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UPSC/IAS/CSE-Civil Services Maths/Mathematics Optional Syllabus Paper-1 2022-2023 

                                      Section-A

 (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; Eigen values and Eigen vectors, characteristic polynomial, Cayley-Hamilton theorem, Symmetric, skew-symmetric, Hermitian, Skew-Hermitian, orthogonal and unitary matrices and their Eigen values.

(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 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.

                          Section-B

 

(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 (Homogeneous linear equations); 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:

(i) Dynamics: 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.

(ii) Statics: 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. 

UPSC/IAS/CSE-Civil Services Maths/Mathematics Optional Syllabus PAPER-2 2022-2023

                                          Section-A

 (1) Modern 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, sub rings and ideals, homeomorphisms 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.

                                        Section-B

(5) Partial differential equations:

Family of surfaces in three dimensions and formulation of partial differential equations; Solution of quasi linear 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 & Computer Programming:

(i) 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-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.

  (ii) 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:

 

(i) Mechanics: Generalized coordinates; D’Alembert’s principle and Lagrange’s equations; Hamilton equations; Moment of inertia; Motion of rigid bodies in two dimensions.

(ii) Fluid Dynamics: Equation of continuity; Euler’s equation of motion for Inviscid flow; Stream-lines, path of a particle; Potential flow; Two-dimensional and asymmetric motion; Sources and sinks, vortex motion; Navier-Stokes Equation for a viscous fluid.

UPSC-Maths-Optional-Syllabus

UPSC Maths Optional Syllabus

About UPSC/IAS/CSE-Civil Services Maths/Mathematics Optional Syllabus 2022-2023

Ramanasri IAS is providing a complete and updated 2022-2023 UPSC Maths Optional Syllabus. We have done an analysis of UPSC Mathematics Syllabus what we observed that UPSC Maths Optional Syllabus incredible in our IAS UPSC Mains Examinations. Maths Syllabus in UPSC is very important before confirming your one of the Optional Subject in IAS, UPSC, Civil Services, CSE, IFoS/IFS Mains Examinations. Maths Syllabus for UPSC majority people saying very easy it needs to be practice more and more number problems. Ramanasri IAS is teaching complete   both Maths Optional Paper 1 and Maths Optional Paper 2. you can feel free to download complete UPSC Mathematics Optional Syllabus PDF in our mathematicsoptional.com website. After downloading the UPSC Maths Optional Syllabus PDF, you can save it. Read by sentence by sentence and word by word Maths Syllabus PDF. Then you can feel most of the UPSC Maths Optional Syllabus 2020 studied in your B.tech or B.Sc. or B.A or B.Com with one subject as Mathematics.

Our Director Ramanasri Sir explaining, every detail of the UPSC Mathematics Syllabus PDF. You can realize that IAS Maths Optional Syllabus is very easy and scoring Optional Subject in the History of UPSC, IAS, IFoS, IFS, Civil Services, CSE Mains Examinations. Click on this link for UPSC Maths Optional Syllabus in Hindi PDF. UPSC Syllabus in Hindi, we have done the analysis and Ramanasri IAS teaching both Hindi medium and English medium. UPSC Maths Optional Syllabus PDF download IAS Maths Syllabus in Hindi the same as English.

Learn more important and vital points About UPSC Maths Optional Syllabus

For UPSC mathematics optional, you can read about the previous years' exam question papers. Taking a look at the question papers will help you identify the topics that you need to study the most. Besides studying the UPSC maths optional syllabus, you should also take notes for difficult concepts and read relevant parts of the study material. The following tips will help you with UPSC mathematics optional. Read on! They'll come in handy!

Complete and detailed UPSC Maths Optional Syllabus with in 6 months

The UPSC maths optional syllabus covers two papers with each paper having 250 marks. The total number of marks is 500. The exam pattern is available online. You can download the syllabus for UPSC maths paper 1 as a PDF. The syllabus contains the key concepts that you need to know. Moreover, you should take notes on the concepts that you have to learn. Practice solving sample questions and taking notes can help you to answer the test questions with a logical flow.

The UPSC mathematics optional syllabus is well-balanced and includes topics related to theorems, proofs, and application. The proofs part is a significant portion of each paper, accounting for around 20-30% of the total mark. To solve a proof, you need to have some basic understanding of the theory, and then follow the steps logically. The syllabus breaks up problems so that you don't get confused between the theory and the proof. It also helps you reduce the chances of making mistakes.

maths optional syllabus for upsc

The UPSC Maths Optional Syllabus requires conceptual clarity and proper time management to prepare for the examination. The syllabus is divided into two parts. Part 1 focuses on Mechanics and Part 2 focuses on Calculus. Mechanics is a good subject to choose if you are interested in a career in engineering. This syllabus will be useful in all levels of engineering, including the Civil Service.

For preparing for paper I, you must know what the exam covers. Mechanics will cover topics like generalized coordinates, homomorphism, and Hamilton equations. The question paper also covers motion of rigid bodies in two dimensions and the Navier-Stokes equation for viscous fluid. It is recommended to study all the required material from standard textbooks, including Schaum series.

upsc maths optional syllabus pdf

There is no common portion between the UPSC Mathematics Optional Syllabus and the GS Paper. This provides the students with ample opportunity to formulate a study plan that addresses all aspects of this optional paper. Practice is the key to success for this subject. Practice solving questions and re-writing them, so that your answers are clear and accurate. The main purpose of this practice is to get the most out of the limited time you have for preparing for the UPSC Mains Exam.

