Page 77 - Handbook Bachelor Degree of Science Academic Session 20212022

Faculty of Science Handbook, Academic Session 2021/2022

References:
References: 1. Boyce, W. E., Diprima, R. C., & Meade, D. B. (2017).
1. Joel R. Hass, Christopher E. Heil, Maurice D. Weir, Elementary Differential Equations and Boundary
Thomas' Calculus, 14th edition, Pearson Education, Inc. Value Problems, 11 ed., John Wiley & Sons, Inc.
th
2019.
2. J. Stewart, Calculus, 8th. edition, Cengage Learning, 2. Trench, W. F. (2021). Elementary Differential
Equations
Values
Problems.
with
Boundary
2016. LibreTexts Project (https://math.libretexts.org/).
3. Robert A. Adams, Christopher Essex, Calculus: A 3. Blanchard, P., Devaney, R. L., & Hall, G. R. (2012).
th
complete course, 8 edition with MyMathLab, Pearson Differential Equations. Cengage Learning.
Education, 2013.
4. R.T. Smith, R.B. Minton, Calculus, 4th ed., McGraw-Hill,
2012.
SIM2001 ADVANCED CALCULUS
Partial derivatives. Differentiability and continuity.
SIM1004 FUNDAMENTALS OF COMPUTING
Linearization and differentials. The Chain Rule, Partial
derivatives with constrained variables. Directional
MATLAB - Matlab environment, matrices, constants and derivatives. Gradient, divergence and curl. Tangent planes.
variables, operations, built-in functions, formatted output, Taylor’s Theorem. Extremum problems of functions of two
plotting graphs, expressions and logical data, branches and
loops, scripting, user-defined functions. Applications to variables. Lagrange multipliers.
selected mathematical problems.
Double integrals, iterated integrals and Fubini’s Theorem.
Applications to areas and volumes. Double integrals in polar
Assessment: form. Triple integrals, iterated integrals. Volumes and
Continuous Assessment: 50%
Final Examination: 50% masses. Triple integrals in cylindrical and spherical
coordinates forms. Substitution in multiple integrals,
Jacobians.
References:
1. Hahn, B. D., & Valentine, D. T. (2019). Essential Basic set theory. Functions, bijective functions, inverse
MATLAB for engineers and scientists. Cambridge,
MA: Academic Press. functions. Finite and infinite sets, countable and uncountable
2. MATLAB ® Primer R2019a. (2019). MathWorks, Inc. sets. The Real Number system. Bounds, supremum and
infimum. Archimedean property. Rational and irrational
3. Chapman, S. J. (2016). MATLAB Programming for numbers. Properties of real numbers. Sequences of real
Engineers. Cengage Learning.
numbers, convergence. Limit Theorems. Monotone
sequences, Cauchy sequences and subsequences. Basic
topology of the real line: Open and closed sets, accumulation
SIM1005 FUNDAMENTALS OF SPREADSHEETS
points.
Basics of worksheets, entering labels, numbers and
formulae. Absolute and relative addressing, Excel functions. Assessment:
Graph plotting. Use of Excel Solver. Applications to some Continuous Assessment: 40%
selected mathematical problems. Final Examination: 60%
References:
Assessment:
Continuous Assessment: 50% 1. Joel R. Hass, Christopher E. Heil, Maurice D. Weir,
Final Examination: 50% Thomas' Calculus, 14th edition, Pearson Education,
Inc. 2019.
2. J. Stewart, Calculus, 8th. edition, Cengage Learning,
References: 2016.
1. Engineering with Excel by Ronald W. Larsen, Upper
Saddle River, NJ: Pearson Prentice Hall, 5 edition, 3. R. G. Bartle & D. R. Sherbert, Introduction to Real
th
2017. Analysis, 4th ed., John Wiley & Sons, 2011.
2. Excel for Engineers and Scientists by S. C. Bloch and 4. R. Lay, Analysis with an introduction to proof, 5th ed.,
Pearson, 2014.
Sylvan Charles Bloch, John Wiley & Sons 2003. 5. M. Field, Essential Real Analysis, Springer
3. Excel for Scientists and Engineers: Numerical Undergraduate Mathematics Series, 2017.
Methods by E. Joseph Billo, Wiley-Interscience;
2007.
SIM2002 LINEAR ALGEBRA
SIM1006 ORDINARY DIFFERENTIAL EQUATIONS
Vector spaces and subspaces, null spaces, sums and direct
sums of subspaces. Linear independences, bases,
First order ODEs: Definitions, solution concepts, valid dimension, the subspaces dimension theorem, row and
solution intervals. Solutions to separable equations, linear column spaces, rank, ordered bases, coordinates, changes
equations, Bernoulli, exact and non-exact, homogeneous of basis. Linear transformations, kernel and range, the rank-
equations. Some applications of first order ODEs.
nullity theorem, isomorphisms, matrix representations.
Eigenvalues, eigenvectors, characteristic polynomials,
Linear ODEs of second and higher orders: Definitions, diagonalizability, the Cayley-Hamilton Theorem.
solution concepts, linear independence, Wronskian.
Solutions to homogeneous and non-homogeneous Assessment:
equations. Method of undetermined coefficients, Variation of
parameters. Series solutions. Frobenius’s method, Continuous Assessment: 40%
Legendre and Bessel’s equations. Final Examination: 60%
Assessment: References:
Continuous Assessment: 40% 1. Axler, S. (2015). Linear algebra done right (3 ed.). New
rd
Final Examination: 60% York: Springer-Verlag.
2. Friedberg, S.H., Insel, A.J., Spence, L.E. (2019). Linear
th
algebra (5 ed.). New Jersey: Pearson Education.
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