Detailed Information About UPSC Maths Optional Syllabus
Are you considering taking Mathematics as your optional subject for the UPSC (Union Public Service Commission) exams mains optional? Look no further! In this article, we will provide you with a detailed breakdown of the IAS Maths Optional Syllabus for UPSC or UPSC Maths Optional Syllabus. Whether you are a mathematics enthusiast or simply looking for a challenging subject to enhance your chances of success, this syllabus will help you understand what to expect and how to prepare.
Overview of the UPSC Mathematics Syllabus or UPSC Maths Syllabus
The Mathematics optional paper consists of two papers (Paper I and Paper II), each carrying a maximum of 250 marks. The syllabus is designed to test the candidate’s understanding of various mathematical concepts and their ability to apply them in real-world scenarios.
Please read below for UPSC Maths Optional detailed Syllabus.
UPSC Maths Optional Syllabus Paper-1
| UPSC Maths Optional Syllabus Paper-1 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. |
| UPSC Maths Optional Syllabus Paper-1 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 Maths Optional Syllabus Paper-2
| UPSC Maths Optional Syllabus Paper-2 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. |
| UPSC Maths Optional Syllabus Paper 2 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. ignore this below family of partial differential equations solution of quasilinear partial differential equations of the second order, elements of partial differential equations solution of quasilinear partial differential equations of the second order |
(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. Elements of unsigned integers signed integers and reals double precision reals and long integers. Family 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 Optional Maths Syllabus
To ace the UPSC Maths optional syllabus in English, candidates must prepare with the right strategy. They must read the UPSC IAS Maths optional syllabus in English or Hindi deopends upon your comfortable about language and read carefully all maths optional previous years exam question papers, and take notes to understand complex concepts. They should also practice and solve questions regularly.They should develop a clear conceptual understanding of the subject and focus on solving problems to build logical flow. This will help them score well in the exam.Welcome to the world of UPSC Optional Maths Syllabus! If you have a passion for numbers, equations, and problem-solving, then you are in the right place. The Mathematics Optional Syllabus for UPSC offers a fascinating journey into the realm of mathematical concepts, theories, and applications. Choosing Mathematics as an optional subject for the UPSC exams can give you a competitive edge, as it demonstrates your ability to handle complex problems and showcases your analytical skills.The UPSC/IAS/CSE-Civil Service Exam Mathematics Optional Syllabus is designed to cover a wide range of topics that will test your understanding and application of mathematical principles. Preparing for the UPSC Mathematics Optional Exam requires a systematic approach and thorough understanding of the syllabus. With the right preparation and dedication, you can unlock the doors to success in the UPSC exams. So, gear up, embrace the world of numbers and equations, and embark on this exciting journey!Are you considering mathematics as an optional subject for the UPSC Civil Services Examination? Look no further! In this article, we will provide you with a comprehensive guide to the UPSC IAS Mathematics Optional Syllabus. Whether you are a mathematics enthusiast or simply looking to explore a new subject, this syllabus will equip you with the knowledge and skills necessary to excel in the examination.UPSC IAS Maths Optional Syllabus
While preparing for the IAS exam, it is important to choose the right subjects. While some subjects are easier to score in than others, if you want to be successful, you must be willing to work hard and dedicate a lot of time to your preparation. The best way to prepare for the maths optional paper is by using previous year papers and studying from expert-recommended books. It is also important to practice solving questions and taking full-length tests.The UPSC IAS maths optional syllabus is well-balanced, with a focus less on theorems and proofs more on understanding their statements to solve the problems and as well as on the application part. It is crucial to understand how to present your answers in a logical order, as this will improve your chances of scoring high marks. It is also helpful to practice as many questions as possible, as this will help you increase your speed and accuracy.In addition to preparing from the best UPSC maths optional lecture videos, you should also spend time reviewing and analyzing upsc maths optioal previous years questions papers. This will help you identify your strengths and weaknesses and will allow you to improve your overall problem-solving skills. In addition, it is a good idea to take notes on concepts that are difficult to understand.The UPSC IAS maths optional syllabus consists of two papers, which carry around 250 marks each. A high score in this subject can significantly boost