Home » Academic » Mathematics with Computer Graphics » Course Synopsis

 

SM10103 MATHEMATICS I

 
This course contains basic concepts of  several topics such as introduction to the logic theory which must be understood by students before taking more advance subjects such as Advance Calculus. This course also covers mathematics in calculus which comprises of topics such as: set, number, inequalities, complex number, relation and function, limits and continuity, differentiation and integration.
 
Reference
 
Abu Osman Md Tap. 1987. Matematik pertama Jilid 1. K.L : DBP.
Abu Osman Md Tap. 1988. Matematik Pertama Jilid II. K.L : DBP.
Peng Yee Hock. 1987. Kalkulus Permulaan. Serdang : UPM.
Leithold, L. 1972. Calculus with Analytical Geometry. New York : Harper and Row.
Thomas Finney. 1996. Calculus. 9 th Edition. Addison Wesley.
Sala, S.L & Hille, E. 1984. Kalkulus Satu dan Banyak Pembolehubah Bahagian 1 (terjemahan). New York : John Wiley & Son.
 
 
 
S M 10203  MATHEMATICS II
 
This course consists the following: vector space, sequence and series, infinite series, power series, polar coordinate system, further coordinate geometry.
 
Reference
 
Abu Osman Md Tap. 1988. Matematik Pertama Jilid 3: Kalkulus Multipembolehubah dan Kalkulus Vektor, Kuala Lumpur: DBP
Apostol, TM. 1969 . Calculus Vol II, New York: John Wiley.
Kaplan, W. 1970. Advance Calculus. New York: Addison Wesley
Marsden, J.E & Tromba, A.J. 1981. Vektor Calculus Second Edition, New York: W.H Freeman & Co.
Stephenson. 1993. Kaedah Matematik Lanjutan Untuk Pelajar Kejuruteraan dan Sains (terjemahan), Kuala Lumpur: DBP.
Thomas Finney. 1996. Calculus 9 th Edition, New York: Addison Wesley
 
 
 
SM10303 ECONOMIC STATISTICS
 
This course gives an exposure to descriptive statistics, probability, and inferential statistics. The topics covered the concept & basic of probability, conditional probability, Baye’s theorem, random variable, mathematical expectation, discrete & continuous probability distribution, several special probability distributions such as Bernoulli, Binomial, Poisson, Multinomial, Uniform, Exponential and Normal, sampling & sampling distribution, estimation and hypotheses testing.
 
Reference
 
Walpole, R.E. & Meyers, P.L. 1987. Kebarangkalian dan Statistik Untuk Jurutera dan Ahli Sains (translation by Mokhtar Abdullah and Zainodin Jubok), DBP, Kuala Lumpur.
Walpole, R.E., Myers, R.H. & Myers, S.L. 1998. Probability and Statistics for Engineers and Scientist. 6 th ed. Prentice Hall, New Jersey
Webster, A.L. 1992. Applied Statistics for Business and Economics. 2 nd ed. Irwin. Inc, Chicago
Weiss, N.A. 1995. Introductory Statistics. 4 th ed. Addison-Wesley
Zainuddin Jubok & Mokhtar Abdullah. 1988. Pengenalan Kebarangkalian dan Statistik, Kuala Lumpur:DBP
 
 
 
 
S M 20103  LINEAR ALGEBRA
 
Prerequisite : SM1053 & SM1063
 
This course introduces the systems of linear equations and its relation to matrices. Linear space: Generalisation of vector geometry, weakness in the definition of vector geometry, general definition of vector and method of vector identification, coordinate system or frame of reference or basis (standard or non-standard), dimension. Application of basis concept in solving m row and n column linear equation, application of vector in a coordinate system in solving simple problems in navigation and dynamic, application of vector and geometry. Inner product (dot and scalar): properties of these products, orthogonality, parallel and anti-parallel, application of these products in geometry and science. Euclidean space: orthogonality and projection. Linear transformation: matrices representative, eigenvalue and eigenvector. Determination by analysis and numerical and its application.
Reference
 
C.M.Ho, K.H.Toh & A.Amran, 2007. Linear Algebra. Penerbit Universiti Malaysia Sabah, Kota Kinabalu.
Anton, H & Busby, R, 2003 . Contemporary Linear Algebra, John Wiley & Sons, New York.
Beauregard, F, 1995. Linear Algebra. Addison Wesley, US.
Lim Voon Ka 1983. Algebra Linear Permulaan, DBP, Kuala Lumpur.
Serge Lang, 1986. Introduction to Linear Algebra Second Edition, Springer-Verlag, New York.
 
