Page 141 - Handbook Bachelor Degree of Science Academic Session 20212022

Faculty of Science Handbook, Academic Session 2021/2022

multipliers, endpoint and boundary point problems; change of variables;
3. The Physics of Vibrations and Waves, H.J.Pain, 6th edition, Wiley
(2005) differentiation of integrals, Leibniz rule.
4. Mathematical Methods in the Physical Sciences, Mary L.Boas, 3th Assessment Method:
edition,Wiley (2005) Final Examination: 60%
5. A First Introduction to Quantum Physics, Pieter Kok (Springer, Continuous Assessment: 40%
2018)
References:
1. Mary L. Boas, Mathematical Methods in the Physical Sciences, 3rd
SIF1016 MECHANICS I (2 CREDITS) ed. (John Wiley & Sons, 2006)

Introduction to classical dynamics; Analysis of motion of single particle 2. S. Hassani, Mathematical Methods: For Students of Physics and
(Newton’s laws of motion, equation of motion, conservation principle, Related Fields, , 2rd Edition (Springer, 2009)
linear momentum, forces depend on time, velocity, force depends on 3. K. F. Riley, M. P. Hobson, Essential Mathematical Methods for the
Physical Sciences (Cambridge University Press, 2011)
position, work-energy theorem, potential function, simulation of practical 4. G.B. Arfken, H.J. Weber, Mathematical Methods for Physicists: A
examples); Oscillation ( simple harmonic oscillation, phase diagram,
damped oscillation, forced oscilation, simulation/demonstration of Comprehensive Guide, 7th Edition (Elsevier Acad. Press, 2012)
oscillation in various systems); Central forces (reduced mass, equation 5. G. N. Felder, K. M. Felder, Mathematical Methods in Engineering
and Physics (John Wiley & Sons, 2015)
of orbital motion, effective potential, qualitative analysis, planetary 6. D. Babusci, G. Dattoli, S. Licciardi, E. Sabia, Mathematical Methods
motion and Kepler’s laws, gravitational force, stability of circular orbit, for Physicists (World Scientific, 2019)
orbital mechanics, satellite orbits, search for exoplanets); Dynamics of
system of particles (center of mass, example of motion in center of mass
coordinates, elastic collision, inelastic collision, Rutherford scattering, SIF1018 MATHEMATICAL METHODS II (4 CREDITS)
simulation of collisions); Motion of systems with variable mass( equation
of motion, rocket equation, simulation of rocket-like motion in various real Mutliple integrals: integrated integrals; applications of Integrations;
world systems) double and triple integrals in cartesian coordinates; double and triple
integrals in polar coordinates; change of variables in integrals;
Assessment Method: Jacobian; surface integrals.
Final Examination: 60%
Continuous Assessment: 40%
Vector analysis: applications of vector multiplication; triple products;
differentiation and partial differentiation of vectors; integration of
References: vectors; scalar and vector fields; directional derivative; unit normal
1 S.T. Thornton & J.B. Marion, Classical Dynamics of Particles and vectors; gradient; divergence of a vector function; curl of a vector
Systems, 6th Ed. (Brooks Cole, 2004) function; Laplacian; vector operators in polar coordinates; line integrals:
2 G.R. Fowles & G.L. Cassiday, Analytical Mechanics, 6th ed.
(Thomson Brooks/Cole, 2005) scalars and vectors; Green’s Theorem in a plane; divergence and
3 D. Strauch, Classical Mechanics An Introduction. (Springer, 2009), divergence theorem; Curl and Stoke’s Theorem.
(UMLibrary eBook) Tensors: coordinate-system transformation; basis vector
4 L. Susskind & G. Hrabovsky, Classical Mechanics: The Theoretical transformation; non-orthogonal coordinate systems; dual basis vectors;
Minimum (Penguin, 2013).
5 G. Genta, Introduction to the Mechanics of Space Robots. finding covariant and contravariant components; index notation;
quantities that transform contravariantly and covariantly; concepts of
(Springer, 2012), (UMLibrary eBook) covariance and contravariance beyond vectors; covariant,
1. M.J. Benacquista, J.D. Romano, Classical Mechanics (Springer, contravariant, and mixed tensors; tensor addition and subtraction;
2018) tensor multiplication; metric tensor; general curvilinear coordinates;
index raising and lowering; tensor derivatives and Christoffel symbols;
covariant differentiation; vectors and one-forms; tensor applications
SIF1017 MATHEMATICAL METHODS I (3 CREDITS)
Ordinary differential equations: separable equations; first-order linear
homogenous and non-homogeneous equations; second-order linear
Differentiation: Differentiation from first principle: products; the chain homogeneous and nonhomogeneous equations.
rule; quotients; implicit differentiation; logarithmic differentiation;
Leibnitz’ theorem; special points of a function; curvature; theorems of Assessment Method:
differentiation Final Examination: 60%
Continuous Assessment: 40%
Integration: Integration from first principles: the inverse of differentiation;
by inspection; sinusoidal functions; logarithmic integration; using partial References:
fractions; substitution method; integration by parts; reduction formulae; 1. Mary L. Boas, Mathematical Methods in the Physical Sciences, 3rd
infinite and improper integrals; plane polar coordinates; integral ed. (John Wiley & Sons, 2006)
inequalities; applications of integration 2. S. Hassani, Mathematical Methods: For Students of Physics and
Related Fields, , 2rd Edition (Springer, 2009)
Complex number: Real and imaginary parts of complex number; 3. K. F. Riley, M. P. Hobson, Essential Mathematical Methods for the
complex plane; complex algebra; complex infinite series; complex Physical Sciences (Cambridge University Press, 2011)
power series; elementary functions of complex numbers; Euler’s 4. G.B. Arfken, H.J. Weber, Mathematical Methods for Physicists: A
formula; powers and roots of complex numbers; exponential and Comprehensive Guide, 7th Edition (Elsevier Acad. Press, 2012)
trigonometric functions; hyperbolic functions; logarithms; complex roots 5. G. N. Felder, K. M. Felder, Mathematical Methods in Engineering
and powers; inverse trigonometric and hyperbolic functions; and Physics (John Wiley & Sons, 2015)
6. B. Borden, J. Luscombe, Mathematical Methods in Physics,
Matrices and solutions for sets of linear equations: matrix and row
reduction; Cramer’s rule; vectors and their notation; matrix operations; Engineering and Chemistry (John Wiley & Sons, 2020).
linear combinations, linear functions, linear operators; matrix operators,
Linear transformation, orthogonal transformation, eigen value and SIX1015 SCIENCE, TECHNOLOGY AND SOCIETY (2 CREDITS)
eigen vector and diagonalization of matrices; special matrices.
This course examines the interaction between science, technology and
Partial differentiation: power series in two variables; total differentials; society from various perspectives. It provides discussion on the impacts
chain rule; implicit differentiation; stationary values of a function with of science and technology (S&T) progress on society, and vice versa.
one variable and two variables; application of partial differentiation to The discussions comprise the various main aspects of S&T Studies,
maximum and minimum problems including constraints; Lagrange
namely scientific research and development, sustainable development,

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