SCITECH STUDY is the India’s best institute for guiding about optional subjects to the candidates for Civil Services Examination (CSE) and Indian Forest Service Examination conducted by the Union Public Service Commission (UPSC) run by its experts MOHAMMED TARIQUE and K.D SINGH who have a teaching experience of 15years and 10 years respectively , SCITECH STUDY is a company registered under Companies Act.

Our students have been consistently scoring top ranks in Civil Services/Forest Service Examination since 2006. Almost all selections in CSE from Physics l Mathematics l Engineering subjects in the last decade have been from SCITECH STUDY.

The best feature of SCITECH STUDY is we make our students to by heart the topics which are taught in the class at the same time with proper concepts so that if any twist comes student should be avle to handle.

# UPSC Civil Service Exam IAS Physics Optional Syllabus

PAPER – I

1.(a) Mechanics of Particles: Laws of motion; conservation of energy and momentum, applications to rotating frames, centripetal and Coriolis accelerations; Motion under a central force; Conservation of angular momentum, Kepler’s laws; Fields and potentials; Gravitational field and potential due to spherical bodies, Gauss and Poisson equations, gravitational self-energy; Two-body problem; Reduced mass; Rutherford scattering; Centre of mass and laboratory reference frames.

(b) Mechanics of Rigid Bodies: System of particles; Centre of mass, angular momentum, equations of motion; Conservation theorems for energy, momentum and angular momentum; Elastic and inelastic collisions; Rigid body; Degrees of freedom, Euler’s theorem, angular velocity, angular momentum, moments of inertia, theorems of parallel and perpendicular axes, equation of motion for rotation; Molecular rotations (as rigid bodies); Di and tri-atomic molecules; Precessional motion; top, gyroscope.

(c) Mechanics of Continuous Media: Elasticity, Hooke’s law and elastic constants of isotropic solids and their inter-relation; Streamline (Laminar) flow, viscosity, Poiseuille’s equation, Bernoulli’s equation, Stokes’ law and applications.

(d) Special Relativity: Michelson-Morley experiment and its implications; Lorentz transformations-length contraction, time dilation, addition of relativistic velocities, aberration and Doppler effect, mass-energy relation, simple applications to a decay process; Four dimensional momentum vector; Covariance of equations of physics.

2. Waves and Optics:

(a) Waves: Simple harmonic motion, damped oscillation, forced oscillation and resonance; Beats; Stationary waves in a string; Pulses and wave packets; Phase and group velocities; Reflection and Refraction from Huygens’ principle.

(b) Geometrical Optics: Laws of reflection and refraction from Fermat’s principle; Matrix method in paraxial optics-thin lens formula, nodal planes, system of two thin lenses, chromatic and spherical aberrations.

(c) Interference: Interference of light-Young’s experiment, Newton’s rings, interference by thin films, Michelson interferometer; Multiple beam interference and Fabry-Perot interferometer.

(d) Diffraction: Fraunhofer diffraction-single slit, double slit, diffraction grating, resolving power; Diffraction by a circular aperture and the Airy pattern; Fresnel diffraction: half-period zones and zone plates, circular aperture.

(e) Polarization and Modern Optics: Production and detection of linearly and circularly polarized light; Double refraction, quarter wave plate; Optical activity; Principles of fibre optics, attenuation; Pulse dispersion in step index and parabolic index fibres; Material dispersion, single mode fibres; Lasers-Einstein A and B coefficients;Ruby and He-Ne lasers; Characteristics of laser light-spatial and temporal coherence; Focusing of laser beams; Three-level scheme for laser operation; Holography and simple applications.

3.Electricity and Magnetism:

(a) Electrostatics and Magnetostatics: Laplace and Poisson equations in electrostatics and their applications; Energy of a system of charges, multipole expansion of scalar potential; Method of images and its applications; Potential and field due to a dipole, force and torque on a dipole in an external field; Dielectrics, polarization; Solutions to boundary-value problems-conducting and dielectric spheres in a uniform electric field; Magnetic shell, uniformly magnetized sphere; Ferromagnetic materials, hysteresis, energy loss.