 
 
S M 20 20 3 DIFFERENTION EQUATIONS
 
Prerequisite : SM1053 & SM1063
 
This course contains topics such as: First Order Differential Equations (Basic concepts and classification., Solving first-order separable, homogeneous, linear and exact equations. Applications of  first order linear differential equations), Second Order Differential Equations with constant coefficients (Solution of homogeneous equations, principle of superposition, Solution of non-homogeneous equations, method of undetermined coefficients, method of variation of parameters, Application of second order linear differential equations), Laplace Transforms and it's applications to initial value and bouncary value and Series Solutions of Linear Equations (using Power Series and Method of Frobenius).
 
Reference
 
G. D. Zill. 2005. A First Couse in Differential Equations. Australia : Thomson Books/Cole.
R. Bronson. 1994. Schaum’s Outlines Differential Equations. New York : McGraw-Hill.
Boyce, W.E & Di Prima. 1977. Elementary Differential Equations. New York : John Wiley & Sons.
Md Nor Mohamad. 1990. Pengenalan Penjelmaan Laplace dan Penggunaannya. Kuala Lumpur : DBP.
Md Nor Mohamad. 1993. Pengenalan Persamaan Terbitan Biasa. Kuala Lumpur : DBP.
Ritger, P.D & Rose, N.J. 1966. Differential Equations and Applications. New York : McGram Hill.
Bahrom Sanugi. 1992. Persamaan Pembezaan. Sekudai, Johor : UTM.
 
 
 
S M 20303 ADVANCE MATHEMATICS I
 
Prerequisite : SM1053 & SM1063
 
Multivariable function, Limit and Continuity, Partial Derivatives, Directional Derivatives, Curl and Divergence, Gradient vector, Extreme of function of several variables, Critical points: Maximum,minimum and saddle point, Tangent plane and Linear approximation, Second Derivatives Test. Optimizations, Absolute maximum and minimum value, Lagrange Multipliers. Constrained Optimizations model.
 
Reference
 
Thomas Finney. 1996. Calculus. 9 th Edition. New York: Addison Wesley.
Abu Osman Md Tap. 1988 Matematik Pertama Jilid 3: Kalkulus Multipembolehubah dan Kalkulus Vektor. K.L : DBP.
Apostol, TM. 1969. Calculus Vol II. New York: John Wiley.
Kaplan, W. 1970. Advance Calculus. New York: Addison-Wesley.
Marsden, J.E & Tromba, A.J. 1981. Vector Calculus Second Edition. New York: W.H Freeman & Co.
Stephenson. 1993. Kaedah Matematik Lanjutan Untuk Pelajar Kejuruteraan dan Sains (terjemahan). Kuala Lumpur : DBP.
 
 
 
SM20402 NUMERICAL COMPUTATION
 
Prerequisite: ST2052 & SM2043
 
This course discusses various numerical methods to solve mathematical problems.    Some of the problems to be discussed are non-linear equations, the system of linear equations, interpolation, Differentiation and integration, ordinary differential equations of order n
 
Reference
 
Abdul Rahman Abdullah. 1990. Pengiraan Berangka. Kuala Lumpur : DBP.
Atkinson. L.V. & Harley. 1993. An Introduction to Numerical Methods With Pascal,. International Computer science series. Addison - Wesley Pub. Co.
Burden, R.L, Faires, J.D. dan Reynolds. A.C . 1981. Numerical Analysis. Baton, Mass, Prindle, Weber dan Schmidt.
Conter & Carl de Boor. 1993. Analisis Berangka Permulaan: Suatu Pendekatan Algoritma (Terjemahan). K.L: DBP.
Smith, G. D. 1978 . Numerical solution of partial differential equations: Finite Difference methods. Oxford: Oxford University Press.
 
 
 
SM20503 DISCRETE MATHEMATICS
 
The field covered by this course particularly includes: counting methods, relations, functions and graphs, graph theory, Boolean algebra, recurrence relations, group theory and modeling computation. Students will learn to apply the necessary mathematical skills in the everyday life examples such as in modeling computation.
 
Reference
 
Dymacek, W.M. & Sharp, H. 1998. Introduction to Discrete Mathematics. Singapore: McGraw-Hill.
Hein, J.L. 1996. Discrete Mathematics. Massachusetts: Jones & Bartlett Publisher
Johnsonbaugh, R. 1997. Discrete Mathematics. Ed. ke-4. New Jersey: Prentice Hall.
Rosen, K.H. 2003. Discrete Mathematics and Its Applications. Ed. ke-5. McGraw-Hill.
Truss, J. 1999. Discrete Mathematics For Computer Scientists. Ed. ke-2. Singapore. Addison Wesley.
 
