# JAM 2012 Exam Syllabus - GP (Geophysics)

## Syllabus: Joint Admission Test For M.Sc. 2012

## Geophysics (GP)

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.

Courtesy: iitb.ac.in