JKPSC/JKPCS Maths Optional Syllabus for JAS 2024. Are you planning to appear for the JKPSC or JKPCS exams and considering Maths as your optional subject? Look no further! In this article, we will provide you with a detailed syllabus for Maths optional for both JKPSC and JKPCS exams. Let’s dive in!

About JKPSC/JKPCS Maths Optional Syllabus:

The syllabus for Maths optional in JKPSC/JKPCS exams is designed to test your understanding and knowledge of various mathematical concepts. It covers a wide range of topics from basic algebra to advanced calculus. Here is a breakdown of the syllabus:

JKPSC/JKPCS Maths Optional Syllabus Paper I:

Linear Algebra
Calculus
Analytical Geometry
Ordinary Differential Equations
Statics and Dynamics

JKPSC/JKPCS Maths Optional Syllabus Paper II:

Modern Algebra
Real Analysis
Complex Analysis
Partial Differential Equations
Numerical Analysis and Computer Programming

It is important to note that the syllabus for Maths optional may vary slightly between JKPSC and JKPCS exams. Therefore, it is recommended to refer to the official notification or syllabus provided by the respective exam authorities for the most accurate and up-to-date information.

Preparation Tips for JKPSC/JKPCS maths optional syllabus:

Preparing for Maths optional can be challenging, but with the right approach and dedication, you can excel in this subject. Here are some tips to help you in your preparation:

Understand the JKPSC/JKPCS Maths Optional Syllabus : Familiarize yourself with the syllabus and make a study plan accordingly. Focus on the topics that carry more weightage in the exam.
Master the Basics of JKPSC/JKPCS Maths Optional Syllabus: Build a strong foundation by mastering the basic concepts of each topic. This will help you tackle more complex problems with ease.
Practice Regularly of JKPSC/JKPCS Maths Optional Syllabus: Mathematics requires practice. Solve a variety of problems from different sources to enhance your problem-solving skills.
Refer to Standard Books from Ramana Sri IAS of JKPSC/JKPCS Maths Optional Syllabus: Consult standard textbooks and reference materials recommended for Maths optional. These books will provide you with in-depth knowledge and clarity on the subject.
Join Coaching or Online Classes for JKPSC/JKPCS Maths Optional Syllabus: Consider joining a coaching institute or enrolling in online classes specifically designed for Maths optional. This will provide you with expert guidance and help you stay on track with your preparation.
Revise and Analyze dialy of JKPSC/JKPCS Maths Optional Syllabus: Regularly revise the topics you have covered and analyze your performance in mock tests. Identify your weaknesses and work on improving them.

Remember, consistency and perseverance are key to success in any competitive exam. Stay focused, stay motivated, and give your best effort.

Conclusion for JKPSC/JKPCS maths optional syllabus:

The Maths optional syllabus for JKPSC/JKPCS exams covers a wide range of mathematical topics. By following a systematic study plan, practicing regularly, and referring to standard books, you can effectively prepare for this subject. Remember, success in any exam requires hard work and dedication. Good luck with your preparation!

JKPSC/JKPCS Maths Optional Syllabus Paper-1

(1) Linear Algebra: Vector spaces over R and C, linear dependence and independence, subspaces, bases, dimensions, 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, mean-value 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 integral; 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 liner 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 and 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 equation. Application to geometry: Curves in space, curvature and torsion; Serret-Frenet’s formulae. Gauss and Stokes’ theorems, Green’s identities.

JKPSC/JKPCS Maths Optional Syllabus Paper-2

(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 function, 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; 69 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 Analysis: 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-Jorden (direct), Gauss-Seidel (iterative) methods. Newton’s (forward and backward) and interpolation, Lagrange’s interpolation. Numerical integration: Trapezoidal rule, Simpson’s rule, Gaussian quadrature formula. Numerical solution of ordinary differential equations: Euler and Runge 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: Generalised 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.