 
 
S M 20 80 3  REAL ANALYSIS
 
Prerequisite: SM1053 & SM1063
 
This course covers the properties of real numbers which include infimum and supremum, function, sequence and subsequence, countable and non-countable set, theorems of countable set, open interval, component of bounded interval, open set in E1, theorems of union and intersection sets, limit point, Bolzano-Wierstrass theorem, and closed set in E1.
 
Reference
 
Anderson, K.W and Hall, D.W. 1972. Elementary Real Analysis, McGraw Hill, New York.
Apostol, T.M. 1974. Mathematical Analysis, Addison-Wesley, New York.
Ash. 1972. Real Analysis and Probability, Academic Press, San Diego.
Rudin, W. 1990. Prinsip Analisis Matematik(terjemahan), DBP, Kuala Lumpur.
Stirling D.S.G. 1987. Mathematical Analysis a Fundamental and Straightforward
Approach, Ellis Horwood, New York.
 
 
SM21202 MATHEMATICAL PROGRAMMING
 
This course will provides some mathematical techniques which are used as the tools for solving maximization or minimization problems. Some important concepts such as game theory and dynamic programming will be covered. Students are also able to understand and solve the mathematical programming problems by using Maple and excel.
 
Reference
 
Winston, W.L. & Venakataramanan. 2003. Introduction to Mathematical Programming. USA: Duxbury.Bradley,
Hamdy A. Taha. 2003. Operation Research: An Introduction. New Jersey: Prentice Hall.
Stephen P., Arnold C. Hax & Thomas L. Magnanti. 1997. Applied Mathematical Programming. Addison-Wesley Pub.Co.
Russell C. Walker. 1999. Introduction to Mathematical Programming. New Jersey: Prentice Hall.
Winston, W.L. 1994. Operation Research, Applications and Algorithms. Duxbury Press.
Williams, H.P .1999. Model Building in Mathematical Programming. Wiley.
 
 
 
SM 30103  PROJECT I / S M 30206 PROJECT II
 
A research project on one subject from selected topics in mathematics will be carry out during the semester under the supervision of a lecturer. The course consists of a seminar presentation of the research results, and dissertation writing on literature review, methodology, results and discussion.
 
 
 
S M 30 302 NUMERICAL METHODS
 
Prerequisite: ST2052 & SM2052
 
This course discusses on the use of computers in solving mathematical models, which is expressed in the form of partial differential equations. The topics considered are numerical methods for solving parabolic, elliptic and hyperbolic equations in multi-dimensional problems. The consistency, convergence, stability and accuracy of several numerical schemes will be included.
Reference
 
Abdul Rahman Abdullah, 1990, Pengiraan Berangka, DBP, Kuala Lumpur.
Atkinson, L.V. and Harley, 1993, An Introduction to Numerical Methods with Pascal, International Computer Science Series, Addison-Wesley Pub. Co.
Burden, R.L., Faires, J.D. and Reynolds, A.C., 1981, Numerical Analysis, Baton Mass, Prindle, Weber dan Schmidt.
Lewis, P.E. and Ward, J.P., 1991, The Finite Element Method: Principles and Applications, Addision-Wesley Pub. Co.
Smith, G.D., 1978, Numerical Solution of Partial Differential Equations: Finite Difference Method, Oxford, Oxford University Press.
 
 
 
SM30403 INDUSTRIAL TRANING
 
Students will be placed in industries or research sectors for atleast 10 weeks. This training will be evaluated and student must produce a report on completion of industrial traning.
 
 
S M 30 503 CALCULUS COMPLEX VARIABLE
 
Prerequisite : SM 2013
 
This course covers topics such as regions in complex plane, connected and multi-connected domain, plane equation in complex form, complex variable functions, analysis functions, Cauchy-Riemann condition, Harmonic functions, elementary functions, Riemann domain, complex integral, Cauchy-Goursat and their applications, Cauchy integral theorem and formula, Morera’s theorem, Liouville theorem and fundamental theorem of algebra, infinite series, Taylor’s theorem, Laurent theorem, interior singular points, Cauchy residue theorem and their applications.
 
Reference
 
Churchill, R.V. 1974. Complex Variable and Applications. McGraw-Hill, New York.
Derrick. W.R. 1991. Analisis Kompleks dan Kegunaannya (translation). DBP, Kuala Lumpur.
Aminuddin Ressang, 1995. Pembolehubah Kompleks Permulaan. Jilid I. DBP, Kuala Lumpur.
Aminuddin Ressang, 1995. Pembolehubah Kompleks Permulaan. Jilid II. DBP, Kuala Lumpur.
Nguyen Huu Bong, 1994. Analisis Kompleks. DBP, Kuala Lumpur.
 
