Ph.D Biotechnology Entrance Exam preparation

Give me list of some best books for preparation of Ph.D Biotechnology Entrance Examination?

[Raman Vij]

Here I am giving you list of some best books for preparation of Ph.D Biotechnology Entrance Examination below :

Books for Molecular Biology
Biochemistry & Molecular Biology of plants by Buchanan
Cell and Molecular Biology; Concepts & Experiments by Karp,G
Lehninger Principles of Biochemistry by Nelson & Cox
Molecular Biology of Cells by Albert’s et al
The Cell: A molecular Approach by Cooper,G.M
Cell proliferation and apoptosis by Hughes & Mehnet
Molecular Cell Biology by Lodish
Cell & Molecular Biology by de Robertis & df Robertis

Books for Biochemistry
Biochemistry & Molecular Biology of plants by Buchanan et al
Lehninger Principles of Biochemistry by Nelson & Cox
Biochemistry by Stryer, L
Text book of Biochemistry by Devlin,Thomas, M
Biochemistry by Zubay,G
Biochemistry Fundamentals by Voet et al
Biochemistry by Friedfider,D.
Practical Biochemistry by Plummer

Books for Enzyme and Enzyme Technology
Enzyme Kinetics by Palmer
The Enzymes by Boyer
Enzyme Structure & Mechanism by Alan Fersht
Enzyme Biotechnology by Tripathi, G
Industrial Enzyme & their Application by Uhlig, H
Enzyme by Dixon M. & Webb, E.C
Enzyme Kinetics by Voet & Voet
Enzyme Kinetics by Dixon
Fundamental of Enzymology by Price & Steven

Books for Genetic Engineering
Genomes by Brown,T.A
Principles of Gene Manipulation by Old and Primerose
Molecular Genetics of Bacteria by Dale
Genes & Genomes by Singer & Berg
Molecular Biotechnology by Glick & Pasternak
Plant Molecular Biology by Gilmartin & Bowler
Recombinant DNA by Watson et al
Gene Cloning: An introduction by Brown
A Passion for DNA: Genes, Genome & Society by Watson
Genetic Engineering: An Introduction to Gene Analysis and Exploitation
Molecular Cloning: A Laboratory Manual by Sambrook & others

Books for Immunology
Essentials of Immunology by Roitt
Immunology by Kuby J
Animal Cell Culture by Freshney, R.T
Animal Cell Culture & Technology – Basic from Background to Bench byTaylor & Fracis
Immunology – An Introduction by Tizard, I.R., Thompson Pub
Immunology by Roitt
Principle & Practice of Immunoassay by Christopher & David

Books for Microbiology
Alcamo’s Fundamental of Microbiology by Pommerville
Brock Biology of Microbiology by Martinko,M.T & Parker,J
Microbiology by Tortora,F
Pharmaceuticals Microbiology by Purohit & Saluja
Principles of Microbiology by Atlas,R.M
Food Microbiology by Adam, M.R
Foundation in Microbiology by Talaro & Talora
Microbiology by Prescott, Harley & Klein

Books for Cell Biology
Molecular Biology of Cells by Albert’s
Molecular Cell Biology by Lodish
Biochemistry & Molecular Biology of plants by Buchanan
Lehninger Principles of Biochemistry by Nelson & Cox
Cell and Molecular Biology; Concepts & Experiments by Karp,G
The Cell: A molecular Approach by Cooper,G.M
Cell & Molecular biology, de Robertis & df Robertis
Cell proliferation and apoptosis by Hughes & Mehnet

(BIOLOGY (10+2+3 level)

