UPSC IFS Mathematics Syllabus
Paper - I
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.
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.
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.
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.
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
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 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.
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 problems, basic solution, basic feasible solution and optimal solution, graphical method and Simplex method of solutions, Duality. Transportation and assignment problems, Travelling salesman problems.
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.
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.
UPSC IFS Geology Syllabus Paper - I Section-A i General Geology nbsp The Solar System meteorities origin and interior of the earth Radioactivity and age of earth Volcanoes-causes and products volcanic belts Earthquakes-causes effects earthquake belts seismicity of India intensityMore Details >>
UPSC IFS exam Important Dates Date of Notification nd February Last Date to Apply th March Last Date to Pay Application Fee th March Date of Exam Prelims th June IFS Main Exam rd DecemberMore Details >>
How to Apply nbsp UPSC IFS Recruitment Go to the online portal ldquo www upsconline nic in rdquo Click on the Online link for various examination link Look for the Indian Forest Service examination and Click on the Part IMore Details >>
IFS Exam Fee Candidates applying excepting Female SC ST PH candidates who are exempted from payment of fee for Civil Services Preliminary Examination are required to pay a fee of Rs - Applicants can pay examination fee either by depositingMore Details >>
Name of Commission Union Public Service Commission Job Type Central Government Job Name of the Post Indian Forest Service Mode of Application Online Official page nbsp www upsc gov in Total No of Posts nbspMore Details >>
Selection Procedure The competitive examination comprises two successive stages I Civil Services Preliminary Examination Objective Type for the screening amp selection of candidates for Indian Forest Service Main Examination and II Indian Forest Service Main Examination Written and Interview forMore Details >>
Eligibility Criteria Nationality Nationality of a candidate must be either of the following Citizen of India Subject of Nepal Subject of Bhutan a Tibetan refugee who came to India before January for permanent settlement in India Migrant from any ofMore Details >>
IFS Exam Centers Agartala Gaya Navi Mumbai Agra Ghaziabad Panaji Goa Ajmer Gorakhpur Patna Ahmedabad Gurgaon Port Blair Aizwal Gwalior Puducherry Aligarh Hyderabad Pune Allahabad Imphal Raipur Ananthapuru Indore Rajkot Aurangabad Itanagar Ranchi Bengaluru Jabalpur Sambalpur Barielly Jaipur Shillong BhopalMore Details >>
IFS Entrance Exam consists of two papers as follows Civil Services Prelims Examination Indian Forest Services Mains Examination Pattern for IFS Preliminary Exam pattern Preliminary exam will have two papers which contains marks for each All questions are of objectiveMore Details >>
Part A - IFS Preliminary Examination Syllabus Paper- I General Knowledge Current Event of National and International importance History of India and Indian National Movement Indian and world Geography Indian polity and nbsp Governance Economic and social Development General ScienceMore Details >>
Main Exam Syllabus General Knowledge Current Event of National and International importance History of India and Indian National Movement Indian and world Geography Indian polity and nbsp Governance Economic and social Development General Science General Issues on Environmental Ecology Bio-DiversityMore Details >>
UPSC IFS Agriculture Syllabus Paper - I Ecology and its relevance to man natural resources their sustainable management and conservation Physical and social environment as factors of crop distribution and production Climatic elements as factors of crop growth impact ofMore Details >>
UPSC IFS Agricultural Engineering Syllabus Paper - I Section A Soil and Water Conservation nbsp Scope of soil and water conservation Mechanics and types of erosion their causes Rainfall runoff and sedimentation relationships and their measurement Soil erosion control measuresMore Details >>
UPSC IFS Animal Husbandry amp Veterinary Science Syllabus Paper ndash I Animal Nutrition Energy sources energy metabolism and requirements for maintenance and production of milk meat eggs and wool Evaluation of feeds as sources of energy Trends in protein nutritonMore Details >>
UPSC IFS Botany Syllabus Paper - I Microbiology and Plant Pathology Viruses bacteria and plasmids-structure and reproduction General account of infection Phytoimmunology Applications of microbiology in agriculture industry medicine and pollution control in air soil and water nbsp Important plantMore Details >>
UPSC IFS Chemical Engineering Syllabus Paper ndash I Section A a nbsp Fluid and Particle Dynamics Viscosity of fluids Laminar and turbulent flows Equation of continuity and Navier-Stokes equition-Bernoulli theorem Flow meters Fluid drag and pressure drop due to frictionMore Details >>
UPSC IFS Chemistry Syllabus Paper ndash I Atomic structure Quantum theory Heisenberg uncertainity principle Schrodinger wave equation time independent Interpretation of wave function particle in one-dimensional box quantum numbers hydrogen atom wave functions Shapes of s p and d orbitalsMore Details >>
UPSC IFS Civil Engineering Syllabus Paper - I Part-A Engineering Mechanics Units and Dimensions SI Units Vectors Concept of Force Concept of particle and rigid body Concurrent Non-Concurrent and parallel forces in a plane moment of force and Varignon rsquoMore Details >>
UPSC IFS Forestry Syllabus Paper - I Section-A Silviculture General General Silvicultural Principles nbsp Ecological and physiological factors influencing vegetation natural and artificial regeneration of forests methods of propagation grafting techniques site factors nursery and planting techniques nursery beds poly-bagsMore Details >>
UPSC IFS Mechanical Engineering Syllabus Paper - I Theory of Machines nbsp Kinematic and dynamic analysis of planar mechanisms Cams Gears and gear trains Flywheels Governors Balancing of rigid rotors Balancing of single and multicylinder engines Linear vibration analysis ofMore Details >>
UPSC IFS Physics Syllabus Paper - I Section-A Classical Mechanics a Particle dynamics nbsp 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 CentrifugalMore Details >>
UPSC IFS Statistics Syllabus Paper - I Probability nbsp Sample space and events probability measure and probability space random variable as a measurable function distribution function of a random variable discrete and continuous-type random variable probability mass function probability densityMore Details >>
UPSC IFS Zoology Syllabus Paper - I Section-A Non-chordata and chordata nbsp a Classification and relationship of various phyla up- to sub-classes Acoelomata and Coelomata Protostomes and Deuterostomes Bilateralia and Radiata Status of Protista Parazoa Onychophora and Hemichordata Symmetry bMore Details >>
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