The UPSC Mathematics Optional syllabus includes topics such as Analytical Geometry, Linear Algebra with matrices, Calculus, Ordinary and Partial Differential Equations, Complex Analysis, Numerical Analysis, Vector Analysis, and Applied & Mathematical Physics. Fluid Dynamics and Mechanics are two topics in UPSC Maths Optional Syllabus Paper 2.

UPSC Maths Optional Syllabus

Upsc Maths optional syllabus contains a number of topics that can be quite challenging to crack. There are formula sheets and a static syllabus, making it an extremely difficult subject to crack. Thankfully, this article will give you some tips to overcome this. You will learn how to make your study time go by much quicker. Here are some helpful tips to help you pass this exam with flying colors. Read on to discover how to make your time count in the exam hall!

Mathematics is a hard science subject

While many students dread mathematics, many take it for its practical application. Although it is considered difficult, it is a subject that many aspirants have aced in the IAS exam. In addition to its difficulty level, mathematics also has a reputation for being a difficult subject in school. Although many aspirants have gotten high marks in maths optional papers, it has been difficult to gauge the effect of the optional on overall performance.

While math is not a particularly popular subject, it is still a popular choice for UPSC examinations. Although it has less competition than subjects such as English, physics, and social science, its syllabus is static and is not connected to current affairs. Despite its low popularity, however, it will never go out of style and the marks scored by students chosen for the exam will speak volumes about their mathematical skills.

It is a static syllabus

The UPSC maths optional syllabus follows the same pattern of most institutes and universities in India. The focus is on building concepts, solving problems, and applying mathematics. Unlike other optional subjects, the maths syllabus does not link current affairs, so students are required to reread the topics and revise them for the examination. This means a less intensive preparation time. The syllabus also focuses on the fundamentals of mathematics rather than current affairs.

The UPSC Maths Optional syllabus is static and does not change with the changing news and current affairs. It is important to know that you do not have to update your syllabus frequently. However, this static syllabus does not mean that you cannot study and prepare. You can prepare for the UPSC maths optional exam by studying books or practice question papers. For help, you can download sample papers for UPSC maths optional. You can also find some question papers on the UPSC website.

It has formula sheets

The UPSC maths optional syllabus follows the curriculum of most Indian institutes and universities. Students are expected to understand the concept very well, revise extensively, and practice solving problems with the help of formula sheets. This syllabus does not involve much of current affairs, so it is a good choice for students who are interested in the subject but do not wish to spend much time studying it. The formula sheets are useful for revision and are available in the exam center.

There are many UPSC aspirants who choose mathematics as their optional subject, and most of them qualify with excellent scores. Toppers usually focus on standard books for static subjects and on the internet for dynamic subjects. Toppers suggest that students choose maths optional if they are strongly interested in the subject. It is not an easy subject to pass, but with hard work, you can achieve good results. If you are passionate about mathematics, you should opt for it.

It is a hard subject to crack

While UPSC has a tough syllabus, the maths optional exam is relatively easier than other subjects. By following a few simple strategies, you can prepare well for the maths optional examination. To prepare for the maths optional syllabus, you can get ready by reading books and getting ready-made question banks. It is also beneficial to practice solving previous year's mock tests and full-length papers.

One of the biggest mistakes candidates make is not preparing adequately for the exam. Most students do not have the time or interest to study for the maths optional. Practicing previous year questions is a great way to improve your accuracy and score. Practice previous year's questions until you're comfortable answering them. Then, try to crack the exam in your first attempt. Make sure you have ample time to study for the maths optional syllabus.

UPSC Maths Optional Syllabus

UPSC Mathematics Optional Syllabus comprises of the following topics: Cauchy-Riemann equations, Taylor's Series, Laurent's Series, contour integration, and Cauchy's Theorem. Conceptual Clarity is important for acing UPSC exams, as well as proper revision to retain the maximum part of the syllabus studied. You can also practice writing UPSC Answers by seeking help from your mentor.

Static syllabus

UPSC maths optional is one of the best scoring subjects for the exam. Applicants must understand the concepts, solve problems, revise and remember them to perform well in the examination. The syllabus is composed of two papers that are three hours each, and contain four questions for each section. The questions are divided into four parts, and there are 250 marks to be earned for each paper. The syllabus is written with a balance between theoretical and applied math.

Less emphasis on memory

One of the most important UPSC exams is the numerical aptitude test and maths is one of the highest scoring subjects. Candidates must understand concepts and solve questions to score well. It is recommended to prepare your maths questions beforehand. The syllabus has less emphasis on memory compared to other optional subjects, and the exam requires less time to prepare. It is important to practice as much as possible. Most questions in maths require you to recall formulas and theorems.

More emphasis on formulas

Unlike GS papers, the UPSC maths optional syllabus has no common portion. However, students can devise a study plan to get ahead of the competition. For effective preparation, practice is the key. Practice helps in improving accuracy and speed. Here are some tips to improve your performance:

No current affairs knowledge

A good reason to choose mathematics for your optional syllabus is the fact that it is less competitive than other subjects. While humanities subjects are more prone to examiner prejudice and subjectivity, math answers are more objective and are either right or wrong. Additionally, the syllabus for mathematics is static and doesn't incorporate current affairs in any way. Candidates can focus on revising instead of learning current affairs. This is great news for candidates who wish to pass the exam without spending too much time studying current affairs.

Predictability of paper

The UPSC mathematics optional syllabus contains topics from various branches of science. The syllabus covers topics like Computer Programming, Physics, Digital Electronics, K-MAPS, Flowcharts, Algorithms, Logic, Analytical(solid or 3-D)Geometry, and Modern(Abstract) Algebra. In the exam, the questions asked will mainly be based on the concepts that students learn in class.

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