your IAS rank, and it can help you develop analytical and problem-solving skills. Moreover, this subject can be useful for those who are planning to become teachers or civil servants. However, it is important to keep in mind that the maths optional paper is not a guarantee of success in the mains exam.The best way to prepare for the UPSC maths optional exam is by reading and understanding upsc maths optional previous years question papers and studying from the best UPSC Maths Optional Lectures Books. Attempting full-length tests is also important, as it will help you improve your time management skills. In addition, it is a great idea to use a study plan and set daily, weekly, and monthly goals for your preparation. You should also try to avoid distractions and make sure that you are getting enough sleep.UPSC CSE Maths Optional Syllabus
Maths is a subject that many aspirants find challenging to master. However, it is a good option for candidates who want to improve their analytical and problem-solving skills. The subject also offers a solid foundation in calculus, analytical geometry, and linear algebra with matrices. It can help you prepare for the exam and score well. However, you must remember that it is a time-consuming and difficult subject. Therefore, it is best to start preparing for it early.One of the key factors in choosing a CSE optional subject is to make sure it covers all the topics that you need for the exam. It is a good idea to read the upsc cse maths optional syllabus and upsc maths optional previous years question papers to get an idea of what to expect. You can also practice solving questions by yourself to see if you understand the concepts well. In addition, it is a good idea to take notes on the subjects that you find confusing.If you are an engineering student, you have already covered most of the IAS Maths syllabus. In that case, you can focus on understanding the topics and revising them. Another benefit of this subject is that it is static and does n’t involve current affairs, so you don’t need to constantly update your knowledge. This makes it easier to keep up with your preparations.When deciding on the right optional subject for the UPSC exam, it is important to choose a topic that you are familiar with and have a strong interest in. This will help you stay focused and motivated during your preparations. You should also consider the time frame needed to prepare for the exam and the amount of weightage that the subject will carry in your final score. Choosing the right optional subject can make or break your chances of getting selected for the IAS exam.To ensure that you are prepared for the exam, you should try to answer as many questions as possible. It is also a good idea to practice a few mock tests before you sit for the exam. This will help you identify any areas where you are struggling and address them quickly. Additionally, you should always try to avoid silly mistakes.UPSC Civil Services Maths Optional Syllabus
If you are planning to write the Civil Services Mains Examination, choosing an optional subject is an important decision. Aspirants should choose a subject that they have a strong grasp of. Moreover, it should be something that can be covered in time. It is also a good idea to choose a subject that can help them score well in the exam. Among the options available, maths is one of the most popular. It is a concept-focused subject, and its syllabus is not linked to current affairs. This makes it an ideal choice for aspirants from a science background.Choosing the right study material is essential for the success of any UPSC exam. It is best to choose books and study materials that are recommended by experts. Moreover, it is also a good idea to make a schedule for your preparations and stick to it. This will ensure that you cover the entire syllabus on time.It is also necessary to practice a lot if you want to do well in the Maths Optional exam. Practicing questions and solving previous year question papers will help you identify your strengths and weaknesses. It is also advisable to make notes on difficult concepts, and to practice solving mock tests. This will help you build a logical flow in your answers and will improve your chances of scoring better marks in the exam.The first step to succeeding in the Maths Optional exam is to understand the syllabus and the types of questions that will be asked. You should also know how to use the formulas and concepts of this subject. The best way to do this is to look at the questions in a similar manner as you would solve a problem. This will help you remember the concepts better.Another thing to keep in mind is that you should always revise the subject thoroughly. This is important because the subject is very concept-based. To do this, you should allocate a fixed amount of time for revision and practice with mock tests and full-length papers from previous years. You should also be systematic in answering questions and try to avoid cramming. It is also important to write your answers neatly and clearly.UPSC Ramana Sri IAS Maths Optional Syllabus
