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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
 
Ho Chong Mun dan Yeo Kiam Beng. 2004. Complex Number. Penerbit SST, Sabah.
Peter Kuhfitting. 2006. Technical Calculus with Aanalytic Geometry. Thomson: Australia.
Rosen H.K. 2003. Discrete Mathematics and Its Applications. McGraw-Hill: New York.
Smith R.T, Minton R.B. 2006.Calculus. McGraw-Hill: New York.
Strauss M.J, Bardley G.L dan Smith K.J. 2002. Calculus. Prentice Hall: New Jersey. 
 
 
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
 
SM10403 OBJECT ORIENTED PROGRAMMING
 
In this course students are introduced to the basics of programming logic and to algorithm design and development, using the C++ programming language. Students will learn the basic constructs of programming in C++, starting with reviews of previously learned topics common with the C programming language, such as variables, constants, expressions, control structures, functions pointers and arrays. In parallel, students will be introduced to C++ programming specifics, such as object-oriented I/O, references (pointers) and C++ memory allocation, the string C++ class, ADTs (abstract data types, including unions and structs), classes, inheritance, polymorphism and virtual functions.
 
References
 
Deitel, H. M. & Deitel, P. J. 2007. C++ How to Program. 6 th Ed. Prentice Hall PTR.
Prata, S. 1998. The Waite Group’s C++ Primer Plus. 3 rd Ed. Sams Publishing.
Schildt. 1995. The Complete Reference. 2 nd Ed. Osborne McGraw-Hill.
Stroustrup, B. 2000. The C++ Programming Language, Special Ed., 3 rd Ed. Addison Wesley.
Ullman, L. & Signer, A. 2006. Visual QuickStart Guide: C++ Programming. Peachpit Press.
 
 
SM10603 INTRODUCTION TO DATA STRUCTURE
 
The topics covered in this course include: concepts of object-oriented programming, basic syntax of C++, creating data objects, array and structs, operators, controlling input and output, program flow, functions, pointers, class, creating and destroying objects, inheritance, and files manipulation.
 
References
 
Drozdek & Adam. 2001. Data Structures and Algorithms in Java. Thompson Learning.
Ian, C. & White, J.D. 2003. Structuring Data & Building Algorithms. McGraw Hill.
Weiss, M. A. 1997. Data Structures & Algorithm Analysis in C. 2 nd Ed. Addison Wesley.
Rowe & Glenn. 1998. An Introduction to Data Structure and Algorithms in Java. Prentice Hall.
Standish & Thomas, A. 1998. Data Structures in Java. Addison Wesley.
 
 
S M 20103  LINEAR ALGEBRA
 
The course starts off from basic concepts on matrices, continues with systems of linear equations and their involvement with matrices, their inverses and determinants. Finally the discussion lead to the idea of linear independence, thus paving the way to the next stage of development, which is the study of vector spaces in a subsequent course.
 
Reference
 
C.M.Ho, K.H.Toh & A.Amran, 2007. Linear Álgebra. Penerbit Universiti Malaysia Sabah, Kota Kinabalu.
Anton, H & Busby, R, 2003 . Contemporary Linear Algebra. John Wiley & Sons, New York.
Beauregard, F, 1995. Linear Algebra, 3 rd Edition. Addison Wesley, New York.
Lim Voon Ka 1983. Algebra Linear Permulaan. DBP, Kuala Lumpur.
Serge Lang, 1986. Introduction to Linear Algebra. 2 nd Edition. Springer-Verlag, New York.
 
SM20203 Differential Equations
 
Prerequisite: SM10103 & SM10203
 
This course covers the analytical techniques to obtain a solution of the linear ordinary differential equations of the first and second-order. The topics including; the first-order differential equations: the exact differential equations, integrating factors, separable equations and linear equations; the second order differential equations will discuss functions that are linearly dependent or independent, reduction of order, homogeneous linear equation with constant coefficients, method of undetermined coefficients and variation of parameters; the introduction to the Laplace transform, including the inverse transform and the convolution and the solution of the linear differential equations with constant coefficients by using Laplace transform; and series solutions of differential equations including power series about an ordinary point and about singular points as commonly called the method of Frobenius.
 
Reference
Boyce, W.E. 2008. Elementary Differential Equations and Boundary Value Problems. Hoboken, New Jersey. John Wiley
Polking, J., Boggesws, A. and Arnold, D. 2006. Differential Equations. Upper Saddle River, New Jersey. Pearson Prentice Hall.
Cushing, J.M. 2004. Differential Equations. Upper Saddle River, New Jersey. Pearson Prentice Hall.
Blanchard, P., Devaney, R.L. and Hall, G.R. 2002. Differential Equations. Pacific Grove, California, Brooks/Cole Thomson Learning.
Bronson, R. 1994. Schaum’s Outline of Theory and Problems of Differential Equations. New York. McGraw-Hill.
Ross, S.L. 1984. Differential Equations. New York. John Wiley.
 
 
S M 20303 ADVANCE MATHEMATICS I
 
Prerequisite : SM10103 & SM10203
 
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 : ST00752 & SM20103
 
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.
 
 
S M 20603 STATISTICAL ANALYSIS
 
Prerequisite: SJ10303
 
This course gives the exposure on intermediate statistics with a statistical package approach. It covers several statistical methods and its applications such as experimental design, regression analysis and categorical data analysis. Statistical package usage (SPSS) will be introduced in every statistical method discussed. Emphasize will be given on the correct technique usage and output interpretation.
 
