Reply to Thread

Re: What is the Syllabus of Mathematics for UPSC Prelims exam?

Hello Guest,

In civil services exam there is no special type of separate subject for mathematics candidate.
Syllabus is same for all the candidate.
CSAT exam have three stage

• prelim exam
• main exam
• interview
  

Preliminary Stage
2 papers (400 marks)
1- General Studies (200 marks)
2- Aptitude Test(200 marks)

Mains stage: 9 papers (Total 2000 marks)
1- G.S. - 2 papers (300 marks each)
2- First Optional - 2 papers (300 marks each)
3- Second Optional - 2 papers (300 marks each)
4- Essay paper - 1 paper (200 marks)
5- English - 1 paper (qualifying only- marks not added in final tally)
6- Indian language - 1 paper (qualifying only- marks not added in final tally)

Re: What is the Syllabus of Mathematics for UPSC Prelims exam?

MATHEMATICS

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. 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.

Re: What is the Syllabus of Mathematics for UPSC Prelims exam?

Re: What is the Syllabus of Mathematics for UPSC Prelims exam?
===============================================

Hi,

The syllabus is as follows-

Mathematics (Maximum Marks - 300)

1. Algebra :-

Concept of a set, operations on sets, Venn diagrams. De Morgan laws. Cartesian product, relation, equivalence relation. Representation of real numbers on a line. Complex numbers - basic properties, modulus, argument, cube roots of unity. Binary system of numbers. Conversion of a number in decimal system to binary system and vice-versa. Arithmetic, Geometric and Harmonic progressions. Quadratic equations with real coefficients. Solution of linear inequations of two variables by graphs. Permutation and Combination. Binomial theorem and its application. Logarithms and their applications.


2. Matrices and Determinants:-

Types of matrices, operations on matrices Determinant of a matrix, basic properties of determinant. Adjoint and inverse of a square matrix, Applications - Solution of a system of linear equations in two or three unknowns by Cramer's rule and by Matrix Method.

3. Trigonometry:-
Angles and their measures in degrees and in radians. Trigonometrical ratios. Trigonometric identities Sum and difference formulae. Multiple and Sub-multiple angles. Inverse trigonometric functions. Applications - Height and distance, properties of triangles.

4. Analytical Geometry of two and three dimensions:-
Rectangular Cartesian Coordinate system. Distance formula. Equation of a line in various forms. Angle between two lines. Distance of a point from a line. Equation of a circle in standard and in general form. Standard forms of parabola, ellipse and hyperbola. Eccentricity and axis of a conic.
Point in a three dimensional space, distance between two points. Direction Cosines and direction ratios. Equation of a plane and a line in various forms. Angle between two lines and angle between two planes. Equation of a sphere.

5. Differential Calculus:-

Concept of a real valued function - domain, range and graph of a function. Composite functions, one to one, onto and inverse functions. Notion of limit, Standard limits - examples. Continuity of functions - examples, algebraic operations on continuous functions. Derivative of a function at a point, geometrical and physical interpreatation of a derivative - applications. Derivatives of sum, product and quotient of functions, derivative of a function with respect of another function, derivative of a composite function. Second order derivatives. Increasing and decreasing functions. Application of derivatives in problems of maxima and minima.

6. Integral Calculus and Differential equations:-

Integration as inverse of differentiation, integration by substitution and by parts, standard integrals involving algebraic expressions, trigonometric, exponential and hyperbolic functions. Evaluation of definite integrals - determination of areas of plane regions bounded by curves - applications. Definition of order and degree of a differential equation, formation of a differential equation by examples. General and particular solution of a differential equation, solution of first order and first degree differential equations of various types - examples. Application in problems of growth and decay.

7. Vector Algebra :-

Vectors in two and three dimensions, magnitude and direction of a vector. Unit and null vectors, addition of vectors, scalar multiplication of vector, scalar product or dot product of two-vectors. Vector product and cross product of two vectors. Applications-work done by a force and moment of a force, and in geometrical problems.

