How To Prepare Maths Optional For UPSC

Introduction:
Choosing a non-obligatory is a project in itself! Both the papers collectively account for 500/1750 marks in UPSC Main Examination. Hence, it ought to be selected with utmost diligence. As a standard rule of thumb, a non-obligatory problem ought to be a topic of your interest. Math is one of the famous non-obligatory topics for the UPSC Main Examination. However, handiest the aspirants who've studied this problem their commencement in Mathematics ought to don't forget opting for it.
Methods To Prepare Maths Optional For UPSC
1)- Conceptual Understanding:
It is crucial to expand crystal-clean conceptual know-how for a topic as concept-targeted as Maths. Hence, first and foremost, expand awesome know-how of every subject this is part of UPSC Maths Optional.
2)- Make A Formula Page:
Maths is a topic of formulation and theorems. It is important to examine them to resolve the questions. Hence, keep a separate method sheet or pocketbook this is handy. Keep revising it now and then to make sure that you remember any vital method.
3)- Become Logical:
Presentation topics are a lot in UPSC solution-writing. Hence, crack the artwork of solution-writing on your elective via way of means of glancing thru toppers’ solution scripts or getting yours evaluated by the mentors.
4)- Revise Regularly:
Secondly, it's miles critical to hold revising something you’re reading to keep the information. Hence, allocate constant time for revision for max retention of the information. Practice thru the preceding 12 months' full-period papers and ridicule tests.
5)- Donot Cram Maths:
Do now no longer try and cram mathematics, as an alternative awareness on
constructing the logical go with the drift of the questions. It will assist you in fixing all of the forms of questions that might be requested with inside the exam.
6)- Avoid Mistakes:
Practice sufficiently to make sure that you’re now no longer doing any stupid errors at the same time as fixing the questions.
Advantages Of Taking Over Maths Optional Subject
1)- Undeviating Syllabus:
UPSC Maths Optional has an undeviating syllabus. If you’ve studied this problem on your graduation, you’ll simply want to comb up the standards alongside revision. The syllabus is likewise now no longer connected to modern affairs, so you’ll now no longer continuously replace your notes for revision.
2)- Extremely Scoring Subject:
Maths, being a goal subject, is extraordinarily scoring. There is simply one accurate answer, hence, the scope of the evaluation is less. Since the questions aren't subjective or opinions primarily based however reality isn't as much as the examiner to provide marks if content material and presentation are each as much as the mark.

3)- Memorization Is Not Required:
You glaringly will want to memorize the theorems and formulas, however overall, the situation is extra logic-primarily based totally, and hence, you'll now no longer memorize an excessive amount of information.
Syllabus For UPSC Maths Optional Subject
(Maths Optional Syllabus For Paper-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 a 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.
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 integrals; Double and triple integrals (evaluation techniques only); Areas, surface, and volumes.
Analytic Geometry:
Cartesian and polar coordinates in three dimensions, second-degree equations in three variables, reduction to Canonical forms; straight lines, the 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; Equations of the first order and first degree, integrating factor; Orthogonal trajectory; Equations of first order but not of the first degree, Claimant’s equation, singular solution. Second and higher order linear equations with constant coefficients, complementary function, particular integral, and general solution. Section order linear equations with variable coefficients, Euler-Cauchy equation; Determination of complete solution when one solution is known using the method of variation of parameters. Laplace and Inverse Laplace transforms and their properties, Laplace transforms elementary functions. Application to initial value problems for 2nd order linear equations with constant coefficients.
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.
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-Furenet's formulae. Gauss and Stokes’ theorems, Green's identities.
(Maths Optional Syllabus For Paper-2)
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.
Real Analysis:
Real number system as an ordered field with the least upper bound property; Sequences, the 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 is calculator allowed in upsc maths optional 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.
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.
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.
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.
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 a 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 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.
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, the path of a particle; Potential flow; Two-dimensional and axisymmetric motion; Sources and sinks, vortex motion; Navier-Stokes equation for a viscous fluid.


Booklist For UPSC Maths Optional
(Booklist For Paper-1)


Linear Algebra:
SCHAUM SERIES - Seymour Lipschutz
LINEAR ALGEBRA - Hoffman and Kunze
Calculus:
MATHEMATICAL ANALYSIS - S C Malik and Savita Arora
ELEMENTS OF REAL ANALYSIS - Shanti Narayan and M D Raisinghania
Analytic Geometry:
ANALYTICAL SOLID GEOMETRY - Shanti Narayan and P K Mittal
SOLID GEOMETRY - P N Chatterjee
Ordinary Differential Equations:
ORDINARY AND PARTIAL DIFFERENTIAL EQUATIONS - M D Raisinghania
Dynamics And Statics:
KRISHNA SERIES
Vector Analysis:
SCHAUM SERIES - Murray R. Spiegel

(Booklist For Paper-2)
Algebra:
CONTEMPORARY ABSTRACT ALGEBRA - Joseph Gallian
Real Analysis:
SAME AS CALCULUS OF PAPER
Complex Analysis:
SCHAUM SERIES - Speigel, Lipschitz, Schiller, Spellman
Linear Programming:
LINEAR PROGRAMMING AND GAME THEORY - Lakshmishree Bandopadhyay
Partial Differential Equations:
SAME AS ODE OF PAPER 1
ADVANCED DIFFERENTIAL EQUATIONS - M D Raisinghania
Numerical Analysis And Computer Programming:
For Numerical Analysis:
COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES - M.Goyal
NUMERICAL METHODS - Jain, Iyengar and Jain
For Computer Programming:
DIGITAL LOGIC AND COMPUTER DESIGN - M. Morris Mano
Mechanics And Fluid Dynamics:
KRISHNA SERIES
Is Calculator Allowed In UPSC Maths Optional?
Yes, in the main papers of math’s optionally available u can use a clinical calculator however now no longer a programmable one.

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