# UPSC Maths

1. UPSC Maths

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