{"id":867,"date":"2024-06-18T08:27:08","date_gmt":"2024-06-18T08:27:08","guid":{"rendered":"https:\/\/upscmentorship.com\/upsc-exam\/?p=867"},"modified":"2024-06-18T09:49:00","modified_gmt":"2024-06-18T09:49:00","slug":"upsc-maths-syllabus","status":"publish","type":"post","link":"https:\/\/upscmentorship.com\/upsc-exam\/upsc-maths-syllabus\/","title":{"rendered":"UPSC Maths Syllabus"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_81 ez-toc-wrap-left counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 eztoc-toggle-hide-by-default' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/upscmentorship.com\/upsc-exam\/upsc-maths-syllabus\/#UPSC_Maths_Syllabus_Overview\" >UPSC Maths Syllabus Overview<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/upscmentorship.com\/upsc-exam\/upsc-maths-syllabus\/#UPSC_Maths_Syllabus_for_Paper_1\" >UPSC Maths Syllabus for Paper 1<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/upscmentorship.com\/upsc-exam\/upsc-maths-syllabus\/#UPSC_Maths_Syllabus_for_Paper_2\" >UPSC Maths Syllabus for Paper 2<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/upscmentorship.com\/upsc-exam\/upsc-maths-syllabus\/#UPSC_Mathematics_Exam_Tips\" >UPSC Mathematics Exam Tips<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/upscmentorship.com\/upsc-exam\/upsc-maths-syllabus\/#UPSC_Mathematics_Optional_Books\" >UPSC Mathematics Optional Books<\/a><\/li><\/ul><\/nav><\/div>\n<p><b>UPSC Maths Syllabus: <\/b><span style=\"font-weight: 400;\">Choosing the appropriate optional subject can have a big impact on your exam results and study plan. Therefore, you must be fully informed if you plan to take Mathematics as an optional subject for the UPSC CSE Exam.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">500 of the 1750 possible marks in the Mains exam are awarded for the combined score of the optional Mathematics Paper I and Paper II. Because it accounts for a sizeable amount of the marks in the UPSC Main Examination, selecting an optional topic is crucial. <\/span><\/p>\n<p><span style=\"font-weight: 400;\">Although it&#8217;s a popular choice, those with a background in mathematics are best suited. Continue reading this guide for in-depth details on the UPSC Mathematics Optional syllabus, study advice, suggested reading lists, and much more.<\/span><\/p>\n<h2><span class=\"ez-toc-section\" id=\"UPSC_Maths_Syllabus_Overview\"><\/span><b>UPSC Maths Syllabus Overview<\/b><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><span style=\"font-weight: 400;\">The purpose of the UPSC Mathematics Optional syllabus is to assess candidates&#8217; knowledge of diverse mathematical ideas and their capacity to use such ideas to solve problems. The following is the syllabus for Papers I and II:<\/span><\/p>\n<h2><span class=\"ez-toc-section\" id=\"UPSC_Maths_Syllabus_for_Paper_1\"><\/span><b>UPSC Maths Syllabus for Paper 1<\/b><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><span style=\"font-weight: 400;\">The syllabus for the UPSC Mathematics Optional Paper I includes topics like analytical geometry, calculus, linear algebra, and ordinary differential equations. The capacity of candidates to apply mathematical concepts to solve problems and their comprehension of those concepts are evaluated. The syllabus for Paper I is as follows:<\/span><\/p>\n<table>\n<tbody>\n<tr>\n<td colspan=\"2\">\n<p style=\"text-align: center;\"><b>\u00a0UPSC Maths Syllabus for Paper 1<\/b><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td><b>Linear Algebra<\/b><\/td>\n<td>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Vector spaces over R and C, linear dependence and independence, subspaces, bases, dimensions, Linear transformations, rank and nullity, matrix of a linear transformation.\u00a0<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Algebra of Matrices; Row and column reduction, Echelon form, congruence 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.<\/span><\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<tr>\n<td><b>Calculus<\/b><\/td>\n<td>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Real numbers, functions of a real variable, limits, continuity, differentiability, mean-value theorem, Taylor\u2019s 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\u2019s method of multipliers, Jacobian.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Riemann\u2019s definition of definite integrals; Indefinite integrals; Infinite and improper integrals; Double and triple integrals (evaluation techniques only); Areas, surface, and volumes.<\/span><\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<tr>\n<td><b>Analytic Geometry<\/b><\/td>\n<td>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">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.<\/span><\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<tr>\n<td><b>Ordinary Differential Equations<\/b><\/td>\n<td>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">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, Clairaut\u2019s equation, singular solution.