General Biology: Taxonomy; Heredity; Genetic variation; Conservation; Principles of ecology; Evolution; Techniques in modern biology. Biochemistry and Physiology: Carbohydrates; Proteins; Lipids; Nucleic acids; Enzymes; Vitamins; Hormones; Metabolism – Glycolysis, TCA cycle, Oxidative Phosphoryation; Photosynthesis. Nitrogen Fixation, Fertilization and Osmoregulation; Vertebrates - Nervous system; Endocrine system; Vascular system; Immune system; Digestive system and Reproductive System. Basic Biotechnology: Tissue culture; Application of enzymes; Antigen-antibody interaction; Antibody production; Diagnostic aids. Molecular Biology: DNA; RNA; Replication; Transcription; Translation; Proteins; Lipids and Membranes; Operon model; Gene transfer. Cell Biology: Cell cycle; Cytoskeletal elements; Mitochondria; Endoplasmic reticulum; Chloroplast; Golgi apparatus; Signaling. Microbiology: Isolation; Cultivation; Structural features of virus; Bacteria; Fungi; Protozoa; Pathogenic micro-organisms.
CHEMISTRY (10+2+3 level)
Atomic Structure: Bohr’s theory and Schrodinger wave equation; Periodicity in properties; Chemical bonding; Properties of s, p, d and f block elements; Complex formation; Coordination compounds; Chemical equilibria; Chemical thermodynamics (first and second law); Chemical kinetics (zero, first, second and third order reactions); Photochemistry; Electrochemistry; Acid-base concepts; Stereochemistry of carbon compounds; Inductive, electromeric, conjugative effects and resonance; Chemistry of Functional Groups: Hydrocarbons, alkyl halides, alcohols, aldehydes, ketones, carboxylic acids, amines and their derivatives; Aromatic hydrocarbons, halides, nitro and amino compounds, phenols, diazonium salts, carboxylic and sulphonic acids; Mechanism of organic reactions; Soaps and detergents; Synthetic polymers; Biomolecules – amino acids, proteins, nucleic acids, lipids and carbohydrates (polysaccharides); Instrumental techniques-chromatography (TLC, HPLC), electrophoresis, UV-Vis, IR and NMR spectroscopy, mass spectrometry.
MATHEMATICS (10+2 level)
Sets, Relations and Functions, Mathematical Induction, Logarithms, Complex numbers, Linear and Quadratic equations, Sequences and Series, Trigonometry, Cartesian System of Rectangular Coordinates, Straight lines and Family, Circles, Conic Sections, Permutations and Combinations, Binomial Theorem, Exponential and Logarithmic Series, Mathematical Logic, Statistics, Three Dimensional Geometry, Vectors, Matrices and Determinants, Boolean Algebra, Probability, Functions, limits and Continuity, Differentiation, Application of Derivatives, Definite and Indefinite Integrals, Differential Equations.
PHYSICS (10+2 level)
Physical World and Measurement, Elementary Statics and Dynamics, Kinematics, Laws of Motion, Work, Energy and Power, Electrostatics, Current electricity, Magnetic Effects of Current and Magnetism, Electromagnetic Induction and Alternating Current, Electromagnetic waves, Optics, Dual Nature of Matter and Radiations, Atomic Nucleus, Solids and Semiconductor Devices, Principles of Communication, Motion of System of Particles and Rigid Body, Gravitation, Mechanics of Solids and Fluids, Heat and Thermodynamics, Oscillations, Waves.
IIT JAM Chemistry (CY) Syllabus
CHEMISTRY (CY)
PHYSICAL CHEMISTRY
Basic Mathematical Concepts: Differential equations, vectors and matrices.
Atomic Structure: Fundamental particles. Bohr’s theory of hydrogen atom; Wave-particle duality; Uncertainty principles; Schrödinger’s wave equation; Quantum numbers, shapes of orbitals; Hund’s rule and Pauli’s exclusion principle.
Theory of Gases: Kinetic theory of gases. Maxwell-Boltzmann distribution law; Equipartition of energy.
Chemical Thermodynamics: Reversible and irreversible processes; First law and its application to ideal and non-ideal gases; Thermochemistry; Second law; Entropy and free energy, Criteria for spontaneity.
Chemical and Phase Equilibria: Law of mass action; Kp , Kc, Kx and Kn; Effect of temperature on K; Ionic equilibria in solutions; pH and buffer solutions; Hydrolysis; Solubility product; Phase equilibria–Phase rule and its application to one-component and two-component systems; Colligative properties.
Electrochemistry: Conductance and its applications; Transport number; Galvanic cells; EMF and Free energy; Concentration cells with and without transport; Polarography.
Chemical Kinetics: Reactions of various order, Arrhenius equation, Collision theory; Theory of absolute reaction rate; Chain reactions – Normal and branched chain reactions; Enzyme kinetics; photochemical processes; Catalysis.
