MAT 110 Mathematics I Differential Calculus and Co-ordinate Geometry

A. Course General Information:

B. Course Catalog Description (Content):

Differential Calculus: Limits. Continuity and differentiability. Successive differentiation of various types of functions. Leibniz's Theorem. Rolle's theorem. Mean Value theorem. Taylor's theorem in finite and infinite forms. Maclaurin's theorem in finite and infinite forms. Lagrange's form of remainders. Expansion of functions. Evaluation of indeterminate forms by L'Hôpitals rule. Partial differentiation. Euler's theorem. Tangent and normal. Subtangent and subnormal in Cartesian and polar coordinates. Determination of maximum and minimum values of functions and points of inflexion. Application. Curvature. Radius of curvature. Centre of curvature.

Coordinate Geometry: Change of axes. Transformation of coordinates. Simplification of equation of curves. Pair of straight lines. Conditions under which general equations of the second degree may represent a pair of straight lines. Homogeneous equations of the second degree. Angle between the pair of lines. Pair of lines joining the origin to the point of intersection of two given curves. System of circles; orthogonal circles. Radical axes, radical centre, properties of radical axes, coaxial circles and limiting points. Equations of ellipse and hyperbola in Cartesian and polar coordinates. Tangent and normal. Pair of tangent. Chord of contact. Chord in terms of its middle points, parametric coordinates. Diameters. Conjugate diameters and their properties. Director circles and asymptotes.

C. Course Objectives and Outcomes:

• To find the rate at which one quantity changes relative to another.
• To understand the concept of limits, continuity, differentiability and optimization.
• To learn some of the important theorems with applications.
• To provide students with a good understanding of the concepts of two dimensional geometry

D. Suggested Text and Reference Book:

• A Text Book on Coordinate geometry and Vector Analysis by Kosh Mohammad.
• L. Loney, "The Elements of Coordinate Geometry", Nelson Thornes
• Anton, H. Bivens, I. Davis, S. Calculus 10th edition, John Wiley and Sons Inc., 2012.
• Stewart, J. Calculus 8th edition, Cengage Learning, 2016.

MAT 120 Mathematics II Integral Calculus and Differential Equations

A. Course General Information:

B. Course Catalog Description (Content):

Integral Calculus: Definitions of integration. Integration by the method of substitution. Integration by parts. Standard integrals. Integration by method of successive reduction. Definite integrals, its properties and use in summing series. Walli's formula. Improper integrals. Beta function and Gamma function. Area under a plane curve in cartesian and polar coordinates. Area of the region enclosed by two curves in cartesian and polar coordinates. Trapezoidal rule. Simpson's rule. Arc lengths of curves in cartesian and polar coordinates, parametric and pedal equations. Intrinsic equations. Volumes of solids of revolution. Volume of hollow solids of revolutions by shell method. Area of surface of revolution.

Ordinary Differential Equations: Degree of order of ordinary differential equations. Formation of differential equations. Solution of first order differential equations by various methods. Solutions of general linear equations of second and higher order with constant coefficients. Solution of homogeneous linear equations. Applications. Solution of differential equations of the higher order when the dependent and independent variables are absent. Solution of differential equations by the method based on the factorization of the operators.

C. Course Objectives and Outcomes:

• To know how to calculate antiderivatives and to understand the relation between derivatives and antiderivatives.
• To learn the applications of Integral Calculus for single variable.
• To provide a platform in obtaining necessary basic information regarding ordinary differential equations.
• To understand the classifications of ordinary differential equations, several methods and techniques to solve these equations.

D. Suggested Text and Reference Book:

• Anton, H. Bivens, I. Davis, S. Calculus 10th edition, John Wiley and Sons Inc., 2012.
• Zill, D.G. A First Course in Differential Equations with Modeling Applications, 9th ed. Brooks/Cole, Cengage Learning, 2009.
• Don, Mathematica, Second Edition, McGraw-Hill, 2009 (For Practical)

MAT 215 Mathematics III Complex Variables and Laplace Transformations

A. Course General Information:

B. Course Catalog Description (Content):

Complex Variables: Complex number systems. General functions of a complex variable. Limits and continuity of a function of complex variables and related theorems. Complex differentiation and Cauchy–Riemann equations. Mapping by elementary functions. Line integral of a complex function. Cauchy's theorem. Cauchy's integral formula. Liouville's theorem. Taylor's and Laurent's theorem. Singular points. Residue. Cauchy's residue theorem. Evaluation of residues. Contour integration. And conformal mapping.

