4
(2/4 & 3/4)
pp. 508 – 512
Tutorial 5
Quiz 5
(25/4 & 26/4)
References
Required:
Anton, H., Bivens, Davies, (2010), Calculus (Late Transcendentals),
9th ed.,,John Wiley & Sons, Inc.
Recommended :
Stewart, J., (2006), Calculus, 6th ed., Belmont, CA: Thomson
Brooks/Cole.
Thomas/Finney, (1996), Calculus and Analytic Geometry, 9th ed.,
Addison-Wesley.
Thomas George B., Maurice D. Weir, Joel Hass, Frank R. Giordano,
(2008), Calculus, 11th ed., Addison-Wesley.
December 2011