ORGANIC CHEMISTRY
Basic Concepts in Organic Chemistry and Stereochemistry: Isomerism and nomenclature, electronic (resonance and inductive) effects. Aromaticity and Huckel’s rule. Optical isomerism in compounds containing one and two asymmetric centres, designation of absolute configuration, conformations of cyclohexanes.
Organic Reaction Mechanism and Synthetic Applications: Methods of preparation and reactions of alkanes, alkenes, alkynes, arenes and their simple functional derivatives. Mechanism and synthetic applications of electrophilic aromatic substitution. Stereochemistry and mechanism of aliphatic nucleophilic substitution and elimination reactions. Diels-Alder reactions, Wittig Reactions, Mechanism of aldol condensation, Claisen condensation, esterification and ester hydrolysis, Cannizzaro reaction, benzoin condensation. Perkin reaction, Claisen rearrangement, Beckmann rearrangement and Wagner-Meerwein rearrangement. Synthesis of simple molecules using standard reactions of organic chemistry. Grignard reagents, acetoacetic and malonic ester chemistry.
Introduction to the following classes of compounds-alkaloids, terpenes, carbohydrates, amino acids, peptides and nucleic acids.
Heterocyclic Chemistry: Furans, thiophenes, pyrrols and pyridines.
Qualitative Organic Analysis: Functional group interconversions, structural problems using chemical reactions, identification of functional groups by chemical tests.
INORGANIC CHEMISTRY
Periodic Table: Periodic classification of elements and periodicity in properties; general methods of isolation and purification of elements.
Chemical Bonding and Shapes of Compounds: Types of bonding; VSEPR theory and shapes of molecules; hybridization; dipole moment; ionic solids; structure of NaCl, CsCl, diamond and graphite; lattice energy.
Main Group Elements (s and p blocks): Chemistry with emphasis on group relationship and gradation in properties; structure of electron deficient compounds of main group elements and application of main group elements.
Transition Metals (d block): Characteristics of 3d elements; oxide, hydroxide and salts of first row metals; coordination complexes; VB and Crystal Field theoretical approaches for structure, colour and magnetic properties of metal complexes. Ligands with back bonding capabilities; molecular orbital theory approaches to explain bonding in metal-carbonyl and metal-phosphine complexes.
Analytical Chemistry: Principles of qualitative and quantitative analysis; acid-base, oxidation-reduction and EDTA and precipitation reactions; use of indicators; use of organic reagents in inorganic analysis; radioactivity; nuclear reactions; applications of isotopes.
IIT JAM Computer Applications (CA) Syllabus
The Computer Applications (CA) test paper comprises of Mathematics, Computer awareness, and Analytical ability and General awareness and they will be in the ratio 4:2:1.
MATHEMATICS
Algebra: Set theory and its simple applications. Basic concepts of groups, fields and vector spaces.
Matrices: Rank of a matrix. Existence and uniqueness of solution of a system of linear equations. Eigenvalues and Eigenvectors. Inverse of a matrix by elementary transformations.
Differential Calculus: Differentiation, Partial differentiation, Taylor series and approximate calculations. Maxima and minima of functions of one and two variables.
Integral Calculus: Single and multiple integration. Definite integrals, Change of order and change of variables. Applications to evaluation of area, surface and volume.
Differential Equations: First order differential equations, linear differential equations of higher order with constant coefficients.
Vector Algebra: Addition, subtraction, dot product, cross product, triple product and their applications.
Numerical Analysis: Solution of non-linear equations using iterative methods. Interpolation (Lagrange’s formula and Newton’s formula for equidistant points). Numerical differentiation and integration (Trapezoidal and Simpson’s rules).
Probability: Basic concepts of probability theory. Binomial and Poisson distributions.
Linear Programming: Formulation and its graphical solution for two variable problems.
COMPUTER AWARENESS
Elements of computers. Number systems. Basic electronic gates. Boolean algebra. Flip-Flops. Algorithmic approach to solve problems. Fundamentals of C language.
ANALYTICAL ABILITY AND GENERAL AWARENESS
Simple questions will be asked to test the analytical ability and general awareness of candidates.
IIT JAM Geology (GG) Syllabus
GEOLOGY (GG)