 
 
S M 3080 3 ADVANCE MATHEMATICS II
 
Prerequisite : SM2013
 
This course contains topics such as: Multiple Integrals, Change of Variables in Multiple Integrals (Theorem), Vector Calculus (Line Integrals, Green’s Theorem, Surface Integrals, The Divergence Theorem, Stokes’ Theorem) and Fourier Series.
 
Reference
 
Smith R.T, Minton R.B. 2006. Calculus: Early Transcendental Functions Multivariable. McGraw-Hill: New York.
Folland G.B. , 2002. Advanse Calculus. New York : Addison-Wesley.
Kaplan, W. 2002. Advanse Calculus. New York : Addison-Wesley.
Spiegel, M.R., 1983. Schaum’s Outline Series: Advanse Mathematics for Engineers and Scientists. New York : McGraw-Hill.
Finney & Thomas. 2001. Calculus (10 th edition). New York : Addison-Wesley
 
 
 
S M 30903 FUZZY MATHEMATICS
 
The purpose of this course is to introduce the basic theory of fuzzy sets and its applications; including fuzzy relations, fuzzy functions, extension principle, linguistic variables, and fuzzy logic. At the end of this course the students are able to understand the concepts of fuzzy theory especially in fuzzy mathematics and fuzzy systems.
 
Reference
 
A. Kandal. 1986. Fuzzy Mathematical Techniques With Applications. New York: Addison-Wesley.
H.J. Zimmermann. 1996. Fuzzy Set Theory and Its Application. Ed. ke-2. New York: Springs-Verlag.
H.T. Nguyen & E.A. Walker. 1999. A first Course in Fuzzy Logic. Ed. ke-2. CRC Press.
K. Tanaka & T. Niimura. 1996. An introduction to Fuzzy Logic For Practical Applications. Springer.
T.J. Ross. 2004. Fuzzy Logic with Engineering Applications. Ed. ke-2. John Wiley & Sons.
               
 
 
S M 31003  MATHEMATICAL MODELING
 
This course expose students to several mathematical models. Models discussed cover both linear and non linear models. Examples of models include electrical networking analysis, traffic flow, supply and demand model, and linear programming model. Psychological model: market research, consumer behavior forecast, voting results forecast and competition model, financial model includes: multiple interest model include mortgage properties analysis. Problems solving techniques include deterministic method, simulation, stochastic simulation and Monte Carlo.
 
 
Reference
 
Saaty, T.L & Alexander, J.M. 1981. “Thinking with models: mathematical models in the Physical, Biological and Social Sciences”. New York: Pergamon Press.
Bendel, E. A. 1978. “An introduction to Mathematical Modelling”. New York: John Wiley & Sons.
Burgles D.N. 1994. “Applying Mathematics care studies in Mathematical Modelling”. New York: Ellis Horwood.
Disucet, P.G & Sloop P.B. 1992. Mathematical modeling in life Sciences. New York: Ellis Horwood.
Meershaert. 1993. Mathematical Modeling. San Diego: Academic Press.
 
 
 
 SM31102 COMPUTATIONAL GEOMETRY
 
The topics covered in this course include: introduction, polygons, convex hull, triangulations, subdivisions, and intersections.
 
Reference
 
Joseph O'Rourke. 1994. Computational Geometry in C. Cambridge University Press.
Ketan Mulmuley. 1994. Computational Geometry: An Introduction Through Randomized Algorithms. Prentice Hall.
Nievergelt & Hinrichs. 1993. Algorithms and Data Structures with Applications to Graphics and Geometry. Prentice Hall.
O'Rourke. 1998. Computational Geometry in C. 2nd Edition. Cambridge University Press.
Preparata & Shamos. 1985. Computational Geometry- An Introduction. Springer-Verlag.
 
 
 
SM31203 CONTROL MATHEMATICS
 
 
The purpose of this course is to introduce the role of mathematics in solving problems of control systems including feedback phenomena, input-output, and so on. Students will learn to solve some of the controlled problems by using various methods such as Laplace transform, Z-transform, and matrices.
 
Reference
 
Che Mat Hazer Mahmud. 1997.  Reka Bentuk Sistem Kawalan. Pulau Pinang: USM.
D’Azzo & John, J. 1995.  Linear Control System Analysis and Design. 4 th Edition. NewYork: Academic Press.
Dorsey, J. 2001.  Control of Linear Systems. New York: McGrawHill Companies.
Jerzy Zabczyk. 1992.  Mathematical Control Theory: An introduction. Boston.
Rohrs, C.E., Melsa, J.L & Schultz, D.G. 1993.  Linear Control Systems. New York: McGrawHill
 
 
 
.
 

 

updated on 2009-08-07 11:22:29 by admin