8. Statistics and Probability :-

Statistics: Classification of data, Frequency distribution, cumulative frequency distribution - examples Graphical representation - Histogram, Pie Chart, Frequency Polygon - examples. Measures of Central tendency - mean, median and mode. Variance and standard deviation - determination and comparison. Correlation and regression.
Probability : Random experiment, outcomes and associated sample space, events, mutually exclusive and exhaustive events, impossible and certain events. Union and Intersection of events. Complementary, elementary and composite events. Definition of probability - classical and statistical - examples. Elementary theorems on probability - simple problems. Conditional probability, Bayes' theorem - simple problems. Random variable as function on a sample space. Binomial distribution, examples of random experiments giving rise to Binominal distribution.



Best of Luck for the exam!

Re: What is the Syllabus of Mathematics for UPSC Prelims exam?

Re: What is the Syllabus of Mathematics for UPSC Prelims exam?
================================================== =

Hi,

The syllabus is as follows-

Mathematics (Maximum Marks - 300)

1. Algebra :-

Concept of a set, operations on sets, Venn diagrams. De Morgan laws. Cartesian product, relation, equivalence relation. Representation of real numbers on a line. Complex numbers - basic properties, modulus, argument, cube roots of unity. Binary system of numbers. Conversion of a number in decimal system to binary system and vice-versa. Arithmetic, Geometric and Harmonic progressions. Quadratic equations with real coefficients. Solution of linear inequations of two variables by graphs. Permutation and Combination. Binomial theorem and its application. Logarithms and their applications.


2. Matrices and Determinants:-

Types of matrices, operations on matrices Determinant of a matrix, basic properties of determinant. Adjoint and inverse of a square matrix, Applications - Solution of a system of linear equations in two or three unknowns by Cramer's rule and by Matrix Method.

3. Trigonometry:-
Angles and their measures in degrees and in radians. Trigonometrical ratios. Trigonometric identities Sum and difference formulae. Multiple and Sub-multiple angles. Inverse trigonometric functions. Applications - Height and distance, properties of triangles.


4. Analytical Geometry of two and three dimensions:-
Rectangular Cartesian Coordinate system. Distance formula. Equation of a line in various forms. Angle between two lines. Distance of a point from a line. Equation of a circle in standard and in general form. Standard forms of parabola, ellipse and hyperbola. Eccentricity and axis of a conic.
Point in a three dimensional space, distance between two points. Direction Cosines and direction ratios. Equation of a plane and a line in various forms. Angle between two lines and angle between two planes. Equation of a sphere.

5. Differential Calculus:-

Concept of a real valued function - domain, range and graph of a function. Composite functions, one to one, onto and inverse functions. Notion of limit, Standard limits - examples. Continuity of functions - examples, algebraic operations on continuous functions. Derivative of a function at a point, geometrical and physical interpreatation of a derivative - applications. Derivatives of sum, product and quotient of functions, derivative of a function with respect of another function, derivative of a composite function. Second order derivatives. Increasing and decreasing functions. Application of derivatives in problems of maxima and minima.

6. Integral Calculus and Differential equations:-

Integration as inverse of differentiation, integration by substitution and by parts, standard integrals involving algebraic expressions, trigonometric, exponential and hyperbolic functions. Evaluation of definite integrals - determination of areas of plane regions bounded by curves - applications. Definition of order and degree of a differential equation, formation of a differential equation by examples. General and particular solution of a differential equation, solution of first order and first degree differential equations of various types - examples. Application in problems of growth and decay.

7. Vector Algebra :-

Vectors in two and three dimensions, magnitude and direction of a vector. Unit and null vectors, addition of vectors, scalar multiplication of vector, scalar product or dot product of two-vectors. Vector product and cross product of two vectors. Applications-work done by a force and moment of a force, and in geometrical problems.

8. Statistics and Probability :-

Statistics: Classification of data, Frequency distribution, cumulative frequency distribution - examples Graphical representation - Histogram, Pie Chart, Frequency Polygon - examples. Measures of Central tendency - mean, median and mode. Variance and standard deviation - determination and comparison. Correlation and regression.
Probability : Random experiment, outcomes and associated sample space, events, mutually exclusive and exhaustive events, impossible and certain events. Union and Intersection of events. Complementary, elementary and composite events. Definition of probability - classical and statistical - examples. Elementary theorems on probability - simple problems. Conditional probability, Bayes' theorem - simple problems. Random variable as function on a sample space. Binomial distribution, examples of random experiments giving rise to Binominal distribution.