\u00a0<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Second and higher-order linear equations with constant coefficients, complementary functions, particular integrals, and general solutions.\u00a0<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">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.\u00a0<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">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.<\/span><\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<tr>\n<td><b>Dynamics and Statics<\/b><\/td>\n<td>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Rectilinear motion, simple harmonic motion, motion in a plane, projectiles; Constrained motion; Work and energy, conservation of energy; Kepler\u2019s laws, orbits under central forces.\u00a0<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">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.<\/span><\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<tr>\n<td><b>Vector Analysis<\/b><\/td>\n<td>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">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.\u00a0<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Application to geometry: Curves in space, curvature, and torsion; Serret-Furenet\u2019s formulae.\u00a0<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Gauss and Stokes\u2019 theorems, Green\u2019s identities.<\/span><\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2><span class=\"ez-toc-section\" id=\"UPSC_Maths_Syllabus_for_Paper_2\"><\/span><b>UPSC Maths Syllabus for Paper 2<\/b><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><span style=\"font-weight: 400;\">Numerical analysis, algebra, real analysis, complex analysis, and linear programming are all included in the UPSC Mathematics Optional Paper II syllabus. It is required of candidates to show mastery of sophisticated mathematical ideas and methods for addressing problems related to these subjects. View the entire syllabus by clicking the link below:<\/span><\/p>\n<table>\n<tbody>\n<tr>\n<td colspan=\"2\">\n<p style=\"text-align: center;\"><b>UPSC Maths Syllabus for Paper 2<\/b><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td><b>Algebra<\/b><\/td>\n<td>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Groups, subgroups, cyclic groups, cosets, Lagrange\u2019s Theorem, normal subgroups, quotient groups, homomorphism of groups, basic isomorphism theorems, permutation groups, Cayley\u2019s theorem.\u00a0<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Rings, subrings and ideals, homomorphisms of rings; Integral domains, principal ideal domains, Euclidean domains, and unique factorization domains; Fields, quotient fields.<\/span><\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<tr>\n<td><b>Real Analysis<\/b><\/td>\n<td>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">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.\u00a0<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Riemann integral, improper integrals; Fundamental theorems of integral calculus.\u00a0<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">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.<\/span><\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<tr>\n<td><b>Complex Analysis<\/b><\/td>\n<td>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Analytic function, Cauchy-Riemann equations, Cauchy\u2019s theorem, Cauchy\u2019s integral formula, power series, representation of an analytic function, Taylor\u2019s series; Singularities; Laurent\u2019s series; Cauchy\u2019s residue theorem; Contour integration.<\/span><\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<tr>\n<td><b>Linear Programming<\/b><\/td>\n<td>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Linear programming problems, basic solution, basic feasible solution, and optimal solution; Graphical method and simplex method of solutions; Duality.\u00a0<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Transportation and assignment problems.<\/span><\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<tr>\n<td><b>Partial Differential Equations<\/b><\/td>\n<td>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Family of surfaces in three dimensions and formulation of partial differential equations; Solution of quasilinear partial differential equations of the first order, Cauchy\u2019s 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.<\/span><\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<tr>\n<td><b>Numerical Analysis and Computer Programming<\/b><\/td>\n<td>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">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-Jordan (direct), Gauss-Seidel (iterative) methods.\u00a0<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Newton\u2019s (forward and backward) and interpolation, Lagrange\u2019s interpolation.