Functions and graphs; limit and continuity; applications of derivative and integral. Conics; Polar coordinates; Convergence of sequence and series. Maclaurin and Taylor series. Partial derivatives. Vector calculus in Rn; vector analysis; theorems of Green, Gauss and Stokes. Complex numbers, analytic functions, Cauchy‟s theorms; elementary functions; series expansions; calculus of residues and applications. Vector space; basis and dimension; linear transformation; range and kernel of a linear transformation; row deduction method and application to linear system of equations. Probability spaces; conditional probability and independence; random variables and probability distributions; marginal and conditional distributions; independent random variables; mathematical expectation; mean and variance; binomial, Poisson‟s and normal distributions; sum of independent random variables; law of large numbers; central limit theorem, sampling distribution and test for mean using normal and students t-distribution; test of hypothesis; correlation and linear regression. Reference books: Thomas, G B & R,L Finney, Calculus and Analutic Geometry, Pearson Edu., 9th ed., 1996 Kolman, Bemard & D R Hill, Introductory Linear Algebra with Applications Churchill, R V and James W Brown, Complex variables and Applications, MGHISE, 7th ed, 2003 Milton. J Susan Core Physics: Linear momentum and its Conservation, Angular momentum and its conservation, Rotational dynamics of rigid bodies, Work-energy theorem, Conservative forces and potential energy, Collision problems, Damped and forced simple harmonic motions, Coupled oscillations and wave motion Coulomb‟s law, Electric fields, Gauss‟ law, Electric potential, Dielectrics and capacitors, Magnetic fields, Biot-Savart law and its applications, Magnetic materials, Ampere‟s law, Faraday‟s law of electromagnetic induction, Maxwell‟s equations and plane electromagnetic waves Young‟s double-slit interference, Interference from thin films, Coherence, Diffraction from single and double slits, Diffraction grating, Photoelectric effect, Compton effect, De-Broglie waves, Uncertainty relation, Schrodinger equation, Particle in a box, Potential barriers and tunneling. Reference books: R. Resnick, D. Halliday & K.S. Krane, Physics Vol. I & II, John Wiley & Sons, 5th ed., 2004 English Language Skills and Principles of Management Pronunciation skills; Vocabulary – Synonyms and antonyms, using words in appropriate contexts, Idioms and Phrasal verbs; Grammar – Word order and effective sentences, use of tenses, conjunctions and prepositions; Reading comprehension; Paragraph writing; Précis Writing; Letter writing. Fundamental concepts of management- planning, organization; staffing; directing and controlling; production, financial, personal, legal and marketing functions, accounting and budgeting, balance sheets. Reference books: Krishna Mohan and Meenakshi Raman, 2000, Effective English Communication, New Delhi: Tata McGraw Hill.: Robbins, Stephen P & M. Coutler, Management, PHI/Pearson Edu, 8th ed., 2005 Computer Programming Basic Data Types and Operations. Control Constructs – Conditionals and Loops Lists - Arrays. Modularity– Functions. Structured Data – Structures, Unions, Pointers. Applications – Strings. Reference books:
Balagurusamy, E. Programming in ANSI C, TMH, 2nd, 2004
SYLLABUS FOR TEST II
Chemical Process Calculations
Units and Dimensions, The Chemical Equation and Stoichiometry, Material Balances, Energy Balances, Properties of Gases, Vapors, Liquids and Solids, Phase Equilibria, Combustion Calculation, Unsteady-State Material and Energy Balances. Reference books: Himmelblau, D. M. “Basic principles & calculations in chemical Engg”, PHI, 6th ed., 1997. Felder, R. M. & R. W. Rousseau, “Elementary Principles of Chemical Processes”, John Wiley & Sons, Inc., 3rd ed., 2000. Fluid Flow Operations
Fundamental Concepts and Fluid Statics, Integral and Differential...