Page 43 - handbook 20162017

Faculty of Science Handbook, Session 2016/2017

sketching. Logarithms, exponential functions. Indeterminate Double integrals, iterated integrals and Fubini’s Theorem.
forms and L'Hospital's Rule. Definite and indefinite Applications to areas and volumes. Double integrals in
integrals. Fundamental theorem of Calculus and polar form. Triple integrals, iterated integrals. Volumes
differentiation of integrals. Integration methods. and masses. Triple integrals in cylindrical and spherical
coordinates forms. Substitution in multiple integrals,
Assessment: Jacobians.
Continuous Assessment: 40%
Final Examination: 60% Basic set theory. Functions, bijective functions, inverse
functions. Finite and infinite sets, countable and
Medium of Instruction: uncountable sets. The Real Number system. Bounds,
English supremum and infimum. Archimedean property. Rational
and irrational numbers. Properties of real numbers.
Humanity Skill: Sequences of real numbers, convergence. Limit Theorems.
CT3, LL2 Monotone sequences, Cauchy sequences and
subsequences. Basic topology of the real line: Open and
References: closed sets, accumulation points.
1. Weir, Maurice D., Hass, J. and Giordano, Frank R.
(2010) Thomas' Calculus, Pearson Education, Inc (12 th Assessment:
edition). Continuous Assessment: 40%
2. Stewart, J. (2015). Calculus, Cengage Learning (8th. Final Examination: 60%
edition).
3. Adams, Robert A. and Essex, C. (2013). Calculus: A Medium of Instruction:
complete course, Pearson Education (8 edition with English
th
MyMathLab).
Humanity Skill:
CS3, CT3, LL2
SIM1003 CALCULUS II
References:
Inverses of trigonometric functions, hyperbolic functions, 1. Weir, Maurice D., Joel Hass Weir, Maurice D., Hass, J.
inverses of hyperbolic functions. Integration by parts, and Giordano, Frank R. (2010) Thomas' Calculus,
integration of rational functions by partial fractions, Pearson Education, Inc (12 th edition).
trigonometric integrals, trigonometric substitutions, 2. Stewart, J. (2015). Calculus, Cengage Learning (8th.
improper Integrals. Sequence, infinite series, integral test, edition).
comparison tests, the ratio and root tests, alternating series 3. Bartle, R.G. & Sherbert, D.R. (2011). Introduction to
th
test, absolute and conditionally convergence, power series, real analysis, John Wiley & Sons (4 edition).
Taylor and Maclaurin series. Vectors, Dot product, Cross 4. Lay, S.R. (2014). Analysis with an introduction to
Product and triple Product, lines and planes. Polar proof, Pearson (5 edition).
th
coordinates. Cyclinder and quadric surfaces.
Vector-valued functions and space curves, differentiation
and integration of vector valued functions. Functions of SIM2002 LINEAR ALGEBRA
several variables, limits and continuity in higher
dimensions. Vector spaces and subspaces, basis and dimension, the
row space and column space, rank and nullity. Linear
Assessment: transformations, kernel and range, composition and
Continuous Assessment: 40% isomorphism, matrix representation, similarity and
Final Examination: 60% diagonalizability, Cayley-Hamilton Theorem.
Medium of Instruction: Assessment:
English Continuous Assessment: 40%
Final Examination: 60%
Humanity Skill:
CT3, LL2 Medium of Instruction:
English
References:
1. Weir, Maurice D., Hass, J. and Giordano, Frank R. Humanity Skill:
(2010) Thomas' Calculus, Pearson Education, Inc (12 th CS3, CT3, LL2
edition).
2. Stewart, J. (2015). Calculus, Cengage Learning (8th. References:
edition). 1. Larson, R. (2013). Elementary Linear Algebra,
th
3. Adams, Robert A. and Essex, C. (2013). Calculus: A Brooks/Cole Cengage Learning (7 edition).
th
complete course, Pearson Education (8 edition with 2. Axler, S (2015). Linear Algebra Done Right, Springer
rd
MyMathLab). (3 edition).
4. R.T. Smith, R.T. and Minton, R.B. (2012). Calculus, 3. Hoffman, K. M. and Kunze, R. (1971). Linear Algebra,
th
McGraw-Hill (4 edition). Pearson (2 edition).
nd
4. S.H. Friedberg, S.H., Insel, A.J. and Spence, L.E.
(2003). Linear Algebra, Prentice Hall (4th edition).
SIM2001 ADVANCED CALCULUS 5. Ma, S.L. and Tan, V. (2006). Linear Algebra I, Pearson
nd
Prentice Hall (2 edition).
Partial derivatives. Differentiability and continuity.
Linearization and differentials. The Chain Rule, Partial
derivatives with constrained variables. Directional SIM2003 INTRODUCTION TOCOMBINATORICS
derivatives. Gradient. Tangent planes. Taylor’s Theorem.
Extremum problems of functions of two variables. Lagrange Ordered and equivalence relations, binomial and
multipliers. multinomial theorems, recurrence relations, principle of
inclusion and exclusion, Latin squares, magic squares,
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