\u00a0<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Numerical integration: Trapezoidal rule, Simpson\u2019s rule, Gaussian quadrature formula.\u00a0<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Numerical solution of ordinary differential equations: Euler and Runga Kutta methods.\u00a0<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Computer Programming: Binary system; Arithmetic and logical operations on numbers; Octal and Hexadecimal Systems; Conversion to and from decimal Systems; Algebra of binary numbers.\u00a0<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Elements of computer systems and concept of memory; Basic logic gates and truth tables, Boolean algebra, normal forms.\u00a0<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Representation of unsigned integers, signed integers and reals, double precision reals, and long integers.\u00a0<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Algorithms and flow charts for solving numerical analysis problems.<\/span><\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<tr>\n<td><b>Mechanics and Fluid Dynamics<\/b><\/td>\n<td>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Generalised coordinates; D\u2019Alembert\u2019s principle and Lagrange\u2019s equations; Hamilton equations; Moment of inertia; Motion of rigid bodies in two dimensions.\u00a0<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Equation of continuity; Euler\u2019s 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.<\/span><\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><b style=\"font-family: var(--heading--font-family); font-size: var(--heading--font-size-h2); letter-spacing: var(--heading--letter-spacing-h2); background-color: var(--global--color-background); color: var(--global--color-primary);\">UPSC Mathematics Optional Exam Pattern<\/b><\/p>\n<p><span style=\"font-weight: 400;\">Paper I and Paper II, the two exams that make up the Mathematics Optional exam, each have 250 marks, for a total of 500 exam marks. For each paper, candidates must complete the questions in a maximum of three hours. The format of a question paper looks like this:<\/span><\/p>\n<table>\n<tbody>\n<tr>\n<td colspan=\"2\">\n<p style=\"text-align: center;\"><b>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 UPSC Mathematics Optional Exam Pattern<\/b><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td><b>Particular<\/b><\/td>\n<td><b>Details<\/b><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">Mains Paper<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Paper VI and Paper VII<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">Subjects<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Mathematics Optional Paper-I and Mathematics Optional Paper-II<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">Total Marks<\/span><\/td>\n<td><span style=\"font-weight: 400;\">500 (250 Each)<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">Time allowed\u00a0<\/span><\/td>\n<td><span style=\"font-weight: 400;\">3 Hours for each paper<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">Sections<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Section A and Section B<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">Questions<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Total 8 questions with subparts<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">Marks Distribution<\/span><\/td>\n<td><span style=\"font-weight: 400;\">10, 15, and 20 marker questions<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2><span class=\"ez-toc-section\" id=\"UPSC_Mathematics_Exam_Tips\"><\/span><b>UPSC Mathematics Exam Tips<\/b><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><span style=\"font-weight: 400;\">Math Optional preparation necessitates a methodical and concentrated approach. The following crucial advice will help you with your preparations:<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Make sure you fully comprehend the syllabus and rank the topics according to importance and your areas of strength.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Use reputable textbooks and expert-recommended study materials to create a solid foundation.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Regular problem-solving practice will increase accuracy and speed.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">To become familiar with the format of the exam and time management, solve past years&#8217; question papers, and take practice exams.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Editing is essential. To help you remember important ideas, take brief notes and edit frequently.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Get comfortable with theorem proofs. Prove and derive from the beginning. Theorem proofs may be requested by examiners, particularly for Paper II.