(b) Current Electricity: Kirchhoff’s laws and their applications; Biot-Savart law, Ampere’s law, Faraday’s law, Lenz’ law; Self-and mutual-inductances; Mean and r m s values in AC circuits; DC and AC circuits with R, L and C components; Series and parallel resonances; Quality factor; Principle of transformer.

(c) Electromagnetic Waves and Blackbody Radiation: Displacement current and Maxwell’s equations; Wave equations in vacuum, Poynting theorem; Vector and scalar potentials; Electromagnetic field tensor, covariance of Maxwell’s equations; Wave equations in isotropic dielectrics, reflection and refraction at the boundary of two dielectrics; Fresnel’s relations; Total internal reflection; Normal and anomalous dispersion; Rayleigh scattering; Blackbody radiation and Planck’s radiation law, Stefan- Boltzmann law, Wien’s displacement law and Rayleigh-Jeans’ law.

4. Thermal and Statistical Physics:.

(a) Thermo dynamics: Laws of thermodynamics, reversible and irreversible processes, entropy; Isothermal, adiabatic, isobaric, isochoric processes and entropy changes; Otto and Diesel engines, Gibbs’ phase rule and chemical potential; van der Waals equation of state of a real gas, critical constants; Maxwell-Boltzman distribution of molecular velocities, transport phenomena, equipartition and virial theorems; Dulong-Petit, Einstein, and Debye’s theories of specific heat of solids; Maxwell relations and applications; Clausius- Clapeyron equation; Adiabatic demagnetisation, Joule-Kelvin effect and liquefaction of gases.

(b) Statistical Physics: Macro and micro states, statistical distributions, Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac distributions, applications to specific heat of gases and blackbody radiation; Concept of negative temperatures.

PAPER – II

1.Quantum Mechanics: Wave-particle dualitiy; Schroedinger equation and expectation values; Uncertainty principle; Solutions of the one-dimensional Schroedinger equation for a free particle (Gaussian wave-packet), particle in a box, particle in a finite well, linear harmonic oscillator; Reflection and transmission by a step potential and by a rectangular barrier; Particle in a three dimensional box, density of states, free electron theory of metals; Angular momentum; Hydrogen atom; Spin half particles, properties of Pauli spin matrices.

2. Atomic and Molecular Physics: Stern-Gerlach experiment, electron spin, fine structure of hydrogen atom; L-S coupling, J-J coupling; Spectroscopic notation of atomic states; Zeeman effect; Frank-Condon principle and applications; Elementary theory of rotational, vibratonal and electronic spectra of diatomic molecules; Raman effect and molecular structure; Laser Raman spectroscopy; Importance of neutral hydrogen atom, molecular hydrogen and molecular hydrogen ion in astronomy; Fluorescence and Phosphorescence; Elementary theory and applications of NMR and EPR; Elementary ideas about Lamb shift and its significance.

3.Nuclear and Particle Physics: Basic nuclear properties-size, binding energy, angular momentum, parity, magnetic moment; Semi-empirical mass formula and applications, mass parabolas; Ground state of deuteron, magnetic moment and non-central forces; Meson theory of nuclear forces; Salient features of nuclear forces; Shell model of the nucleus – successes and limitations; Violation of parity in beta decay; Gamma decay and internal conversion; Elementary ideas about Mossbauer spectroscopy; Q-value of nuclear reactions; Nuclear fission and fusion, energy production in stars; Nuclear reactors. Classification of elementary particles and their interactions; Conservation laws; Quark structure of hadrons; Field quanta of electroweak and strong interactions; Elementary ideas about unification of forces; Physics of neutrinos.

4.Solid State Physics, Devices and Electronics: Crystalline and amorphous structure of matter; Different crystal systems, space groups; Methods of determination of crystal structure; X-ray diffraction, scanning and transmission electron microscopies; Band theory of solids – conductors, insulators and semiconductors; Thermal properties of solids, specific heat, Debye theory; Magnetism: dia, para and ferromagnetism; Elements of superconductivity, Meissner effect, Josephson junctions and applications; Elementary ideas about high temperature superconductivity. Intrinsic and extrinsic semiconductors; pn-p and n-p-n transistors; Amplifiers and oscillators; Op-amps; FET, JFET and MOSFET; Digital electronics-Boolean identities, De Morgan’s laws, logic gates and truth tables; Simple logic circuits; Thermistors, solar cells; Fundamentals of microprocessors and digital computers.