The Planet Earth: Origin of the Solar System and the Earth; Geosphere and the composition of the Earth; Shape and size of the earth; Earth-moon system; Formation of continents and oceans; Dating rocks and age of the Earth; Energy in the earth system; Volcanism and volcanic landforms; Interior of earth; Earthquakes; Earth’s magnetism and gravity, Isostasy; Elements of Plate tectonics; Orogenic cycles.
Geomorphology: Weathering and erosion; Transportation and deposition due to wind, ice, river, sea, and resulting landforms, Structurally controlled landforms.
Structural Geology: Concept of stratum; Contour; Outcrop patterns; Maps and cross sections; Dip and strike; Classification and origin of folds, faults, joints, foliation and lineation, unconformities; shear zones.
Palaeontology: Major steps in the evolution of life forms; Fossils; their mode of preservation and utility; Morphological characters, major evolutionary trends and ages of important groups of animals - Brachiopoda, Mollusca, Trilobita, Graptolitoidea, Anthozoa, Echinodermata; Gondwana plant fossils; Elementary idea of verterbrate fossils in India.
Stratigraphy: Principles of stratigraphy; Litho-, chrono- and biostratigraphic classification; distribution and classification of the stratigraphic horizons of India from Archaean to Recent.
Mineralogy: Symmetry and forms in common crystal classes; Physical properties of minerals; Isomorphism and polymorphism, Classification of minerals; Structure of silicates; Mineralogy of common rock-forming minerals; Mode of occurrence of minerals in rocks. Transmitted polarised light microscopy and optical properties of uniaxial and biaxial minerals.
Petrology: Definition and classification of rocks; Igneous rocks - forms of igneous bodies; Crystallization from magma; classification, association and genesis of igneous rocks; Sedimentary rocks - classification, texture and structure; size and shape of sedimentary bodies. Metamorphic rocks - classification, facies, texture and properties.
Economic Geology: Properties of common economic minerals; General processes of formation of mineral deposits; Physical characters; Mode of occurrence and distribution in India both of metallic and non-metallic mineral deposits; Coal and petroleum occurrences in India.
Applied Geology: Ground Water; Mineral exploration, elements of Mining Geology and Environmental Geology; Principles of Engineering Geology.
IIT JAM Geophysics (GP) Syllabus
There will be Three Sections in the Geophysics (GP) test paper, namely, Geology, Mathematics and Physics, each with a weightage of 50%. A candidate has to attempt any Two Sections. The syllabus for the Geology, Mathematics and Physics Sections of the Geophysics (GP) test paper are given below:
GEOLOGY SECTION
The Planet Earth: Origin of the Solar System and the Earth; Geosphere and the composition of the earth; Shape and size of the Earth; Earth-moon system; Formation of continents and oceans; dating the rocks and age of the Earth; Energy in the earth system; Volcanism and volcanic landforms; Interior of earth; Earthquakes. Earth's magnetism and gravity, Elements of plate tectonics.
Geomorphology: Weathering and erosion; transportation and deposition due to wind, ice, river, sea, and resulting landforms, structurally controlled landforms.
Structural Geology: Concept of stratum; Contour; Outcrop patterns; Maps and cross sections; Dip and strike; classification and origin of folds, faults, joints, foliation and lineation, unconformities; shear zones.
Mineralogy: Symmetry and forms in common crystal classes; physical properties of minerals; Isomorphism and polymorphism, Classification of minerals; Structure of silicates; Mineralogy of common rock-forming minerals; Mode of occurrence of minerals in rock.
Stratigraphy: Principles of Stratigraphy, Geological Time Scale and ages of major stratigraphic units of India.
Petrology: Definition and classification of rocks; Igneous rock-forms of igneous bodies; Crystallisation from magma; classification, association and genesis of igneous rocks; Sedimentary rocks-classification, texture and structure; Metamorphic rocks-Classification, facies, texture and structure.
Economic Geology: Physical properties of common ore minerals, General processes of formation of mineral deposits; Mode of occurrence of important metallic and non-metallic deposits in India; Coal, petroleum and ground water occurrences in India.
MATHEMATICS SECTION
Sequences, Series and Differential Calculus: Sequences of real numbers, Convergent sequences and series. Mean Value Theorem, Taylor's theorem, Maxima and Minima, functions of several variables.
Integral Calculus: Fundamental theorem of calculus, Integration, Double and Triple integrals, Surface Areas and Volumes.
Differential Equations: Linear and Non-linear ODE, existence and uniqueness (without proof), Linear Differential Equations of second order with constant coefficients.