Best of Luck for the exam!

Re: What is the Syllabus of Mathematics for UPSC Prelims exam?

Hi buddy,mathematics in upsc will be comprising of anything and everything in mathematics that you have learnt till class-12.So,time to revise school stuffz!!!!Good Luck..

Re: What is the Syllabus of Mathematics for UPSC Prelims exam?

UPSC stands for union public service commisssion, This examination is conducted by central government of india for every year. upsc conduct the various examinations like

>>IAS
>>IPS
>>IFS
>>IES
>>NDA
>>CDS
ETC....

STEPS OF UPSC EXAMINATION:
>>Preliminary
>>Main Written examination
>>Interview.

Syllabus of mathematics(preliminary):
>>Algebra
>>Geometry and vectors
>>Calculus
>>Vector spaces and matrices
>>Mechanics
>>Application of derivatives

I attached subject of preliminary examination in below(pdf format).

more details visit on official website:-http://www.upsc.gov.in

Re: What is the Syllabus of Mathematics for UPSC Prelims exam?

hello friend,

********SYLLABUS OF MATHEMATICS*********

The preliminary syllabus as follows:-------

1. Algebra:---

elements of set theory

Algebra of real and complex number

systemic function of roots

elements of group theory

cyclic group

permutation

Integral domain and fields

2.Geometry and vectors

Analytic geometry of straight lines and conics in Cartesian and polar coordinates

three dimensional geometry for planes.

straight line

sphere

cones

cylinder

Addition

subtractions

Product of vectors

Simple application of geometry


Apart from that

3.Calculus

4.Application of derivatives

5.Ordinary differential equations

6.Mechanics

7.Vector spaces and Matrices

Re: What is the Syllabus of Mathematics for UPSC Prelims exam?

Originally Posted by Unregistered

math syllabus for upsc prelimnary exam

there is no mathematics for UPSC IAS prelims exam.

it consists of 2 papers each of 200 marks & 2 hrs duration each.
check the attached file for detailed syllabus of prelims.

Re: What is the Syllabus of Mathematics for UPSC Prelims exam?

Syllabus of Mathematics:

1. Algebra :

Elements of Set Theory;
Algebra of Real and Complex numbers including Demoviere's theorem;
Polynomials and Polynomial equations,
relation between Coefficients and roots;
Symmetric functions of roots;
Elements of Group theory;
Sub-Group, Cyclic groups;Permutation,Groups and their elementary properties.
Rings,Integral Domains and Fields and their elementary properties.

2. Vector Spaces and Matrices :

Vector Space, Linear Dependance and Independance.
Sub-spaces.
Basis of Diamensions,Finite Dimensional Vector spaces,Matrix Representation,Rank and Nullity

Matrices :
Addition, Multiplication,Determinants of a matrix,Prroperties of Determinants of order,Inverse of a matrix,Cramer's rule.

3. Geometry and vectors :

Analytic Geometry of straight lines conics in cartesian and polar coordinates;
Three Dimensional geometry for planes,
Straight lins,sphere, cone and cyllinder.Addition, Subtraction and products of vectors and simple applications to Geometry.

4. Calculus :

Functions,Sequences Series,Limits,Continuity,Derivatives.
Application of Derivatives :
Rates of change,Tangents,Normals,Maxima,Minima,Rolle's Theorem,Mean Theorem of Lagrange and cauchy,Asymptotes,Curvature.
Methods of finding indefinite integrals,Definite Integrals,Fundamenals Theorem of Integrals and Calculus.Application of Definite integrals to area,Length of a plane curve,Volume and surfaces of revolution.

5. Ordinary Differential Equations :

Order and Degree of a Differential Equation,First order differential Equation,Singular solution,Geometrical Interpretation,Second order Equations with constants coefficients.

