Page 119 - Handbook Bachelor Degree of Science Academic Session 20202021

Faculty of Science Handbook, Academic Session 2020/2021

References:
SIM1003 CALCULUS II 1. Weir, Maurice D., & Hass, J. (2016). Thomas' calculus
th
(13 ed.). Pearson Education, Inc.
Inverses of trigonometric functions, hyperbolic functions, 2. Stewart, J. (2015). Calculus (8 ed.). Cengage
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inverses of hyperbolic functions. Integration by parts, Learning.
integration of rational functions by partial fractions, 3. Bartle, R.G., & Sherbert, D.R. (2011). Introduction to
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trigonometric integrals, trigonometric substitutions, improper real analysis (4 ed.). John Wiley & Sons.
Integrals. Sequence, infinite series, integral test, comparison 4. Lay, S.R. (2014). Analysis with an introduction to proof
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tests, the ratio and root tests, alternating series test, absolute (5 ed.). Pearson.
and conditionally convergence, power series, Taylor and
Maclaurin series. Vectors, Dot product, Cross Product and
triple Product, lines and planes. Polar coordinates. Cyclinder SIM2002 LINEAR ALGEBRA
and quadric surfaces. Vector-valued functions and space
curves, differentiation and integration of vector valued Vector spaces and subspaces, basis and dimension, the row
functions. Functions of several variables, limits and space and column space, rank and nullity. Linear
continuity in higher dimensions. transformations, kernel and range, composition and
isomorphism, matrix representation, similarity and
Assessment: diagonalizability, Cayley-Hamilton Theorem.
Continuous Assessment: 40%
Final Examination: 60% Assessment:
Continuous Assessment: 40%
Medium of Instruction: Final Examination: 60%
English
Medium of Instruction:
Soft Skills: English
CTPS3, LL2
Soft Skills:
References: CS3, CTPS3, LL2
1. Weir, Maurice D., & Hass, J. (2016). Thomas' calculus
(13 ed.) Pearson Education, Inc. References:
th
2. Stewart, J. (2015). Calculus (8 ed.). Cengage 1. Larson, R. (2017). Elementary Linear algebra (8 ed.).
th
th
Learning. Mason, OH: Cengage Learning.
rd
3. Adams, Robert A., & Essex, C. (2013). Calculus: A 2. Sheldon, A. (2015). Linear algebra done right (3 ed.).
th
complete course (8 ed. With MyMathLab). Pearson New York, NY: Springer International Publishing.
nd
Education. 3. Hoffman, K. M., Kunze, R. (1971). Linear algebra (2
4. R.T. Smith, R.T., & Minton, R.B. (2012). Calculus (4 ed.). Englewood Cliffs, NJ: Prentice-Hall.
th
ed.). McGraw-Hill. 4. Friedberg, S.H., Insel, A.J., & Spence, L.E. (2002).
th
Linear algebra (4 ed.). Upper Saddle River, NJ:
Prentice – Hall.
SIM2001 ADVANCED CALCULUS 5. Ma, S.L., Tan, V., & Ng, K.L. (2007). Linear algebra I
(3 ed.). Singapore: Pearson Prentice-Hall.
rd
Partial derivatives. Differentiability and continuity.
Linearization and differentials. The Chain Rule, Partial
derivatives with constrained variables. Directional SIM2003 INTRODUCTION TO COMBINATORICS
derivatives. Gradient. Divergence and Curl. Tangent planes.
Taylor’s Theorem. Extremum problems of functions of two Ordered and equivalence relations, binomial and multinomial
variables. Lagrange multipliers. theorems, recurrence relations, principle of inclusion and
exclusion, Latin squares, magic squares, basic properties of
Double integrals, iterated integrals and Fubini’s Theorem. graphs, circuits and cycles in graphs, trees and their
Applications to areas and volumes. Double integrals in polar applications.
form. Triple integrals, iterated integrals. Volumes and
masses. Triple integrals in cylindrical and spherical Assessment:
coordinates forms. Substitution in multiple integrals, Continuous Assessment: 40%
Jacobians. Final Examination: 60%

Basic set theory. Functions, bijective functions, inverse Medium of Instruction:
functions. Finite and infinite sets, countable and uncountable English
sets. The Real Number system. Bounds, supremum and
infimum. Archimedean property. Rational and irrational Soft Skills:
numbers. Properties of real numbers. Sequences of real CS3, CTPS3, LL2
numbers, convergence. Limit Theorems. Monotone
sequences, Cauchy sequences and subsequences. Basic References:
topology of the real line: Open and closed sets, accumulation 1. Erickson, M.J. (2013). Introduction to combinatorics
nd
points. (2 ed.). Wiley.
2. Chen, C.C., & Koh, K.M. (1992). Principles and
Assessment: techniques in combinatorics. World Scientific.
Continuous Assessment: 40% 3. Lovasz, L., Pelikan, J., & Vesztergombi, K. (2003).
Final Examination: 60% Discrete mathematics: Elementary and beyond.
Springer.
Medium of Instruction: 4. Matousek J., & Nesetril J. (2008). Invitation to discrete
English mathematics (2 ed.). Oxford University Press.
nd

Soft Skills:
CS3, CTPS3, LL2
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