PROFORMA KURSUS
PUSAT PENGAJIAN TEKNOLOGI MAKLUMAT
FAKULTI TEKNOLOGI DAN SAINS MAKLUMAT
UNIVERSITI KEBANGSAAN MALAYSIA
Pusat Pengajian Teknologi Maklumat
School of Information Technology
TTT1323 MATEMATIK II
SEMESTER 1
Pensyarah/Lecturer:
Prof Madya Dr Noraidah Sahari @ Ashaari
SESI 2013/2014
Prasyarat/Pre-requisites:
TIADA
1.0 Hasil Pembelajaran/Learning Outcomes
Di akhir kursus, pelajar mampu:
At the end of the course, students will be able to:
i.
ii.
iii.
iv.
v.
vi.
vii.
Mentakrif dan menentukan prinsip suatu fungsi pemboleh ubahtunggal dan operasinya.
Define and identify single variable function properties.
Mengenal pasti fungsi permulaan, dan sifat asas serta grafnya.
Identify elementary functions, basic properties and their graphs.
Mentakrif limit dan keselanjaan serta menyelesaikan masalah berkaitan dengannya.
Define limits and continuity and solve their related problems.
Membeza fungsi permulaan dengan menggunakan petua pembezaan.
Differentiate elementary functions using differentiation rules.
Menggunakan petua pembezaan bagi menyelesaikan masalah persamaan garis, titik
maksima dan minima serta masalah dinamik.
Using differentiation rules to solve tangen line problems, maximum and minimum points
and dynamics problems.
Mengkamir fungsi permulaan dan fungsi lain dengan menggunakan petua kamiran.
Integrate elementary and other functions using integration rules.
Mengguna teknik kamiran bagi menyelesaikan masalah luas rantau, isipadu putaran
serta masalah dinamik.
Use integration techniques to solve area, volume of revolution and dynamic problems.
1
2.0 Sinopsis/Synopsis
Kursus ini memperkenalkan aspek matematik selanjar dan aplikasinya. Topik kursus ini meliputi
fungsi pembolehubah tunggal, fungsi permulaan seperti fungsi pemalar, identiti, kuadratik,
polinomial, eksponen, trigonometri dan fungsi hiperbolik dan sifat asasinya. Kursus ini juga
menjelaskan konsep had dan keselanjaran fungsi diikuti dengan teknik pembezaan dan
pengamiran serta aplikasinya. Fungsi multipemboleubah dan aplikasi juga diperkenal.
This course introduces the aspects of continuous mathematics and its applications. The topics to
be covered include functions of single variable, which are constant, identity, linear, quadratic,
polynomial, exponential, trigonometric, and hyperbolic functions and their properties. This course
also covers concepts of limits and continuity of functions, differentiation and integration
techniques of a single variable and their applications. Multivariable functions and their
applications also introduced.
3.0 Rujukan/References
1.
2.
3.
4.
5.
Stewart, J. 2009. Calculus 7th ed. Metric International Version. Thomson.
Anton, H., Bivens, I. & Davis, S. 2005. Calculus (8th Edition), John Wiley & Sons.
Bradley, G.L. & Smith, K. 2002. Calculus 3rd Edition, Prentice-Hall New Jersey.
Thomas, G.B., Weir, M.D. and Hass, J.R. 2010. Thomas’ Calculus 11th Edition. Pearson.
Larzon, R. and Edward, H. E. 2010. Calculus of Single Variables 9th Edition.
Brooks/Cole.
