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Faculty of Science Handbook, Session 2017/2018

Humanity Skill: subsequences. Basic topology of the real line: Open and
CT3, LL2 closed sets, accumulation points.
References: Assessment:
1. Weir, Maurice D. and Hass, J. (2016) Thomas' Continuous Assessment: 40%
Calculus, Pearson Education, Inc (13 edition). Final Examination: 60%
th
2. Stewart, J. (2015). Calculus, Cengage Learning (8th.
edition). Medium of Instruction:
3. Adams, Robert A. and Essex, C. (2013). Calculus: A English
complete course, Pearson Education (8 edition with
th
MyMathLab). Humanity Skill:
CS3, CT3, LL2
SIM1003 CALCULUS II References:
1. Weir, Maurice D. and Hass, J. (2016) Thomas'
th
Inverses of trigonometric functions, hyperbolic functions, Calculus, Pearson Education, Inc (13 edition).
inverses of hyperbolic functions. Integration by parts, 2. Stewart, J. (2015). Calculus, Cengage Learning (8th.
integration of rational functions by partial fractions, edition).
trigonometric integrals, trigonometric substitutions, 3. Bartle, R.G. & Sherbert, D.R. (2011). Introduction to
improper Integrals. Sequence, infinite series, integral test, real analysis, John Wiley & Sons (4 edition).
th
comparison tests, the ratio and root tests, alternating series 4. Lay, S.R. (2014). Analysis with an introduction to
test, absolute and conditionally convergence, power series, proof, Pearson (5 edition).
th
Taylor and Maclaurin series. Vectors, Dot product, Cross
Product and triple Product, lines and planes. Polar
coordinates. Cyclinder and quadric surfaces. SIM2002 LINEAR ALGEBRA
Vector-valued functions and space curves, differentiation
and integration of vector valued functions. Functions of Vector spaces and subspaces, basis and dimension, the
several variables, limits and continuity in higher row space and column space, rank and nullity. Linear
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:
Humanity Skill: English
CT3, LL2
Humanity Skill:
References: CS3, CT3, LL2
1. Weir, Maurice D. and Hass, J. (2016) Thomas'
Calculus, Pearson Education, Inc (13 edition). References:
th
2. Stewart, J. (2015). Calculus, Cengage Learning (8th. 1. Larson, R. (2013). Elementary Linear Algebra,
th
edition). Brooks/Cole Cengage Learning (7 edition).
3. Adams, Robert A. and Essex, C. (2013). Calculus: A 2. Axler, S (2015). Linear Algebra Done Right, Springer
rd
complete course, Pearson Education (8 edition with (3 edition).
th
MyMathLab). 3. Hoffman, K. M. and Kunze, R. (1971). Linear Algebra,
nd
4. R.T. Smith, R.T. and Minton, R.B. (2012). Calculus, Pearson (2 edition).
McGraw-Hill (4 edition). 4. S.H. Friedberg, S.H., Insel, A.J. and Spence, L.E.
th
(2003). Linear Algebra, Prentice Hall (4th edition).
5. Ma, S.L. and Tan, V. (2006). Linear Algebra I, Pearson
SIM2001 ADVANCED CALCULUS Prentice Hall (2 edition).
nd
Partial derivatives. Differentiability and continuity.
Linearization and differentials. The Chain Rule, Partial SIM2003 INTRODUCTION TOCOMBINATORICS
derivatives with constrained variables. Directional
derivatives. Gradient. Divergence and Curl. Tangent Ordered and equivalence relations, binomial and
planes. Taylor’s Theorem. Extremum problems of functions multinomial theorems, recurrence relations, principle of
of two variables. Lagrange multipliers. inclusion and exclusion, Latin squares, magic squares,
basic properties of graphs, circuits and cycles in graphs,
Double integrals, iterated integrals and Fubini’s Theorem. trees and their applications.
Applications to areas and volumes. Double integrals in
polar form. Triple integrals, iterated integrals. Volumes Assessment:
and masses. Triple integrals in cylindrical and spherical Continuous Assessment: 40%
coordinates forms. Substitution in multiple integrals, Final Examination: 60%
Jacobians.
Medium of Instruction:
Basic set theory. Functions, bijective functions, inverse English
functions. Finite and infinite sets, countable and
uncountable sets. The Real Number system. Bounds, Humanity Skill:
supremum and infimum. Archimedean property. Rational CS3, CT3, LL2
and irrational numbers. Properties of real numbers.
Sequences of real numbers, convergence. Limit Theorems.
Monotone sequences, Cauchy sequences and

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