If you want to score well in the UPSC Maths optional, it is important to prepare properly. You need to understand the syllabus, study carefully, and practice often. This will help you improve your speed and accuracy. Moreover, it will also help you gain a deeper understanding of the subject and understand how to solve advanced questions. In addition to practicing, you should also use expert-recommended study materials. In this way, you can be sure of passing the exam with flying colours.If you are not able to prepare on your own, you can join a coaching institute for better results. There are many reputable coaching institutes that provide UPSC Mathematics Optional coaching to their students. These institutes have experienced faculty members who can guide you through the whole process of preparation. They also offer study materials and mock tests to improve your performance. Choosing the right coaching institute is essential for your success, but it is best to research multiple options and visit their demo classes before making a decision. You should consider factors such as faculty expertise, batch size, and learning materials before deciding on one.Among the most important things to remember when preparing for the Syllabus of UPSC Maths optional is to study the syllabus thoroughly and practice past years upsc maths optional question papers. Then, create a study plan and allocate time to different topics based on their weightage in the mains examination. Also, make sure to choose reliable study materials and revise them regularly. In addition, it is a good idea to practice full-length mock tests and solve previous years UPSC Maths optional questions to improve your skills.Another important tip is to memorize the necessary formulas and theorems. A lot of the questions in the maths optional are based on these formulas, so it is important to have a list of them handy. Additionally, you should focus on building a logical flow in your questions. This will help you in answering even the most difficult questions. You can even take a look at topper’s answer scripts to get an idea of how to write the answers.Why Choose UPSC Mathematics as an Optional Subject? | UPSC Syllabus Maths Optional
Mathematics is a popular optional subject among UPSC aspirants for several reasons. Firstly, it offers a logical and systematic approach to problem-solving, which is highly valued in the field of administration. Secondly, mathematics has a well-defined syllabus that allows candidates to focus their preparation on specific topics. Lastly, mathematics is a scoring subject, and a strong performance in this optional can significantly boost your overall marks in the examination.Mathematics is not just about calculations and formulas; it is a subject that trains your mind to think logically, analytically, and critically. Choosing Mathematics as an optional subject for the UPSC exams can give you a competitive edge, as it demonstrates your ability to handle complex problems and showcases your analytical skills.Are you considering mathematics as an optional subject for the UPSC Civil Services Examination? This article provides a comprehensive guide to the UPSC CSE Mathematics Optional Syllabus. Learn why mathematics is a popular optional subject, explore the syllabus structure, and get tips for preparing for the examination. Follow a systematic study plan, refer to standard textbooks, practice regularly, take mock tests, and stay updated with current affairs to excel in the IAS/UPSC/CSE-Civil Service Exam Mathematics Optional Syllabus. Dedication, perseverance, and a genuine interest in mathematics are key to success. Good luck with your preparation!The UPSC Mathematics Optional Syllabus
The UPSC Mathematics Optional Syllabus is designed to cover a wide range of topics that will test your understanding and application of mathematical principles. The syllabus is divided into two papers, each carrying a weightage of 250 marks.Optional Maths Syllabus for UPSC Mains Paper 1:
The first paper focuses on Pure Mathematics and applied mathematics, which includes topics such as Linear Algebra, Calculus, Analytical Geometry, Ordinary Differentail Equations, Vector Analysis, Dynamics & Statics. It aims to assess your understanding of fundamental mathematical concepts and their applications.IAS Maths Syllabus for UPSC Paper 2:
The second paper also focuses on Pure Mathematics and applied mathematics, which includes topics such as like Modern Algebra, Real Analysis, Complex Analysis, Linear Programming, Partial Differential Equations, Numerical Analysis, Computer Programming, Mechanics & Fluid Dynamics.Preparing for the Maths Optional Syllabus for Paper 2024 Exam
Preparing for the UPSC Mathematics Optional Exam requires a systematic approach and thorough understanding of the syllabus. Here are a few tips to help you excel in your preparation:Preparation Tips- Start by familiarizing yourself with the syllabus and understanding the weightage of each topic.
- Refer to standard textbooks and study materials recommended by experts to build a strong foundation.
- Practice solving previous years’ question papers and sample papers to get a feel of the exam pattern and improve your problem-solving skills.
- Join online forums and discussion groups to interact with fellow aspirants and gain insights from their experiences.
- Stay updated with current affairs and the latest developments in the field of Mathematics to enhance your understanding of the subject.