**UPSC Civil Service Exam IAS Mathematics Optional Syllabus**

Paper – I

(1) Linear Algebra: Vector spaces over R and C, linear dependence and independence, subspaces, bases, dimension; Linear transformations, rank and nullity, matrix of a linear transformation. Algebra of Matrices; Row and column reduction, Echelon form, congruence’s and similarity; Rank of a matrix; Inverse of a matrix; Solution of system of linear equations; Eigenvalues and eigenvectors, characteristic polynomial, Cayley-Hamilton theorem, Symmetric, skew-symmetric, Hermitian, skew-Hermitian, orthogonal and unitary matrices and their eigenvalues.

(2) Calculus: Real numbers, functions of a real variable, limits, continuity, differentiability, meanvalue theorem, Taylor’s theorem with remainders, indeterminate forms, maxima and minima, asymptotes; Curve tracing; Functions of two or three variables: limits, continuity, partial derivatives, maxima and minima, Lagrange’s method of multipliers, Jacobian. Riemann’s definition of definite integrals; Indefinite integrals; Infinite and improper integrals; Double and triple integrals (evaluation techniques only); Areas, surface and volumes.

(3) Analytic Geometry: Cartesian and polar coordinates in three dimensions, second degree equations in three variables, reduction to canonical forms, straight lines, shortest distance between two skew lines; Plane, sphere, cone, cylinder, paraboloid, ellipsoid, hyperboloid of one and two sheets and their properties.

(4) Ordinary Differential Equations: Formulation of differential equations; Equations of first order and first degree, integrating factor; Orthogonal trajectory; Equations of first order but not of first degree, Clairaut’s equation, singular solution. Second and higher order linear equations with constant coefficients, complementary function, particular integral and general solution. Second order linear equations with variable coefficients, Euler-Cauchy equation; Determination of complete solution when one solution is known using method of variation of parameters. Laplace and Inverse Laplace transforms and their properties; Laplace transforms of elementary functions. Application to initial value problems for 2nd order linear equations with constant coefficients.

(5) Dynamics & Statics: Rectilinear motion, simple harmonic motion, motion in a plane, projectiles; constrained motion; Work and energy, conservation of energy; Kepler’s laws, orbits under central forces. Equilibrium of a system of particles; Work and potential energy, friction; common catenary; Principle of virtual work; Stability of equilibrium, equilibrium of forces in three dimensions.

(6) Vector Analysis: Scalar and vector fields, differentiation of vector field of a scalar variable; Gradient, divergence and curl in cartesian and cylindrical coordinates; Higher order derivatives; Vector identities and vector equations. Application to geometry: Curves in space, Curvature and torsion; Serret-Frenet’s formulae. Gauss and Stokes’ theorems, Green’s identities.

Paper – II

(1) Algebra: Groups, subgroups, cyclic groups, cosets, Lagrange’s Theorem, normal subgroups, quotient groups, homomorphism of groups, basic isomorphism theorems, permutation groups, Cayley’s theorem. Rings, subrings and ideals, homomorphisms of rings; Integral domains, principal ideal domains, Euclidean domains and unique factorization domains; Fields, quotient fields.

(2) Real Analysis: Real number system as an ordered field with least upper bound property; Sequences, limit of a sequence, Cauchy sequence, completeness of real line; Series and its convergence, absolute and conditional convergence of series of real and complex terms, rearrangement of series. Continuity and uniform continuity of functions, properties of continuous functions on compact sets. Riemann integral, improper integrals; Fundamental theorems of integral calculus. Uniform convergence, continuity, differentiability and integrability for sequences and series of functions; Partial derivatives of functions of several (two or three) variables, maxima and minima.

(3) Complex Analysis: Analytic functions, Cauchy-Riemann equations, Cauchy’s theorem, Cauchy’s integral formula, power series representation of an analytic function, Taylor’s series; Singularities; Laurent’s series; Cauchy’s residue theorem; Contour integration.

(4) Linear Programming: Linear programming problems, basic solution, basic feasible solution and optimal solution; Graphical method and simplex method of solutions; Duality. Transportation and assignment problems.

