Eligibility for admission into Geophysics course at IITs:
Programme in Applied Geophysics
IITB: Bachelor’s degree with both Mathematics and Physics as subjects for two years and at least one of them as a subject for three years.
M.Sc.- Ph.D. Dual Degree Programme in Applied Geophysics
IITB: Bachelor’s degree with Maths and Physics as subjects for two years and at least one of them as a subject for three years.
M.Tech. in Geophysical Technology
IITR: Bachelor’s degree with Mathematics and Physics as subjects and anyone of the following subjects: Chemistry, Geology, Statistics, Electronics and Computer Science.
Syllabus for IIT JAM Geophysics
Geophysics Exam Pattern: Objective type, descriptive type and fill in the blanks questions
Subjects: 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.
Marking Scheme: one fourth mark will be deduct for wrong answer in objective type section only.
Geology Syllabus:
The Planet Earth, Geomorphology, Structural Geology, Mineralogy, Palaeontology, Stratigraphy, Petrology, Economic Geology: For detailed syllabus for these topics go to IIT JAM GG Syllabus
Mathematics Syllabus:
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, change of order of integration, 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.
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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.
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.
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, Newton- Raphson method for finding the solution of f(x)=0.
Physics Syllabus:
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.
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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.
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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: Inertial frames and Galilean invariance. Postulates of special relativity. Lorentz transformations. Length contraction, time dilation. Relativistic velocity addition theorem, mass energy equivalence. Black body 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.