Laplace Transformations: Definition. Laplace transformations of some elementary functions. Sufficient conditions for existence of Laplace transforms. Inverse Laplace transforms. Laplace transforms of derivatives. The unit step function. Periodic function. Some special theorems on Laplace transforms. Partial fractions. Solutions of differential equations by Laplace transforms. Evaluation of improper integrals.

C. Course Objectives and Outcomes:

• To know about complex number system in details.
• To introduce with the basic theorems and their applications in engineering problems.
• To learn Laplace and Inverse Laplace transforms with their applications in solving higher order ordinary differential equations.

D. Suggested Text and Reference Book:

• BROWN, J.W., CHURCHILL, R.V. COMPLEX VARIABLES AND APPLICATIONS, 8TH ED. MCGRAW-HILL, 2009.
• ZILL, D.G. A FIRST COURSE IN DIFFERENTIAL EQUATIONS WITH MODELING APPLICATIONS, 9TH ED. BROOKS/COLE, CENGAGE LEARNING, 2009.
• KREYSZIG, E. ADVANCED ENGINEERING MATHEMATICS, 10TH ED. JOHN WILEY & SONS INC., 2011.

MAT 216 Mathematics IV Linear Algebra and Fourier Analysis

A. Course General Information:

B. Course Catalog Description (Content):

Linear Algebra: Matrices. Algebra of matrices. Adjoint and inverse of a matrix. Elementary transformations of matrices. Rank and Nullity. Normal and canonical forms. Solution of linear equations. Vector spaces, Linear dependence, and independence of vectors. Definition of line, surface and volume integrals. Gradient, divergence and curl of point functions. Various formulae. Gauss's theorem, Stroke's theorem, Green's theorem.

Fourier Analysis: Real and complex form. Finite transform. Fourier integral. Fourier transforms and their uses in solving boundary value problems.

C. Course Objectives and Outcomes:

• To provide students with a good understanding of the concepts and methods of linear algebra.
• To learn about matrices, determinant, vector spaces and linear transformations with applications.
• To understand the theories and applications of Integral Calculus for multivariable and Vector Calculus.
• To know the basic concepts of Fourier series, Fourier integral and Fourier transforms with applications.

D. Suggested Text and Reference Book:

• Anton, H., Rorres, C. Elementary Linear Algebra, Applications Version 11th ed. Wiley 2013
• Kreyszig, E. Advanced Engineering Mathematics, 10th ed. John Wiley & Sons Inc., 2011.
• Brown, J.W., Churchill, R.V. Fourier Series and Boundary Value Problems, 7th ed. McGraw-Hill, 2008.
• Spiegel, M.R. Schaum's Outline of Theory and Problems of Fourier Analysis with Applications to Boundary Value Problems, McGraw-Hill Inc., 1974.

STA 201 Elements of Statistics and Probability

A. Course General Information:

B. Course Catalog Description (Content):

Introduction to Statistics & Representation of Data. Central Tendency & Measures of Dispersion: Mean (Arithmetic, Geometric, Harmonic, Weighted), Median, Mode, Quartiles. Range, Deviation (Quartile, Mean, Standard), Variance, Coefficient of Variation, Skewness, Kurtosis. Correlation & Regression: Correlation, Scatter Diagram, Correlation Coefficient with interpretation. Regression Analysis, Linear Regression Model, Estimation of Parameters, Least Square Regression. Set Theory & Basics of Probability, Bayes' Theorem. Set theory concepts, Relation of set theory with probability, Probability basics (addition, multiplication, simultaneous incidents, dependent/independent incidents etc). Conditional probability (dependent/independent cases), Bayes’ theorem (with application examples). Random Variables, Joint Probability, Marginalization, Expectation of Random Variables. Random variable basics, Product rule of random variables, Joint probability, Basics of marginalization of probability. More on joint distribution (marginalization and other stuff), Basics of conditioning on random variables, Expectation of random variables, Linearity of expectations. Probability Distributions: Discrete Probability distribution basics (Binomial, Poisson, Geometric) with proper graphs. Continuous Probability distribution basics (Normal, Exponential) with proper graphs. Basic ideas of Hypothesis testing and Different kinds of testing. Shannon Entropy & Marginalization of 2 or more Random Variables. Shannon information content, Shannon Entropy. Information divergence, Marginalization of random variables. Conditioning on Random Variables, Bayes' Rule for Random Variables, Conditional Independence. More on conditioning on random variables, Bayes' rule for random variables. Conditional independence, Mutual vs Pairwise independence. Decision Making: Intro to decision making, Maximum Likelihood . Medical Diagnosis Risk. Maximum A Posteriori (MAP) Estimation. Introduction to Different Models: Intro to Hidden Markov Model, Introduction to Naive Bayes Model. Sampling and Review of the Course.