(5) Partial differential equations: Family of surfaces in three dimensions and formulation of partial differential equations; Solution of quasilinear partial differential equations of the first order, Cauchy’s method of characteristics; Linear partial differential equations of the second order with constant coefficients, canonical form; Equation of a vibrating string, heat equation, Laplace equation and their solutions.

(6) Numerical Analysis and Computer programming: Numerical methods: Solution of algebraic and transcendental equations of one variable by bisection, Regula-Falsi and Newton- Raphson methods; solution of system of linear equations by Gaussian elimination and Gauss-Jordan (direct), Gauss- Seidel(iterative) methods. Newton’s (forward and backward) interpolation, Lagrange’s interpolation. Numerical integration: Trapezoidal rule, Simpson’s rules, Gaussian quadrature formula. Numerical solution of ordinary differential equations: Euler and Runga Kutta-methods. Computer Programming: Binary system; Arithmetic and logical operations on numbers; Octal and Hexadecimal systems; Conversion to and from decimal systems; Algebra of binary numbers. Elements of computer systems and concept of memory; Basic logic gates and truth tables, Boolean algebra, normal forms. Representation of unsigned integers, signed integers and reals, double precision reals and long integers. Algorithms and flow charts for solving numerical analysis problems.

(7) Mechanics and Fluid Dynamics: Generalized coordinates; D’ Alembert’s principle and Lagrange’s equations; Hamilton equations; Moment of inertia; Motion of rigid bodies in two dimensions. Equation of continuity; Euler’s equation of motion for inviscid flow; Stream-lines, path of a particle; Potential flow; Two-dimensional and axisymmetric motion; Sources and sinks, vortex motion; Navier-Stokes equation for a viscous fluid.

**Minimum Educational Qualifications to appear for UPSC Civil Services Exam**

Any degree (graduation)

From:

any of the Universities incorporated by an Act of the Central or State Legislature in India.

or other educational institutions established by an Act of Parliament.

or declared to be deemed as a University Under Section-3 of the University Grants Commission Act, 1956.

or possess an equivalent qualification.

Note: Final year students can also apply.

Minimum age to appear for UPSC IAS Exam?

The minimum age to appear for IAS Exam is 21 years. This means that the candidate must have at-least 21 years of age on 1st August of that given year when the exam is held. For example, if the candidate is appearing for 2017 prelims, he/she should be above 21 years of age by Aug 1, 2017.

Upper age-limit to appear for UPSC IAS Exam?

Upper age limit is also calculated on the date Aug 1. This means if the candidate is appearing for 2017 prelims, he/she should be below the mentioned maximum limit by Aug 1, 2017. Upper age limit is fixed different for different categories, which is as given below.

Upper age limit for General category: 32 years.

Upper age limit for OBC: 35 years.

Upper age limit for SC/ST: 37 Years.

Upper age limit for Citizens of Jammu and Kashmir: 37 years.

Upper age limit for Defense Services personnel disabled in operations during hostilities with any foreign country or in a disturbed area and released as a consequence thereof: 35 years.

Upper age limit for Ex-servicemen including Commissioned Officers and ECOs/SSCOs who have rendered at least five years Military Service: 37 years.

Upper age limit for blind, deaf-mute and Orthopaedically handicapped persons (general category) : 42 years.

Apart from the mentioned limits, OBC/ SC/ ST candidates will get the benefit of cumulative age relaxation. This means age relaxations gets added in special cases, say for example, if the person is OBC + Ex-service men, he will get an extension of 5 + 7 = 12 years, ie his upper age limit now stands at 42 years.

**UPSC IFoS Physics Optional Syllabus **

Paper – I

Section-A

1. Classical Mechanics

(a) Particle dynamics: Centre of mass and laboratory coordinates, conservation of linear and angular momentum, The rocket equation, Rutherford scattering, Galilean transformation, inertial and non-inertial frames, rotating frames, centrifugal and Coriolls forces, Foucault pendulum.

(b) System of particles : Constraints, degrees of freedom, generalised coordinates and momenta.Lagrange’s equation and applications to linear harmonic oscillator, simple pendulum and central force problems. Cyclic coordinates, Hamiltonian Lagrange’s equation from Hamilton’s principle.

