Page 104 - handbook 20152016

Faculty of Science Handbook, Session 2015/2016

SIM1002 CALCULUS I SIM2001 ADVANCED CALCULUS

Real numbers and real line. Inequality and absolute values. Partial derivatives. Differentiability and continuity.
Functions and their graphs. Combining Functions. Limits: Linearization and differentials. The Chain Rule, Partial
Intuitive, limit laws, one-sided limits, limits involve infinity, derivatives with constrained variables. Directional
epsilon-delta definition for limits. Continuity. Derivatives: derivatives. Gradient, divergence and curl. Tangent
tangent lines and definition for derivatives. Differentiation planes. Taylor’s Theorem. Extremum problems of functions
Rules including the Chain Rule and implicit differentiation. of two variables. Lagrange multipliers.
Rolle's Theorem, The Mean Value Theorem, Maximum,
minimum, concavity and points of inflection. Graph Double integrals, iterated integrals and Fubini’s Theorem.
sketching. Logarithms, exponential functions. Indeterminate Applications to areas and volumes. Double integrals in
forms and L'Hospital's Rule. Definite and indefinite polar form. Triple integrals, iterated integrals. Volumes
integrals. Fundamental theorem of Calculus and and masses. Triple integrals in cylindrical and spherical
differentiation of integrals. Integration methods. coordinates forms. Substitution in multiple integrals,
Jacobians.
Assessment:
Continuous Assessment: 40% Basic set theory. Functions, bijective functions, inverse
Final Examination: 60% functions. Finite and infinite sets, countable and
uncountable sets. The Real Number system. Bounds,
Medium of Instruction: supremum and infimum. Archimedean property. Rational
English and irrational numbers. Properties of real numbers.
Sequences of real numbers, convergence. Limit Theorems.
Humanity Skill: Monotone sequences, Cauchy sequences and
CT3, LL2 subsequences. Basic topology of the real line: Open and
closed sets, accumulation points.
References:
1. Weir, Maurice D., Hass, J. and Giordano, Frank R. Assessment:
th
(2010) Thomas' Calculus, Pearson Education, Inc (12 Continuous Assessment: 40%
edition). Final Examination: 60%
2. Stewart, J. (2015). Calculus, Cengage Learning (8th.
edition). Medium of Instruction:
3. Adams, Robert A. and Essex, C. (2013). Calculus: A English
th
complete course, Pearson Education (8 edition with
MyMathLab). Humanity Skill:
CS3, CT3, LL2

SIM1003 CALCULUS II References:
1. Weir, Maurice D., Joel Hass Weir, Maurice D., Hass, J.
Inverses of trigonometric functions, hyperbolic functions, and Giordano, Frank R. (2010) Thomas' Calculus,
th
inverses of hyperbolic functions. Integration by parts, Pearson Education, Inc (12 edition).
integration of rational functions by partial fractions, 2. Stewart, J. (2015). Calculus, Cengage Learning (8th.
trigonometric integrals, trigonometric substitutions, edition).
improper Integrals. Sequence, infinite series, integral test, 3. Bartle, R.G. & Sherbert, D.R. (2011). Introduction to
th
comparison tests, the ratio and root tests, alternating series real analysis, John Wiley & Sons (4 edition).
test, absolute and conditionally convergence, power series, 4. Lay, S.R. (2014). Analysis with an introduction to
th
Taylor and Maclaurin series. Vectors, Dot product, Cross proof, Pearson (5 edition).
Product and triple Product, lines and planes. Polar
coordinates. Cyclinder and quadric surfaces.
Vector-valued functions and space curves, differentiation SIM2002 LINEAR ALGEBRA
and integration of vector valued functions. Functions of
several variables, limits and continuity in higher Vector spaces and subspaces, basis and dimension, the
dimensions. row space and column space, rank and nullity. Linear
transformations, kernel and range, composition and
Assessment: isomorphism, matrix representation, similarity and
Continuous Assessment: 40% diagonalizability, Cayley-Hamilton Theorem.
Final Examination: 60%
Assessment:
Medium of Instruction: Continuous Assessment: 40%
English Final Examination: 60%

Humanity Skill: Medium of Instruction:
CT3, LL2 English

References: Humanity Skill:
1. Weir, Maurice D., Hass, J. and Giordano, Frank R. CS3, CT3, LL2
th
(2010) Thomas' Calculus, Pearson Education, Inc (12
edition). References:
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
th
complete course, Pearson Education (8 edition with (3 edition).
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).
th
McGraw-Hill (4 edition). 4. S.H. Friedberg, S.H., Insel, A.J. and Spence, L.E.
(2003). Linear Algebra, Prentice Hall (4th edition).
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