Vector Calculus: Gradient, Divergence, Curl, Laplacian, Green's, Stokes and Gauss theorems and their Applications.
Linear Algebra: System of Linear Equations, Matrices, Rank, Determinant, Inverse, eigenvalues and eigenvectros. Dimension, Linear transformations.
Real Analysis: Open and closed sets and limit points in R and completeness in R, Uniform Continuity, Power Series, Uniform Convergence.
Probability: Probability spaces, Conditional Probability, Independence, Bayes Theorem, Univariate and Bivariate Random Variables, Moment Generating and Characteristic Functions, Binomial, Poisson and Normal distributions.
Statistics: Sampling Distributions of Sample Mean and Variance, Exact Sampling Distribution (Normal Population), Simple and Composite hypothesis, Best critical region of a Test, Neyman-Pearson theorem, Likelihood Ratio Testing and its Application to Normal population, comparison of normal populations, large sample theory of test of hypothesis, approximate test on the parameter of a binomial population, comparison of two binomial populations.
Complex Analysis: Analytical functions, Harmonic functions, Cauchy's theorem, Cauchy's Integral Formula, Taylor and Laurent Expansion, Poles and Residues.
Numerical Analysis: Difference table, symbolic operators, differences of a factorial, representation of a polynomial by factorials. Forward, backward and central difference approximation formulae. Simpson's one-third rule and the error in it, Gauss-Siedel method and method of elimination for numerical solution of a system of linear equations, iteration method and its convergence, Gradient and Newton-Raphson method and their convergence.
PHYSICS SECTION
Mechanics and General Properties of Matter
Newton’s laws of motion and applications, Kepler’s laws, Gravitational Law and field, Conservative and non-conservative forces. System of particles, Centre of mass (CM), equation of motion of the CM, conservation of linear and angular momentum, conservation of energy. Elastic and inelastic collisions. Rigid body motion, fixed axis rotations, rotation and translation, moments of Inertia and products of Inertia. Principal moments and axes. Elasticity, Hooke’s law and elastic constants of isotropic solid, stress energy. Kinematics of moving fluids, equation of continuity, Euler’s equation, Bernoulli’s theorem, viscous fluids, surface tension and surface energy, capillarity.
Oscillations, Waves and Optics
Differential equation for simple harmonic oscillator and its general solution. Superposition of two or more simple harmonic oscillators. Lissajous figures. Damped and forced oscillators, resonance. Wave equation, travelling and standing waves in one-dimension. Energy density and energy transmission in waves. Group velocity and phase velocity. Sound waves in media. Doppler Effect. Fermat’s Principle. General theory of image formation. Thick lens, thin lens and lens combinations. Interference of light, optical path retardation. Fraunhofer diffraction. Rayleigh criterion and resolving power. Diffraction gratings. Polarization: linear, circular and elliptic polarization. Double refraction and optical rotation.
Electricity and Magnetism
Coulomb’s law, Gauss’s law. Concept of Potential, Field and Boundary Conditions, Solution of Laplace’s equation for simple cases. Conductors, capacitors, dielectrics, dielectric polarization, volume and surface charges, electrostatic energy. Magnetic susceptibility, bar magnet, Earth’s magnetic field and its elements. Biot-Savart law, Ampere’s law, Lenz’s law, Faraday’s law of electromagnetic induction, self and mutual inductance. Alternating currents. Simple DC and AC circuits with R, L and C components. Displacement current, Maxwell’s equations and plane electromagnetic waves. Lorentz Force and motion of charged particles in electric and magnetic fields.
Kinetic theory, Thermodynamics: Elements of Kinetic theory of gases. Velocity distribution and Equipartition of energy. Specific heat of Mono-, di- and tri-atomic gases. Ideal gas, Van-der-Waals gas and equation of state. Mean free path . Laws of thermodynamics. Zeroeth law and concept of thermal equilibrium. First law of thermodynamics and its consequences. Isothermal and adiabatic processes. Reversible, irreversible and quasi-static processes. Second law of thermodynamics. Carnot cycle.
Modern Physics
Blackbody radiation, photoelectric effect, Bohr’s atomic model, X-rays. Wave-particle duality, Uncertainty principle, Pauli Exclusion Principle, Structure of atomic nucleus, mass and binding energy. Radioactivity and its applications. Laws of radioactive decay and half life, Fission and fusion
Solid State Physics and Electronics
Crystal structure, Bravais lattices and basis. Miller indices. X-ray diffraction and Bragg’s law, Origin of energy bands. Concept of holes. Intrinsic and extrinsic semiconductors. p-n junctions, transistors. Amplifier circuits with transistors.
IIT JAM Mathematics (MA) Syllabus
MATHEMATICS (MA)