6. Mechanics :

Concepts of particles-Lamina;
Rigid body ; Displacements;force;mass;weight;Motion;Velocity;Sp eed;Acceleration;Parrallelogram of forces;Parallelogram of velocity;acceleration;resultant;equillibrium of coplanner forces.Moments,Couples;Friction;centre of mass,Gravity,Escape velocity

7. Elements of Computer Programming:

Binary system,Hexadecimal system,logic gates,logical operations,flow chart algorithm

Re: What is the Syllabus of Mathematics for UPSC Prelims exam?

friend
The topics you should practice throughout are:
1. Algebra: complex numbers,Roots,permutation,combinations,
Vectors and Matrices,inverse trignometric functions and equations,integral calculus,differential calculus,application of calculus like maxima and minima,limit,velocity and acceleration
You must go through some concepts of physics maths too like mass,weight and vectors.
As there is no special syllabus for maths in prelim of UPSC,so you must practice..your intermediatary syllabus and will b through.
good luck

Re: What is the Syllabus of Mathematics for UPSC Prelims exam?

Syllabus of maths:
Paper-I

1. Linear algebra
2. Calculus
3. Analytic geometry
4. Ordinary differential equations
5. Dynamics & statics
6. Vector analysis

Paper-II

1. Algebra
2. Real analysis
3. Complex analysis
4. Linear programming
5. Partial differential equations
6. Numerical analysis & computer analysis
7. Mechanics & fluid dynamics

Re: What is the Syllabus of Mathematics for UPSC Prelims exam?

Minimum Educational Qualifications for This Exam :

>The candidate must hold a degree of any of 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.
>For the Indian Administrative Service and the Indian Police Service, a candidate must be a citizen of India.

Syllabus of Mathematics For UPSC Prelims exam:-
>[FONT=Arial,Helvetica,Geneva,Swiss,SunSans-Regular] Algebra [/FONT]
>[FONT=Arial,Helvetica,Geneva,Swiss,SunSans-Regular]Vector Spaces and Matrices
>[/FONT][FONT=Arial,Helvetica,Geneva,Swiss,SunSans-Regular] Geometry and Vectors
>[/FONT][FONT=Arial,Helvetica,Geneva,Swiss,SunSans-Regular]Calculus
>[/FONT][FONT=Arial,Helvetica,Geneva,Swiss,SunSans-Regular]Ordinary Differential Equations
>[/FONT][FONT=Arial,Helvetica,Geneva,Swiss,SunSans-Regular]Mechanics
>[/FONT][FONT=Arial,Helvetica,Geneva,Swiss,SunSans-Regular]Elements of Computer Programming[/FONT]

Re: What is the Syllabus of Mathematics for UPSC Prelims exam?

Hello,
There is not any separated Syllabus for Mathematics for UPSC Prelims exams.

Syllabus for UPSC prelims exams as follows:
PRELIMINARY EXAMINATION
The Examination shall comprise two compulsory

papers of 200 marks each.
Paper I - (200 marks) Duration : Two hours
1. Current events of national and internationalimportance.
2. History of India and Indian National Movement.
3. Indian and World Geography - Physical, Social, Economic Geography of India and the World.
4. Indian Polity and Governance - Constitution, Political System, Panchayati Raj, Public Policy, Rights Issues, etc.
5. Economic and Social Development - Sustainable Development, Poverty, Inclusion, Demographics, Social Sector initiatives, etc.
6. General issues on Environmental Ecology, Bio-diversity and Climate Change - that do not require subject specialisation
7. General Science.

Paper II- (200 marks) Duration: Two hours
1. Comprehension
2. Interpersonal skills including communication skills;
3. Logical reasoning and analytical ability
4. Decision-making and problem solving
5. General mental ability
6. Basic numeracy (numbers and their relations, orders of magnitude, etc.) (Class X level), Data interpretation(charts, graphs, tables, data sufficiency etc. - Class X level)
7. English Language Comprehension
skills (Class X level).

Wish you all the best
Homi Kohli
[email protected]

What is the Syllabus of Mathematics for UPSC Prelims exam?

math syllabus for upsc prelimnary exam