UPSC Maths
About the Exam
About this Course
In this course, we are going to cover all the topics of Mathematics Optional for UPSC Mains, with an objective of scoring 360+ marks in the Optional Exam.
The Optional subject has 2 papers: Paper I and Paper II. Each of these papers is of 250 marks, thus making the total optional marks to 500. This is approximately 25% of the total marks (2025) of UPSC Exam (including Mains + Interview). Thus, it becomes extremely crucial to prepare a systematic strategy supported by a balanced and dedicated schedule to score good marks in Optional Exam.
Exam Structure
Maths Optional consists of two Paper: Paper I and Paper II. Both of these papers are paper-and-pen, subjective exams with 3 hours in duration. Each Paper is divided into 2 Sections: Section A and Section B, with each Section having 4 questions. Thus, each Paper has 8 questions with a total of 250 Marks.
Paper I: Modules and Topics
| Module | Topics |
|---|---|
| Linear Algebra | Vector Spaces, Linear Transformations, Algebra of Matrices |
| Calculus | Functions of a Real Variable, Functions of Two or Three Variables, Integrals; Areas, Surfaces and Volumes |
| Analytic Geometry | Cartesian and Polar Coordinates, Second Degree Equations, Straight Lines, Geometric Objects |
| Ordinary Differential Equations | First Order ODEs, Second and Higher Order ODEs, Laplace Transform |
| Dynamics and Statics | Motion, Kepler’s Laws, Equiliobrium |
| Vector Analysis | Scalar and Vector Fields; Gradient, Divergence & Curl; Higher Order Derivatives, Identities & Equations, Applications to Geometry, Thereoms & Identities |
Paper II: Modules and Topics
| Module | Topics |
|---|---|
| Algebra | Group Theory; Rings, Ideals & Domains, Fields |
| Real Analysis | Sequence, Series, Continuity, Integral Calculus, Analysis of Sequence & Series, Partial Derivatives |
| Complex Analysis | Analytic Functions, Power Series, Cauchy’s Residue Theroem, Contour Integration |
| Linear Programming | Linear Programming Problems, Graphical and Simplex Methods, Duality, Transportation Problems, Assignment Problems |
| Partial Differential Equations | Introduction, First Order PDEs, Second Order PDEs, Examples of PDEs |
| Numerical Analysis | Numerical Methods, Numerical Integration, Numerical Solution of ODEs |
| Computer Programming | Computer Programming, Algorithms & Flow Charts |
| Mechanics and Fluid Dynamics | Mechanics, Fluid Dynamics |
Why Maths as Optional
Maths has many advantages over other subjects which can be taken as optional subjects for the Mains exam. Some of these are listed below:
- Static Syllabus: Syllabus does not change from year to year
- Objective Scoring: This eliminates the instructor bias in grading to a large extent
- Less Preparation Time: The logical nature of the exam reduces the preparation time