Sequences, Series and Differential Calculus: Sequences of real numbers. Convergent sequences and series, absolute and conditional convergence. Rolle’s Theorem, Mean value theorem. Taylor's theorem. Maxima and minima of functions of a single variable. Functions of two and three variables. Limit, Continuity, Partial derivatives, differentiability, maxima and minima.
Integral Calculus: Double and triple integrals, Areas, Volumes, and Surface areas.
Differential Equations: Ordinary differential equations of the first order of the form y'=f(x,y). Linear differential equations of second and higher order with constant coefficients. Cauchy- Euler equation.
Vector Calculus: Gradient, divergence, curl and Laplacian. Green's, Stokes and Gauss theorems and their applications.
Group Theory: Groups, subgroups and normal subgroups, Lagrange's Theorem for finite groups, group homomorphisms and basic concepts of quotient groups.
Linear Algebra: Vector spaces, Linear dependence of vectors, basis, dimension, linear transformations and matrix representation with respect to an ordered basis, rank and inverse of a matrix, determinant, solutions of systems of linear equations, consistency conditions. Eigenvalues and eigenvectors.
Real Analysis: Open and closed sets, limit points, completeness of R, Uniform convergence, Power series.
IIT JAM Mathematical Statistics (MS) Syllabus
The Mathematical Statistics (MS) test paper comprises of Mathematics (40% weightage) and Statistics (60% weightage).
Mathematics
Sequences and Series: Convergence of sequences of real numbers, Comparison, root and ratio tests for convergence of series of real numbers.
Differential Calculus: Limits, continuity and differentiability of functions of one and two variables. Rolle's theorem, mean value theorems, Taylor's theorem, indeterminate forms, maxima and minima of functions of one and two variables.
Integral Calculus: Fundamental theorems of integral calculus. Double and triple integrals, applications of definite integrals, arc lengths, areas and volumes.
Matrices: Rank, inverse of a matrix. systems of linear equations. Linear transformations, eigenvalues and eigenvectors. Cayley-Hamilton theorem, symmetric, skew-symmetric and orthogonal matrices.
Differential Equations: Ordinary differential equations of the first order of the form y' = f(x,y). Linear differential equations of the second order with constant coefficients.
Statistics Probability: Axiomatic definition of probability and properties, conditional probability, multiplication rule. Theorem of total probability. Bayes’ theorem and independence of events.
Random Variables: Probability mass function, probability density function and cumulative distribution functions, distribution of a function of a random variable. Mathematical expectation, moments and moment generating function. Chebyshev's inequality.
Standard Distributions: Binomial, negative binomial, geometric, Poisson, hypergeometric, uniform, exponential, gamma, beta and normal distributions. Poisson and normal approximations of a binomial distribution.
Joint Distributions: Joint, marginal and conditional distributions. Distribution of functions of random variables. Product moments, correlation, simple linear regression. Independence of random variables.
Sampling distributions: Chi-square, t and F distributions, and their properties.
Limit Theorems: Weak law of large numbers. Central limit theorem (i.i.d.with finite variance case only).
Estimation: Unbiasedness, consistency and efficiency of estimators, method of moments and method of maximum likelihood. Sufficiency, factorization theorem. Completeness, Rao-Blackwell and Lehmann-Scheffe theorems, uniformly minimum variance unbiased estimators. Rao-Cramer inequality. Confidence intervals for the parameters of univariate normal, two independent normal, and one parameter exponential distributions.
Testing of Hypotheses: Basic concepts, applications of Neyman-Pearson Lemma for testing simple and composite hypotheses. Likelihood ratio tests for parameters of univariate normal distribution.
IIT JAM Physics (PH) Syllabus