Reference
 
AhmadSyukri Y., Amran A., Darmesah G & Chin Su Na. Problems & Solutions inStatistics for Engineers & Scientists. 2008. Petaling Jaya : Prentice Hall.
Miller,I & Miller, M. 2004. Mathematical Statistics with Applications SeventhEdition. New Jersey : Prentice-Hall
Norusis,M. J. & SPSS Inc. 1994. SPSS Advanced Statistics 6.1. Chicago: SPSS Inc.
Wackerly,D.D, Mendenhall, W & Sceaffer, R.L. 2002. Mathematical Statistics withApplications Sixth Edition. Thomson.
Walpole, R.E., Myers, R.H. & Myers,S.L. 1998. Probability and Statistics for Engineers and Scientist. 6th ed. New Jersey : Prentice Hall.
 
S M 20 80 3  REAL ANALYSIS
 
Prerequisite: SM10103 & SM10203
 
This course covers some properties of rational numbers and the properties of real numbers which include the real field, the order properties, some properties of absolute value, principle of mathematical induction, inequalities, upper and lower bound, completeness axiom, cardinal numbers, finite, countable and uncountable sets, the algebraic properties of cardinal numbers, numerical sequences and series..
 
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.
 
SM 21003 OPERATIONAL RESEARCH
 
Prerequisite : SM10103 & SM10203
 
Linear Programming Formulation: Introduction to various problem solving techniques such as graph, simplex algorithm, revised simplex algorithm, primal dual, sensitivity analysis. Problem solving with integer decision variables: Gomory cutting plane. Introduction to various problems solving in transportation model, competition model and computer output interpretation: ORSTAT or TORA package.
 
Reference
 
Hiller, F.S. & Lieberman, G.J. 1990. Introduction to Operations Research. New York: Holden-Day, Inc.
Haji Ismail Mohamad. 1991. Teori dan Penggunaan Pengaturcaraan Linear. Kuala Lumpur: Dewan Bahasa & Pustaka.
Kalvelagen, E. & Tijms, H.C. 1990. Exploring Operations Research & Statistics in the Micro Lab. New York: Prentice-Hall Inc.
Taha, H.A. 1993. Penyelidikan Operasi: Pengenalan (Malay translation). Kuala Lumpur: USM & DBP.
Winston, L. Wayne. 1991. Operations Research: Application and Algorithms. Boston: PWS-Kent Publishing.
 
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 : ST00702 & SM20402
 
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 305 03 CALCULUS COMPLEX VARIABLE
 
Pre-requisite : SM 20303
 
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
 
Aminuddin Ressang, 1995. Pembolehubah Kompleks Permulaan. Jilid I dan II. DBP, Kuala Lumpur.
Brown, J.W. & Churchill, R.V. 1996. Complex Variables and Applications, 6th ed. McGraw-Hill Book Co., Singapore.
Mathews, J.H. 1988. Complex Variables for Mathematics & Engineering, 2nd ed. WCB Publisher, Iowa
Nguyen Huu Bong, 1994. Analisis Kompleks dan Penerapan. DBP, Kuala Lumpur.
Osborne, A.D. 1999. Complex Variables and Their Applications. Addison Wesley Longman, Singapore.
Wunsch, A.D. 2005. Complex Variables with Applications, 3rd ed. Pearson Education Inc., Singapore.
 
S M 306 03      DECISION SCIENCE
 
Prerequisite :  SM10103 & SM10203
 
Decision science is a study of techniques in analyzing complex decision problems rationally and logically. It includes development of mathematical models development, simulation, computerize model and several quantitative methods. This course also covers basic decision theory, decision analysis, criteria of certainty and uncertainty decision making, network flow, inventory model, queuing system, Markov process and simulation.
 
Reference
 
Anderson, D.R., Sweeney, D.J. & Williams, T.A. 2003. An Introduction To Management Science : Quantitative Approaches to Decision Making. 10 th Edition. Thompson Learning.
Bernard W. Taylor. 2004. Introduction To Management Science. 8 th Edition. Pearson Hall.
Hamdy A. Taha. 2003. Operations Research : An Introduction. 8 th Edition. Prentice Hall, New Jersey.
 
S M 30703  OPTIMISATION
 
Prerequisite :  SM10103 & SM10203
 
This course is the continuation from Operational Research. Topics that will be discussed here are nonlinear programming: univariable optimisation, multiple variable without constraints, Deterministic Dynamic Programming, Decision process at several levels and network Analysis: networking optimisation problem, CPM, minimum cost flow problem, and transportation problems. Applications of computer softwares in solving optimisation problem are encouraged.
 
Reference
 
Hamdy A. Taha. 2003. Operations Research : An Introduction. 7 th Edition. Prentice Hall, New Jersey.
Hiller, F.S. & Lieberman, G.J. 2001. Introduction to Operations Research, Holden-Day, Inc, New York.
Paul A. Jensen & Jonathon F. Bard. 2003. Operations Research : Models and Methods. John Wiley & Sons, USA.
Rohani Yaacob. 2001. Pengaturcaraan Linear & Integer. USM, Pulau Pinang.
Winston, L. W. 1991. Operations Research: Application and Algorithms. 2 nd ed. PWS-Kent Publishing, Boston.
 
 
 

 

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