Table of contents
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.
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.
|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|
|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|
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