<\/span><\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"UPSC_Mathematics_Optional_Books\"><\/span><b>UPSC Mathematics Optional Books<\/b><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><span style=\"font-weight: 400;\">To adequately cover the syllabus for the UPSC Mathematics Optional, applicants should consult reputable books and study tools. The optional booklist for UPSC Mathematics is as follows:<\/span><\/p>\n<table style=\"width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 98.9899%;\" colspan=\"2\">\n<p style=\"text-align: center;\"><b> \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 UPSC Mathematics Optional Books<\/b><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 44.3001%;\"><b>Paper I<\/b><\/td>\n<td style=\"width: 54.6898%;\"><b>Paper II<\/b><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 44.3001%;\"><span style=\"font-weight: 400;\">Dynamics, Statics, and Hydrostatics \u2013 M. Ray<\/span><\/td>\n<td style=\"width: 54.6898%;\"><span style=\"font-weight: 400;\">Linear Programming &amp; Theory of Games \u2013 SD Sharma<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 44.3001%;\"><span style=\"font-weight: 400;\">Differential Calculus \u2013 Shanti Narayan, PK Mittal<\/span><\/td>\n<td style=\"width: 54.6898%;\"><span style=\"font-weight: 400;\">Algebra \u2013 K C Prasad, KB Datta<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 44.3001%;\"><span style=\"font-weight: 400;\">Analytic Geometry \u2013 Shanti Narayan, DK Jha, HC Sinha and Sharma<\/span><\/td>\n<td style=\"width: 54.6898%;\"><span style=\"font-weight: 400;\">Complex Analysis \u2013 GK Ranganath<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 44.3001%;\"><span style=\"font-weight: 400;\">Linear Algebra \u2013 K.C. Prasad, K B Datta<\/span><\/td>\n<td style=\"width: 54.6898%;\"><span style=\"font-weight: 400;\">Mechanics &amp; Fluid Dynamics \u2013 Azaroff Leonid, AP Mathur, Mechanics by Krishna Series<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 44.3001%;\"><span style=\"font-weight: 400;\">Differential equations:- Golden series \u2013 NP Bali<\/span><\/td>\n<td style=\"width: 54.6898%;\"><span style=\"font-weight: 400;\">Introductory Methods of Numerical Analysis \u2013 SS Sastry<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 44.3001%;\"><span style=\"font-weight: 400;\">Vector Analysis \u2013 Shanti Narayan, PK Mittal<\/span><\/td>\n<td style=\"width: 54.6898%;\"><span style=\"font-weight: 400;\">Ordinary &amp; Partial Differential Equation \u2013 M.D. Raisinghania<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 44.3001%;\"><span style=\"font-weight: 400;\">\u201cHigher Algebra\u201d by Hall &amp; Knight<\/span><\/td>\n<td style=\"width: 54.6898%;\"><span style=\"font-weight: 400;\">Real Analysis \u2013 H.L Royden<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 44.3001%;\"><span style=\"font-weight: 400;\">Statics Krishna Series, Dynamics by Krishna Series<\/span><\/td>\n<td style=\"width: 54.6898%;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"excerpt":{"rendered":"<p><span class=\"rt-reading-time\" style=\"display: block;\"><span class=\"rt-label rt-prefix\">Read Time: <\/span> <span class=\"rt-time\">5<\/span> <span class=\"rt-label rt-postfix\">minutes<\/span><\/span> UPSC Maths Syllabus: Choosing the appropriate optional subject can have a big impact on your exam results and study plan. Therefore, you must be fully informed if you plan to take Mathematics as an optional subject for the UPSC CSE Exam. 500 of the 1750 possible marks in the Mains exam are awarded for the&hellip; <a class=\"more-link\" href=\"https:\/\/upscmentorship.com\/upsc-exam\/upsc-maths-syllabus\/\">Continue reading <span class=\"screen-reader-text\">UPSC Maths Syllabus<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":130,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[1],"tags":[],"acf":[],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/upscmentorship.com\/upsc-exam\/wp-json\/wp\/v2\/posts\/867"}],"collection":[{"href":"https:\/\/upscmentorship.com\/upsc-exam\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/upscmentorship.com\/upsc-exam\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/upscmentorship.com\/upsc-exam\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/upscmentorship.com\/upsc-exam\/wp-json\/wp\/v2\/comments?post=867"}],"version-history":[{"count":5,"href":"https:\/\/upscmentorship.com\/upsc-exam\/wp-json\/wp\/v2\/posts\/867\/revisions"}],"predecessor-version":[{"id":872,"href":"https:\/\/upscmentorship.com\/upsc-exam\/wp-json\/wp\/v2\/posts\/867\/revisions\/872"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/upscmentorship.com\/upsc-exam\/wp-json\/wp\/v2\/media\/130"}],"wp:attachment":[{"href":"https:\/\/upscmentorship.com\/upsc-exam\/wp-json\/wp\/v2\/media?parent=867"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/upscmentorship.com\/upsc-exam\/wp-json\/wp\/v2\/categories?post=867"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/upscmentorship.com\/upsc-exam\/wp-json\/wp\/v2\/tags?post=867"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}