4.0 Jam Pertemuan/Contact Hours (Notional Hours)
Aktiviti
Kuliah/Lecture
Group Project (PBL)
Kuiz/Ujian/Peperiksaan
Pembentangan
Tutorial
Pembelajaran sendiri
Jumlah
Jam Pertemuan
28
5
4
3
14
70
124
2
5.0 Pelaksanaan/Implementations
Kuiz, ujian,
Pameran/
Belajar
kumpulan
peperiksaan
Pembentangan
Kendiri
Perancangan
Kuliah
Tutorial
1
Function of single variable
2
1
2
Function of single variable
2
1
3
Limits and Continuity
2
1
5
4
Limits and Continuity
2
1
5
5
Limits and Continuity
2
1
6
Differentiation
2
1
5
7
Differentiation
2
1
5
8
Differentiation
2
1
9
L’Hopital Rules
2
1
5
10
Integration
2
1
5
11
Integration
2
1
5
12
Integration
2
1
13
Function of Several
Variables
Function of Several
Variables
2
1
2
1
28
14
14
Jumlah Jam
Pembelajaran dalam
Satu Semester
5.0 Pelaksanaan/Implementations
Week
1-2
PBL
Diskusi
Minggu
5
1
1
1
2
1
5
1
5
1
5
1
5
5
5
Topics
1. Function of1 single
1 variable.
Definition of- real value function.
i. Domain
2
ii. Range
iii. Interval
–
- iv.
1 Graph
Independent
1
and dependent variables.
Function
1
operations.
i. Multiplication with a scalar (cf)
ii. Addition (f+g)
iii. Difference (f-g)
iv. Product (fg)
4
3
(Satu pembentangan
pada minggu terakhir)
5
3
70
Lecture
Hours
4
Tutorial
3
3-4
5-7
8
v. Quotient (f/g)
vi. Composition (fg)
Elementary functions, basic properties and their graphs:
i. Constant functions
ii. Identity
iii. Linear
iv. Quadratic
v. Polynomial
vi. Rational function
vii. Exponential
viii. Logarithm
ix. Trigonometric
x. Hyperbolic
2. Limit and continuity
Limit concept by intuition (not using  and )
i. Limit of a function is defined as the behaviour of a
function when it approaches a certain point
ii. Left limit
iii. Right limit
iv. Non exist limit
Limit calculations
i. Using graph of functions and piecewise-defined
functions
ii. Using theorems (rules)
- constant
- limit of x
- multiple
- sum and difference
- product and quotient
- power
Non existence of a limit and limit at infinity
Limit of trigonometric functions
Continuity
i. Operations of continuous functions
ii. Composition of continuous functions
iii. Discontinuity
iv. Continuity of trigonometric functions
v. mean value theorem
3. Differentiation
i. Derivative and Rates of Change
ii. The Derivatives as a Function
iii. Differentiation Formulas
iv. Derivatives of Trigonometric Functions
v. The Chain Law
vi. Implicit Differentiation
vii. Differentiation Application
Maximum and Minimum Values
The Mean Value Theorem
How Derivatives Affect the Shape of a Graph
Newton’s Method
4. Limit revisited. L’ Hospital law to determine the limit of the
forms: 0/0 ,  /  , 0.  ,0 , 00,  0,10, 1 ,  , - 
4
T1, T2 and
T3
Project 1
Presentatio
n
(Week 4)
6
T4, T5 , T6
2
T7
Project 2
Presentatio
n
(Week 8)
4
9-11
12-13
14
5. Integration
i. Definition of integration
ii. Riemann sum (area under a graph)
iii. Fundamental theorem of calculus
iv. Integration techniques and its application, up to integration by
parts
v. Definite integration
vi. Improper integration
vii. Area between two curves
viii. Volume of a rotation
6. Function of several variables (double)
i. Level curve
ii. Partial derivatives and its geometrical interpretations
iii. Determining maximum and minimum relative of a function,
saddle points of a function using second partial derivatives
test
iv. Multiple integration (double)
v. Techniques and the meaning of multiple integration of two
variable
vi. Functions over a region
Revision
Total
6
T8 and T9
4
T10
1
Final
project
presentatio
n
14
6.0 Penilaian/Evaluations
Perkara
Tutorial
Kuiz
Projek
Peperiksaan Akhir Semester
Total
Peratus
30%
10%
20%
40%
100%
5