INTERNATIONAL ISLAMIC UNIVERSITY MALAYSIA
COURSE OUTLINE
Kulliyyah
Centre for Foundation Studies
Department
Department of Mathematics
Programme
Engineering, Physical Science and Information and
Communications Technology
Name of Course
Mathematics III
Course Code
MAT0134
Name (s) of Academic staff /
Instructor(s)
Hasnun Zahibi
Muhammad Izzuddin Sidek
Pahsha Ismail
Nor Aini Abd Rahman
Semester and Year Offered
Semester 1, Semester II, Semester III
Status
Core
Level
2
Credit Value / Hours
4 credit hours / 5 contact hours
Pre-requisites (if any)
MAT0114
MAT0124
Co-requisites (if any)
Nil
The objectives of this course are to:
1.
2.
3.
Course Objectives
4.
5.
Semester I, 2015/2016
learn the basics of the calculus of functions of one variable;
study transcendental functions, limits, differentiation and
an introduction to the integral, culminating with the
Fundamental Theorem of Calculus;
interpret the concepts of Calculus algebraically, graphically
and verbally;
study the concept of and some methods of solving first
order linear differential equations;
improve the student’s ability to think critically, to analyze
and to solve a problem using a wide array of tools. These
skills will be invaluable to them in whatever path they
choose to follow, be it as a mathematics major or in pursuit
of a career in one of the other sciences fields.
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Upon completion of this course, students should be able to:
1.
2.
Learning Outcomes
3.
4.
5.
evaluate various limit problems both algebraically and
graphically; check the continuity of various types of
functions;
differentiate various types of functions using the
differentiation rules: Power, Sum, Difference, Product,
Quotient and Chain; Implicit and Logarithmic
Differentiation; find the first and second derivatives of
parametric equations;
apply differentiation to find extrema, equations of tangent
and normal lines to the curve, to solve some optimization
and related rates problems;
find anti-derivative of some simple functions; apply basic
techniques of integration and other techniques of
integration (substitutions, by parts, trigonometric
substitution and partial fractions) to evaluate integrals;
solve first order differential equations which are separable
and linear (by means of integrating factor)
Course Synopsis
This course covers topics on limits and continuity; derivatives and
its applications; principles and techniques of integration; first
order differential equation.
Mode of Delivery
Lecture and Tutorial
Assessment Methods and Type /
Course Assessement
Weeks
1
8/6-12/6
LO
1,2,3,4,5
1,2,3,4,5
1,2,3,4,5
Method
Assignment
Quizzes
Mini Project / Applications
%
10
20
10
1,2,3,4,5
End-of-Semester Examination
60
TOTAL
100
Content outline of the course / module and the SLT per topic
Learning
Topics
Task/Reading
Hours
Topic 1: LIMITS & CONTINUITY
[5 hours]
Anton
1.1 Limits (An Intuitive Approach)
0.5
pp. 49 – 58
1.2 Computing Limits
1.5
pp. 62 – 68
1.3 Limits at Infinity; End Behavior
1
pp. 71 – 77
Tutorial
2
Semester I, 2015/2016
Page 2 of 4
1.3 Limits at Infinity; End Behavior
1.4 Continuity
2
15/6-19/6
3
22/6-26/6
4
29/6-3/7
5
6/7-10/7
6
13/7-14/7 &
22/7-24/7
15/7-21/7
Topic 2: DERIVATIVE
2.1 Definition of the Derivatives
2.2 Introduction to Techniques of Differentiation
Tutorial
2.3 The Product and Quotient Rules
2.4 Derivatives of Trigonometric Functions
2.5 The Chain Rule
Tutorial
Quiz Chapter 1
2.5 The Chain Rule
2.6 Implicit Differentiation
2.7 Derivatives of Logarithmic and Exponential
Function
Tutorial
2.7 Derivatives of Logarithmic and Exponential
Function
2.8 Derivatives of Inverse Trigonometric Functions
Tutorial
2.8 Derivatives of Inverse Trigonometric Functions
2.9 Parametric Differentiation
Tutorial
Mid-Semester Break & Eid Ul Fitri
Topic 3: APPLICATION OF
DIFFERENTIATION
7
27/7-31/7
8
3/8-7/8
9
10/8-14/8
Semester I, 2015/2016
3.1 Tangents and Normals
3.2 Relative Extrema
3.3 Optimization Problems
Tutorial
Quiz Chapter 2
3.3 Optimization Problems
3.4 Related Rates
Tutorial
Discussion on Mini Project
Topic 4: INTEGRATION
4.1 Anti-derivative; Basic Integration Formulas
4.2 Definite Integral
4.3 Integration by Substitution
Tutorial
Quiz Chapter 3
0.5
1.5
pp. 90 – 94
[13 hours]
0.5
0.5
2
1
1
1
1
1
0.5
2
0.5
Anton
pp. 110 – 113
pp. 122 – 139
pp. 142 – 146
pp. 148 – 149
pp. 153 – 157
pp. 161 – 165
pp. 420 – 423
pp. 429 – 430
2
1.5
1.5
2
0.5
2.5
2
pp. 466 – 467
pp. 695, 697
[6 hours]
Anton
1
pp. 123, 695
1
pp. 198 –201
1
pp. 224 –230
1
1
1
2
pp. 168 – 172
1
1
Anton
[13 hours]
pp. 271 – 276
1
pp. 281 – 285
1
pp. 303 – 305
1
pp. 310 – 313
1
pp. 423 – 424
1
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10
17/8-21/8
11
24/8-28/8
12
31/8-4/9
(31/8-National
Day)
13
7/9-11/9
14
14/9-18/9
(16/9-Malaysia
Day)
4.3 Integration by Substitution
4.4 Integrals Involving Inverse Trigonometric
Functions
4.5 Integration by Parts
Tutorial
4.5 Integration by Parts
4.6 Integrating Trigonometric Functions
Tutorial
4.6 Integrating Trigonometric Functions
4.7 Trigonometric Substitutions
4.8 Integrating Rational Functions by Partial
Fractions
Tutorial
4.8 Integrating Rational Functions by Partial
Fractions
1
1.5
pp. 430 – 431
pp 467 – 468
0.5
2
1.5
1.5
2
0.5
2
0.5
pp. 491 - 496
Topic 5: FIRST ORDER DIFFERENTIAL
EQUATIONS
[5 hours]
5.1 Separation of Variables
Quiz Chapter 4 (4.1-4.5)
Discussion on Mini Project
5.2 First Order Linear Differential Equations
Tutorial
Quiz Chapter 5 (4.6-5.1)
21/9-27/9
Revision week
28/9-8/10
Final Examination
pp. 497 - 505
pp. 508 – 512
pp. 516 – 521
2
1
2
1
1
3
1
1
Anton
pp. 561 - 563
pp. 568 – 570
pp. 586– 588
Main references supporting the course
Required
Mathematics III (MAT0134) Workbook
Anton, H., Bivens, Davies, (2011), Calculus ( Late Transcendentals) (10th edition), John Wiley & Sons,
Inc.
Additional references supporting the course
Recommended
Stewart, J., (2012), Calculus ( 7th edition), Belmont, CA: Thomson Brooks/Cole.
Thomas/Finney. (1996).Calculus and Analytic geometry 9th edition, Addison Wesley.
Thomas, George B., Maurice D. Weir, Joel Hass, Frank R. Giordano (2008), Calculus, 11th ed.,
Addison-Wesley.
Semester I, 2015/2016
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