- Seek guidance from experienced mentors or join coaching institutes specializing in UPSC Mathematics Optional preparation.
- Preparing for the Maths Optional Syllabus for UPSC requires a systematic and well-structured approach. Here are some tips to help you get started:
- Understand the UPSC Mains Maths Optional Syllabus first: Familiarize yourself with the topics mentioned in the syllabus. This will help you create a study plan and allocate time to each topic accordingly.
- Refer to Standard Textbooks: Use standard textbooks recommended by experts and previous successful candidates. These books will provide you with in-depth knowledge and practice problems.
- Practice Regularly: Mathematics is a subject that requires regular practice. Solve a variety of problems to strengthen your understanding of different concepts.
- Take Mock Tests: Mock tests are an essential part of your preparation. They will help you assess your progress, identify your weak areas, and improve your time management skills.
- Stay Updated: Keep yourself updated with current affairs related to mathematics. This will help you in answering application-based questions and linking mathematical concepts to real-world scenarios.
- Preparing for the UPSC-IAS-CSE(Civil Services Exams) Mathematics Optional Syllabus requires a systematic approach and dedication.
- Remember, success in the UPSC/IAS/CSE(Civil Services Exams) Mathematics Optional Syllabus is not just about rote memorization but also about understanding the underlying concepts and their practical applications.
- Stay Updated: Keep yourself updated with the latest developments in the field of mathematics. Subscribe to relevant journals and publications to stay ahead of the curve.
- Seek Guidance: If you find certain topics challenging, don’t hesitate to seek guidance from experts or join a coaching institute. They can provide valuable insights and help clarify any doubts you may have.
- Practice, Practice, Practice: Mathematics is a subject that requires regular practice. Solve previous years’ question papers and attempt mock tests to improve your problem-solving skills and time management.
- Refer to Standard Textbooks: There are several recommended textbooks available that cover the entire syllabus. Choose the ones that suit your learning style and make sure to study them thoroughly.
- Here are some tips to help you get started:
- Understand the Syllabus: Familiarize yourself with the topics mentioned in the syllabus. Create a study plan that covers each topic in a structured manner.
Conclusion for UPSC/IAS/CSE(Civil Services Exams) Mathematics Optional Syllabus
The UPSC/IAS/CSE(Civil Services Exams) Mathematics Optional Syllabus offers a wide range of topics that cover various branches of mathematics. By following a structured study plan and practicing regularly, you can master these topics and perform well in the examination. Remember, choosing mathematics as an optional subject requires dedication, perseverance, and a genuine interest in the subject. Good luck with your preparation!The UPSC mains Mathematics Optional Syllabus offers a challenging yet rewarding opportunity for aspiring candidates. By choosing Mathematics as your optional subject, you not only showcase your mathematical prowess but also develop a strong analytical mindset. With the right preparation and dedication, you can unlock the doors to success in the UPSC exams. So, gear up, embrace the world of numbers and equations, and embark on this exciting journey!The UPSC/IAS/CSE(Civil Services Exams) offers a unique opportunity for candidates with a strong mathematical inclination to showcase their skills and knowledge. By following the tips mentioned in this article and dedicating yourself to regular practice and study, you can excel in this subject and increase your chances of success in the UPSC exams. Good luck! maths upsc optional is one your wonderful decision. We don’t have any information about upsc maths optional syllabus drishti ias. Once we will get then definitely we will update as soon as possible.Click on this link for UPSC Maths Optional Syllabus in Hindi PDF.UPSC Optional Maths Syllabus PDF download or UPSC Optional Mathematics Syllabus PDF or UPSC Maths Optional Syllabus PDF download or UPSC Mathematics Optional Syllabus PDF download or Maths Optional Syllabus for UPSC PDF or Maths Optional UPSC Syllabus PDF download below.What is the easiest optional subject for UPSC is Mathematics Optional. It will contain many patterns you can remember easily compared to other UPSC optional subjects.
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It is one of the best optional for UPSC even if you studied and know very well Intermediate or 11th & 12th classes mathematics.
It is much more easier than JEE.
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More than 20,000 students take Maths as optional in UPSC