(c) Rigid body dynamics : Eulerian angles, inertia tensor, principal moments of inertia. Euler’s equation of motion of a rigid body, force-free motion of a rigid body, Gyroscope.

2. Special Relativity, Waves & Geometrical Optics :

(a) Special Relativity : Michelson-Morley experiment and its implications, Lorentz transformationslength contraction, time dilation, addition of velocities, aberration and Doppler effect, mass energy relation, simple application to a decay process, Minkowski diagram, four dimensional momentum vector. Covariance of equations of physics.

(b) Waves: Simple harmonic motion, damped oscillation, forced oscillation and resonance, Beats, Stationary waves in a string. Pulses and wave packets. Phase and group velocities. Reflection and Refraction from Huygens’ principle.

(c) Geometrical Optics : Laws of reflection and refraction from Format’s principle. Matrix method in paraxial optic-thin-lens formula, nodal planes, system of two thin lenses, chromatic and spherical aberrations.

3. Physical Optics :

(a) Interference : Interference of light-Young’s experiment, Newton’s rings, interference by thin films, Michelson interferometer. Multiple beam interference and Fabry-Perot interferometer. Holography and simple applications.

(b) Diffraction : Fraunhofer diffraction-single slit, double slit, diffraction grating, resolving power. Fresnel diffraction:- half-period zones and zones plates. Fersnel integrals. Application of Cornu’s spiral to the analysis of diffraction at a straight edge and by a long narrow slit. Deffraction by a circular aperture and the Airy pattern.

(c) Polarisation and Modern Optics : Production and detection of linearly and circularly polarised light. Double refraction, quarter wave plate. Optical activity. Principles of fibre optics attenuation; pulse dispersion in step index and parabolic index fibres; material dispersion, single mode fibres. Lasers-Einstein A and B coefficients, Ruby and He-Ne lasers. Characteristics of laser light-spatial and temporal coherence. Focussing of laser beams. Three-level scheme for laser operation.

Section-B

4. Electricity and Magnetism:

(a) Electrostatics and Magneto-statics : Laplace and Poisson equations in electrostatics and their applications. Energy of a system of charges, multiple expansion of scalar potential. Method of images and its applications. Potential and field due to a dipole, force and torque on a dipole in an external field.Dielectrics, polarisation, Solutions to boundary-value problemsconducting and dielectric spheres in a uniform electric field. Magnetic shell, uniformly magnetised sphere. Ferromagnetic materials, hysteresis, energy loss.

(b) Current Electricity: Kirchhoff’s laws and their applications, Biot- Savart law, Ampere’s law, Faraday’s law, Lenz’ law. Self and mutual inductances. Mean and rms values in AC circuits, LR, CR and LCR circuits-series and parallel resonance, Quality factor, Principle of transformer.

5. Electromagnetic Theory & Black Body Radiation :

(a) Electromagnetic Theory : Displacement current and Maxwell’s equations. Wave equations in vacuum, Poynting theorem, Vector and scalar potentials, Gauge invariance, Lorentz and Coulomb gauges, Electromagnetic field tensor, covariance of Maxwell’s equations. Wave equations in isotropic dielectrics, reflection and refraction at the boundary of two dielectrics. Fresnel’s relations, Normal and anomalous dispersion, Rayleigh scattering.

(b) Blackbody radiation: Blackbody radiation ad Planck radiation law-Stefan-Boltzmann law, Wien displacement law and Rayleigh-Jeans law, Planck mass, Planck length, Planck time, Plank temperature and Planck energy.

6. Thermal and Statistical Physics : (a) Thermodynamics: Laws of thermodynamics, reversible and irreversible processes, entropy, Isothermal, adiabatic, isobaric, isochoric processes and entropy change, Otto and Diesel engines, Gibbs’ phase rule and chemical potential. Van der Waals equation of state of real gas, critical constants. Maxwell-Boltzman distribution of molecular velocities, transport phenomena, equipartition and virial theorems, Dulong-Petit, Einstein, and Debye’s theories of specific heat of solids. Maxwell relations and applications. Clausius-Clapeyron equation. Adiabatic demagnetisation, Joule-Kelvin effect and liquefication of gases.