C. Course Objectives and Outcomes

The main objective of the course is to make familiar with the basic concepts of statistics and its applications for life science and engineering students. Attempts will be made to provide a clear, concise understanding of the fundamental features and methods of statistics along with relevant interpretations and applications for conducting quantitative analyses. This course will help students to develop skills in thinking and analyzing a wide range of problem in the field of life science and engineering from a probabilistic and statistical point of view.  

At the end of this course, students will be able to:

• Develop fundamental concepts of probability and statistics commonly used in life sciences, engineering and other fields.
• Evaluate various quantities for probability distributions and random variables.
• Perform statistical computations & interpret the outcomes effectively.
• Develop probabilistic and statistical models for some applications, and a           Statistical method to a range of problems in life sciences, engineering and other fields.
• Comprehend the theoretical foundations that leads to choosing the appropriate analysis (i.e. hypothesis testing).

D. Suggested Text and Reference Book:

• Applied Statistics for Engineers and Scientists, 3rd edition, Devore J. Farnum N., Duxbury.
• Probability and Statistics in Engineering, 4th edition, William W. Hines, Douglas C. Montgomery, David M. Goldsman and Connie M. Borror, Wiley.
• A First Course in Probability, 9th edition, Sheldon M. Ross (2018).
• Probability and Random Processes, 3rd edition, G. R. Grimmett and D. R. Stirzaker,Oxford University Press (2001)
• Probability and Statistical Inference, 9th edition, R. V. Hogg and E. A. Tanis Prentice Hall, (2007)
• Foundations of Biostatistics, 1st edition. Springer, New York. M. Ataharul Islam, Abdullah Al-Sinha (2018).
• An Introduction to Statistics and Probability, 4th edition, M. Nurul Islam (2017).
• Fundamentals of Probability & Probability Distributions, 4th edition, Manindra Kumar Roy (2014).

PHY 111 Principles of Physics I

A. Course General Information:

B. Course Catalog Description (Content):

Vectors and scalars, unit vector, scalar and vector products, static equilibrium, Newton's Laws of motion, principles of conservation of linear momentum and energy, friction, elastic and inelastic collisions, projectile motion, uniform circular motion, centripetal force, simple harmonic motion, rotation of rigid bodies, angular momentum, torque, moment of inertia and examples, Newton's Law of gravitation, gravitational field, potential and potential energy. Structure of matter, stresses and strains, Modulii of elasticity Poisson's ratio, relations between elastic constants, work done in deforming a body, bending of beams, fluid motion and viscosity, Bernoulli's Theorem, Stokes' Law, surface tension and surface energy, pressure across a liquid surface, capillarity. Temperature and Zeroth Law of thermodynamics, temperature scales, their propagation, differential equation of wave motion, stationary waves, vibration in strings isotherms, heat capacity and specific heat, Newton's Law of cooling, thermal expansion, First Law of thermodynamics, change of state, Second Law of thermodynamics, Carnot cycle, efficiency, kinetic theory of gases, heat transfer. Waves & & columns, sound wave & its velocity, Doppler effect, beats, intensity & loudness, ultrasonics and its practical applications. Huygens' principle, electromagnetic waves, velocity of light, reflection, refraction, lenses, interference, diffraction, polarization..

C. Course Objectives and Outcomes:

By the end of this course, the students will be able to:

• Describe and explain the introductory mechanics principles.
• Apply these principles together with logical reasoning to real life situations.
• Analyze and solve problems with the aids of mathematics.
• Acquire and interpret experimental data to examine the mechanical laws

D. Suggested Text and Reference Book:

• Fundamentals of Physics. Author: Halliday, Resnick & Walker (10th Edition, Extended).
• University Physics by F. W. Sears, M. W. Zemansky and H. D. Young.

PHY 112 Principles of Physics II

A. Course General Information:

B. Course Catalog Description (Content):

Electric charge, Coulomb's Law, electric field & flux density, Gauss's Law, electric potential, capacitors, steady current, Ohm's law, Kirchhoff's Laws. Magnetic field, Biot-Savart Law, Ampere's Law, electromagnetic induction, Faraday's Law, Lenz's Law, self inductance and mutual inductance, alternating current, magnetic properties of matter, diamagnetism, paramagnetism and ferromagnetism. Maxwell's equations of electromagnetic waves, transmission along wave-guides. Special theory of relativity, length contraction and time dilation, mass-energy relation. Quantum theory, Photoelectric effect, x-rays, Compton effect, dual nature of matter and radiation, Heisenberg uncertainty principle. Atomic model, Bohr's postulates, electron orbits and electron energy, Rutherford nuclear model, isotopes, isobars and isotones, radioactive decay, half-life, alpha, beta and gamma rays, nuclear binding energy, fission and fusion. Fundamentals of solid state physics, lasers, holography.