Mathematical Methods: Calculus of single and multiple variables, partial derivatives, Jacobian, imperfect and per¬fect differentials, Taylor expansion, Fourier series. Vector algebra, Vector Calculus, Multiple integrals, Divergence theorem, Green’s theorem, Stokes’ theorem. First and lin¬ear second order differential equations. Matrices and de¬terminants, Algebra of complex numbers.
Mechanics and General Properties of Matter: Newton’s laws of motion and applications, Velocity and acceleration in Cartesian, polar and cylindrical coordinate systems, uni¬formly rotating frame, centrifugal and Coriolis forces, Mo¬tion under a central force, Kepler’s laws, Gravitational Law and field, Conservative and non-conservative forces. Sys¬tem of particles, Centre of mass, equation of motion of the CM, conservation of linear and angular momentum, con¬servation of energy, variable mass systems. Elastic and inelastic collisions. Rigid body motion, fixed axis rotations, rotation and translation, moments of Inertia and products of Inertia. Principal moments and axes.. Kinematics of moving fluids, equation of continuity, Euler’s equation, Bernoulli’s theorem.
Oscillations, Waves and Optics: Differential equation for simple harmonic oscillator and its general solution. Super¬position of two or more simple harmonic oscillators. Lissajous figures. Damped and forced oscillators, reso¬nance. Wave equation, traveling and standing waves in one-dimension. Energy density and energy transmission in waves. Group velocity and phase velocity. Sound waves in media. Doppler Effect. Fermat’s Principle. General theory of image formation. Thick lens, thin lens and lens combina¬tions. Interference of light, optical path retardation. Fraunhofer diffraction. Rayleigh criterion and resolving power. Diffraction gratings. Polarization: linear, circular and elliptic polarization. Double refraction and optical rotation.
Electricity and Magnetism: Coulomb’s law, Gauss’s law. Electric field and potential. Electrostatic boundary condi¬tions, Solution of Laplace’s equation for simple cases. Conductors, capacitors, dielectrics, dielectric polarization, volume and surface charges, electrostatic energy. Biot-Savart law, Ampere’s law, Faraday’s law of electromag¬netic induction, Self and mutual inductance. Alternating currents. Simple DC and AC circuits with R, L and C com¬ponents. Displacement current, Maxwell’s equations and plane electromagnetic waves, Poynting’s theorem, reflec¬tion and refraction at a dielectric interface, transmission and reflection coefficients (normal incidence only). Lorentz Force and motion of charged particles in electric and mag¬netic fields.
Kinetic theory, Thermodynamics: Elements of Kinetic theory of gases. Velocity distribution and Equipartition of energy. Specific heat of Mono-, di- and tri-atomic gases. Ideal gas, van-der-Waals gas and equation of state. Mean free path. Laws of thermodynamics. Zeroeth law and concept of thermal equilibrium. First law and its consequences. Iso¬thermal and adiabatic processes. Reversible, irreversible and quasi-static processes. Second law and entropy. Carnot cycle. Maxwell’s thermodynamic relations and simple applications. Thermodynamic potentials and their applications. Phase transitions and Clausius-Clapeyron equation.
Modern Physics: Inertial frames and Galilean invariance. Postulates of special relativity. Lorentz transformations. Length contraction, time dilation. Relativistic velocity addi¬tion theorem, mass energy equivalence. Blackbody radia¬tion, photoelectric effect, Compton effect, Bohr’s atomic model, X-rays. Wave-particle duality, Uncertainty principle, Schrödinger equation and its solution for one, two and three dimensional boxes. Reflection and transmission at a step potential, Pauli exclusion prin¬ciple. Structure of atomic nucleus, mass and binding energy. Ra¬dioactivity and its applications. Laws of radioactive decay.
Solid State Physics, Devices and Electronics: Crystal structure, Braves lattices and basis. Miller indices. X-ray diffraction and Bragg's law Intrinsic and extrinsic semiconductors. Fermi level. p-n junctions, transistors. Transistor circuits in CB, CE, CC modes. Amplifier circuits with transistors. Operational amplifiers. OR, AND, NOR and NAND gates.