(b) Statistical Physics: Saha ionization formula, Bose-Einstein condensation, Thermodynamic behaviour of an ideal Fermi gas, Chandrasekhar limit, elementary ideas about neutron stars and pulsars, Brownian motion as a random walk, diffusion process. Concept of negative temperatures.

Paper – II

Section-A

1. Quantum Mechanics I: Wave-particle duality. Schroedinger equation and expectation values. Uncertainty principle, Solutions of the onedimensional Schroedinger equation free particle (Gaussian wave-packet), particle in a box, particle in a finite well, linear, harmonic oscillator, Reflection and transmission by a potential step and by a rectangular barrier, use of WKB formula for the life-time calculation in the alphadecay problem.

2. Quantum Mechanics II & Atomic Physics :

(a) Quantum Mechanics II : Particle in a three dimensional box, density of states, free electron theory of metals, The angular momentum problem, The hydrogen atom, The spin half problem and properties of Pauli spin matrices.

(b) Atomic Physics : Stern-Gerlack experiment, electron spin, fine structure of hydrogen atom, L-S coupling, J-J coupling, Spectroscopic notation of atomic states, Zeeman effect, Frank-Condon principle and applications.

3. Molecular Physics : Elementary theory of rotational, vibrational and electronic spectra of diatomic molecules, Raman effect and molecular structure, Laser Raman spectroscopy importance of neutral hydrogen atom, molecular hydrogen and molecular hydrogen ion in astronomy Fluorescence and Phos-phorescence, Elementary theory and applications of NMR. Elementary ideas about Lamb shift and its significance.

Section-B

4. Nuclear Physics : Basic nuclear properties-size, binding energy, angular momentum, parity,magnetic moment, Semi-empirical mass formula and applications, Mass parabolas, Ground state of deuteron magnetic moment and non-central forces, Meson theory of nuclear forces, Salient features of nuclear forces, Shell model of the nucleus-success and limitations, Violation of parity in beta decay, Gamma decay and internal conversion, Elementary ideas about Mossbauer spectroscopy, Q-value of nuclear reactions, Nuclear fission and fusion, energy production in stars, Nuclear reactors.

5. Particle Physics & Solid State Physics:

(a) Particle Physics: Classification of elementary particles and their interactions, Conservation laws, Quark structure of hadrons. Field quanta of electro-weak and strong interactions. Elementary ideas about Unification of Forces, Physics of neutrinos.

(b) Solid State Physics : Cubic crystal structure, Band theory of solids-conductors, insulators and semiconductors, Elements of superconductivity, Meissner effect, Joseph-son junctions and applications, Elementary ideas about high temperature superconductivity.

6. Electronics: Intrinsic and extrinsic semiconductors-pn- p and n-p-n transistors, Amplifiers and oscillators, Op-amps, FET, JFET and MOSFET, Digital electronics-Boolean identities, De-Morgan’s laws, Logic gates and truth tables, Simple logic circuits, Thermistors, solar cells, Fundamentals of microprocessors and digital computers.

**UPSC IFoS Mathematics Optional Syllabus**

Paper – I

Section-A.

Linear Algebra : Vector, space, linear dependence and independence, subspaces, bases, dimensions. Finite dimensional vector spaces. Matrices, Cayley-Hamilition theorem, eigen-values and eigenvectors, matrix of linear transformation, row and column reduction, Echelon form, equivalences, congruences and similarity, reduction to cannonical form, rank, orthogonal, symmetrical, skew symmetrical, unitary, hermitian, skewhermitian forms- their eigenvalues. Orthogonal and unitary reduction of quadratic and hermitian forms, positive definite quardratic forms.

Calculus : Real numbers, limits, continuity ,differentiability, mean-value theorems, Taylor’s theorem with remainders, indeterminate forms, maxima and minima, asymptotes. Functions of several variables: continuity, differentiability, partial derivatives, maxima and minima, Lagrange’s method of multipliers, Jacobian. Riemann’s definition of definite integrals, indefinite integrals, infinite and improper integrals, beta and gamma functions. Double and triple integrals (evaluation techniques only). Areas, surface and volumes, centre of gravity.