C. Course Objectives and Outcomes:

By the end of this course, the students will be able to:

• Describe and explain the introductory electricity and magnetism principles i.e. Coulomb's law, Gauss's law, Biot-Savart and Ampere's laws
• Understand the basic concepts of special theory of relativity, atomic model, nuclear and solid state physics
• Apply these principles, together with logical reasoning to real life situations
• Analyze and solve problems with the aids of mathematics
• Acquire and interpret experimental data to examine the laws of electricity and magnetism.

D. Suggested Text and Reference Book:

• Principles of Physics. Author: Halliday, Resnick & Walker (10thedition, International). (Any edition is sufficient. However, the topics may have different section numbers depending on the edition).
• Concepts of Modern Physics by Arthur Beiser.
• Beiser, "Perspectives of Modern Physics", McGraw-Hill, 6th ed., 2002.

CHE 110 Principles of Chemistry

A. Course General Information:

B. Course Catalog Description (Content):

Nature of Atoms: Structure of atoms, Dalton’s postulates, J.J. Thompson’s atomic mode, Rutherford’s atomic model, Bohr’s atomic model, Max Planck’s theory of quantum, spectra of hydrogen atom, quantum numbers, concept of orbit and orbital, electronic configuration, Aufbau principle, Pauli’s exclusion principle, Hund’s principle, isotope, isotones, isobars, periodic table, periodic nature of elements etc. Radio Activity: Radioactive elements, nuclear fission, chain reaction, decay Law, α,β,γ ray and their properties, mean life and half-life. Chemical Reaction: types of chemical bonding, chemical reaction classifications, thermochemistry, oxidation reduction, acid and bases, reaction equilibrium, chemical kinetics etc. Gas Law: Ideal gas, Real gas, Charle’s law, Boyel’s Law, ideal gas combined law, kinetic theory of gasses and related mathematical problems. Environmental Chemistry: Environments and its chemistry, environmental Pollution and Its sources, types of environmental pollution and their effects, Atmospheric Chemistry, Aerosols, influence of CFC gases, creation of ozone hole, green house effects etc. Colligative properties: introduction to colligative properties, dilute solution, types of solution, depression of freezing point. Lowering of vapor pressure, elevation of boiling point, Roult’s law, osmotic pressure. 

C. Course Objectives and Outcomes:

At the end of this course, students will be able to:

• Understand and be able to explain the general principles, laws and theories of chemistry that are discussed and presented throughout the semester.
• Analyze the importance of intra- and intermolecular attraction to predict trends in physical properties.
• Identify characteristics  of  acids,  bases  and  salts  and  solve  problems  based  on  their quantitative relationships.
• Identify and balance oxidation – reduction reaction.
• Apply quantitative skill to determine the rate of reaction and its dependence on different factors.
• Develop an awareness of the value of chemistry in our daily life.

D. Suggested Text and Reference Book:

• Ebbing, D. and Gammon, S.D., 2016. General chemistry. Cengage Learning.
• Silberberg, M., 2012. Principles of general chemistry. McGraw-Hill Education.
• Haider, S.Z., 2000. Introduction to modern inorganic chemistry.
• Tuli, G.D. and Bahl, B.S., 2010. Essentials of Physical Chemistry. S Chand & Co Ltd.
• Sharma, K.K. and Sharma, L.K., 2016. A textbook of physical chemistry. Vikas Publishing House.
• Adamson, A., 2012. A textbook of physical chemistry. Elsevier.
• Shoemaker, D.P., Garland, C.W., Nibler, J.W. and Feigerle, C.S., 1996. Experiments in physical chemistry (Vol. 378). New York: McGraw-Hill.
• Mosher, M., 1992. Organic Chemistry. (Morrison, Robert Thornton; Boyd, Robert Neilson).
• Rabinovich, D., 2000. Advanced Inorganic Chemistry, (Cotton, FA; Wilkinson, G.; Murillo, CA; Bochmann, M.).
• Denney, R.C., Jeffery, G.H. and Mendham, J. eds., 1978. Vogel's textbook of quantitative inorganic analysis including elementary instrumental analysis (p. 743). English Language Book Society.