Analytical Geometry : Cartesian and polar coordinates in two and three dimensions, second degree equations in two and three dimensions, reduction to cannonical forms, straight lines, shortest distance between two skew lines, plane, sphere, cone, cylinder, paraboloid, ellipsoid, hyperboloid of one and two sheets and their properties.

Section-B

Ordinary Differential Equations: Formulation of differential equations, order and degree, equations of first order and first degree, integrating factor, equations of first order but not of first degree, Clariaut’s equation, singular solution. Higher order linear equations with constant coefficients, complementary function and particular integral, general solution, Euler-Cauchy equation. Second order linear equations with variable coefficients, determination of complete solution when one solution is known, method of variation of parameters.

Dynamics, Statics and Hydrostatics: Degree of freedom and constraints, rectilinear motion, simple harmonic motion, motion in a plane, projectiles, constrained motion, work and energy, conservation of energy, motion under impulsive forces, Kepler’s laws, orbits under central forces, motion of varying mass, motion under resistance. Equilibrium of a system of particles, work and potential energy, friction, common catenary, principle of virtual work, stability of equilibrium, equilibrium of forces in three dimensions. Pressure of heavy fluids, equilibrium of fluids under given system of forces, Bernoulli’s equation, centre of pressure, thrust on curved surfaces, equilibrium of floating bodies, stability of equilibrium, meta-centre, pressure of gases.

Vector Analysis: Scalar and vector fields, triple products, differentiation of vector function of a scalar variable, gradient, divergence and curl in Cartesian, cylindrical and spherical coordinates and their physical interpretations. Higher order derivatives, vector identities and vector equations.

Application to Geometry: Curves in space curvature and torision. Serret-Frenet’s formulae, Gauss and Stokes’ theorems, Green’s identities.

Paper – II

Section-A .

Algebra: Groups, sub-groups, normal subgroups, homomorphism of groups, quotient groups, basic isomorphism theorems, Sylow’s group, permutation groups, Cayley theorem, rings and ideals, principal ideal domains, unique factorization domains and Euclidean domains. Field extensions, finite fields.

Real Analysis: Real number system, ordered sets, bounds, ordered field, real number system as an ordered field with least upper bound property, Cauchy sequence, completeness, Continuity and uniform continuity of functions, properties of continuous functions on compact sets. Riemann integral, improper integrals, absolute and conditional convergence of series of real and complex terms, rearrangement of series, Uniform convergence, continuity, differentiability and integrability for sequences and series of functions. Differentiation of functions of several variables, change in the order of partial derivatives, implicit function theorem, maxima and minima, Multiple integrals.

Complex Analysis: Analytic function Cauchy-Riemann equations, Cauchy’s theorem, Cauchy’s integral formula, power series, Taylor’s series, Laurent’s Series, Singularities, Cauchy’s residue theorem, contour integration, Conformal mapping, bilinear transformations.

Linear Programming: Linear programming problems, basic solution, basic feasible solution and optimal solution, graphical method and Simplex method of solutions, Duality. Transportation and assignment problems, Travelling salesman problems.

Section-B

Partial differential equations: Curves and surfaces in three dimensions, formulation of partial differentiation equations, solutions of equations of type dx/p=dy/q=dz/r; orthogonal trajectories, Pfaffian differential equations; partial differential equation of the first order, solution by Cauchy’s method of characteristics; Charpit’s method of solutions, linear partial differential equations of the second order with constant coefficients, equations of vibrating string, heat equation, Laplace equation.

Numerical analysis and Computer programming: Numerical methods: solution of algebraic and transcendental equations of one variable by bisection, Regula-Falsi and Newton-Raphson methods, solution of system of linear equations by Gaussian elimination and Gauss-Jordan (direct) methods, Gauss-Seidel (iterative) method. Newton’s (Forward and backward) and Lagrange’s method of interpolation.

Numerical integration: Simpson’s onethird rule, tranpezodial rule, Gaussian quardrature formula.

Numerical solution of ordinary differential equations: Euler and Runge Kuttamethods. Computer Programming: Storage of numbers in computers, bits, bytes and words, binary system, arithmetic and logical operations on numbers, Bitwise operations. AND, OR, SOR, NOT, and shift/rotate operators, Octal and Hexadecimal Systems. Conversion to and form decimal Systems. Representation of unsigned integers, signed integers and reals, double precision reals and long integrers. Algorithms and flow charts for solving numerical analysis problems. Developing simple programs in Basic for problems involving techniques covered in the numerical analysis. Mechanics and Fluid Dynamics: Generalised coordinates, constraints, holonomic and non-holonomic, systems, D’ Alembert’s principle and Lagrange’s equations, Hamilton equations, moment of inertia, motion of rigid bodies in two dimensions. Equation of continuity, Euler’s equation of motion for inviscid flow, stream-lines, path of a particle, potential flow,two-dimensional and axisymetric motion, sources and sinks, vortex motion, flow past a cylinder and a sphere, method of images. Navier- Stokes equation for a viscous fluid.

**Features of SCITECH STUDY UPSC Optional Mains Test Series:**

Tentative Time 10:00 AM to 01:00 PM

Discussion on Every SAT & SUN at 09:00 AM

12 Tests, including 10 Topicwise and 2 Full Syllabus tests.

Objective is to cover the complete syllabus in its length and breadth by 10 Topicwise Tests

2 Full Syllabus tests will be conducted on the pattern of UPSC-CSE.

Tests are designed by concerned experts.

Detailed analysis and answer checking with proper remarks by MOHAMMED TARIQUE sir & K.D. SINGH sir.

Discussion classes are designed i such that it will provide boostup to other related areas .Copy correction

and feedback system is designed to provide relevant checks and feedback to each candidate as per performance.

Many Questions of Civil Services Examinations 2014,2015,2016,2017,2018 UPSC Optional Mains with SCITECH STUDY Test Series 2018

Online UPSC/IAS Physics Test Series is also Available for those who are not able to come at our institute.

Fee: Rs.9,800/- Only

**About UPSC Civil Services Examination **

Civil Services Examination is the most reputed examination conducted by the Union Public Service Commission for recruitment to various All India Services including IAS, IFoS, IPS etc., and various Group A and Group B Services. There are about 24 services which come under the Civil Services Exam conducted by UPSC every year.

UPSC conducts Civil Service Exams for Central Government job vacancies.

List of Civil Services are

(i) Indian Administrative Service.

(ii) Indian Foreign Service.

(iii) Indian Police Service.

(iv) Indian P & T Accounts & Finance Service, Group ‘A’.

(v) Indian Audit and Accounts Service, Group ‘A’.

(vi) Indian Revenue Service (Customs and Central Excise), Group ‘A’.

(vii) Indian Defence Accounts Service, Group ‘A’.

(viii) Indian Revenue Service (I.T.), Group ‘A’.

(ix) Indian Ordnance Factories Service, Group ‘A’ (Assistant Works Manager, Administration).

(x) Indian Postal Service, Group ‘A’.

(xi) Indian Civil Accounts Service, Group ‘A’.

(xii) Indian Railway Traffic Service, Group ‘A’.

(xiii) Indian Railway Accounts Service, Group ‘A’.

(xiv) Indian Railway Personnel Service, Group ‘A’.

(xv) Post of Assistant Security Commissioner in Railway Protection Force, Group ‘A’

(xvi) Indian Defence Estates Service, Group ‘A’.

(xvii) Indian Information Service (Junior Grade), Group ‘A’.

(xviii) Indian Trade Service, Group ‘A’ (Gr. III).

(xix) Indian Corporate Law Service, Group “A”.

(xx) Armed Forces Headquarters Civil Service, Group ‘B’ (Section Officer’s Grade).

(xxi) Delhi, Andaman & Nicobar Islands, Lakshadweep, Daman & Diu and Dadra & Nagar

Haveli Civil Service, Group ‘B’.

(xxii) Delhi, Andaman & Nicobar Islands, Lakshadweep, Daman & Diu and Dadra & Nagar

Haveli Police Service, Group ‘B’.

(xxiii) Pondicherry Civil Service, Group ‘B’.

(xxiv) Pondicherry Police Service, Group ‘B’.

Course | Subject | Fee | Register |
---|---|---|---|

UPSC Optional | Mathematics | Rs. 45,500 | Enroll |

UPSC Optional | Physics | Rs. 45,500 | Enroll |

UPSC Optional | Electrical Engineering | Rs. 45,500 | Enroll |