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Index

Linear Algebra

Calculus

Analytic Geometry

Ordinary Differential Equations

Dynamics & Statics

Vector Analysis

Modern Algebra

Real Analysis

Complex Analysis

Linear Programming Problems

Partial Differential Equations

Numerical Analysis and Computer Programming

Mechanics and Fluid Dynamics

Linear Algebra

Calculus

Analytic Geometry

Ordinary Differential Equations

Dynamics & Statics

Vector Analysis

Algebra

Real Analysis

Complex Analysis

Linear Programming

Numerical Analysis and Computer programming

Mechanics and Fluid Dynamics

Class 6 Mathematics

Class 7 Mathematics

Class 8 Mathematics

Class 9 Mathematics

Class 10 Mathematics

Class 11 Mathematics

Class 12 Mathematics

2024

2023

2022

2021

2020

2019

2018

All Exams > UPSC > Mathematics Optional Notes for UPSC > All Notes

All notes of Mathematics Optional Notes for UPSC for UPSC CSE Exam

Linear Algebra

Vector Space over R and C

17 pages

Linear Transformations

22 pages

Matrix

47 pages

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Calculus

Function of a Real Variable

24 pages

Functions of Two and Three Variables

29 pages

Homan's Definition of Definite Integrals

6 pages

Indefinite Integrals

1 page

Infinite and Improper Integrals

14 pages

Area, Surface and Volume

6 pages

Analytic Geometry

Straight lines

3 pages

Shortest Distance between Two Skew lines

4 pages

Plane and its Properties

8 pages

Sphere and its Properties

15 pages

Cone and its properties

19 pages

Paraboloid and it Properties

15 pages

Ellipsoid and its Properties

4 pages

Hyperboloid of One and Two Sheets and its Properties

6 pages

Mathematics Optional Notes for UPSC

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Ordinary Differential Equations

Formulation of Differential Equations

6 pages

Equation of 1st Order and 1st Degree

27 pages

Equation of 1st Order but Nor of 1st Degree

8 pages

Second and Higher Order Linear Equation with Constant coefficients

12 pages

Wronskian

1 page

Second Order Linear Equations with Variable Coefficient

13 pages

Determination of Complete Solution when one solution is known and Method of Variation of Parameter

15 pages

Laplace and inverse Laplace Transformation and Properties

15 pages

Application to Initial Value Problem for 2nd Order Linear Equation with Constant Coefficient

2 pages

Dynamics & Statics

Rectilinear Motion

13 pages

Motion in a Pane

24 pages

Constrained Motion

5 pages

Work & Energy

13 pages

Equilibrium of a System or Particles

29 pages

Work and Potential Energy

4 pages

Principle of Virtual Work

5 pages

Vector Analysis

Scalar and Vector Herts

4 pages

Gradient, Divergence and Cur in Cartesian and Cylindrical Coordinate and Directional Derivative

12 pages

Vector Identity and Vector Equations

5 pages

Application to Geometry

6 pages

Curves in Space

8 pages

Gauss-Divergence Theorem Stoles Theorem and Green’s to Identity

35 pages

Modern Algebra

Groups

30 pages

Rings

24 pages

Fields

11 pages

Real Analysis

Real Number System

2 pages

Sequences

9 pages

Series

49 pages

Functions of Several (Two or Three) Variables

14 pages

Complex Analysis

Analytic Functions

18 pages

Taylor's Series

6 pages

Singularity

2 pages

Laurant's Series

9 pages

Cauchy's Residue Theorem

8 pages

Contour integration

14 pages

Linear Programming Problems

Basic Feasible Solutions

4 pages

Optimal Solutions

4 pages

Graphical Method of Solution

9 pages

Simplex Method of Solution

30 pages

Duality

6 pages

Transportation Problems

13 pages

Assignment Problems

7 pages

Partial Differential Equations

Formulation of P.D.E.

10 pages

Solution of Quasilinear Partial Differential Equations of 1st Order, Lagrange's Auxiliary Equations

16 pages

Cauchy's Method of Characteristics

7 pages

Linear P.D.E. of Second Order with Constant Coefficient

15 pages

Canonical Form

21 pages

Application of PDE

46 pages

Numerical Analysis and Computer Programming

Solution of Algebraic and Transcendental Equation of One Variable

9 pages

Solutions of System of Linear Equations

15 pages

Interpolation

15 pages

Numerical Integration

12 pages

Ordinary Differential Equation

5 pages

Computer Programming

28 pages

Mechanics and Fluid Dynamics

Generalised coordinate

26 pages

Moment of Inertia

16 pages

Motion of Rigid Bodies in Two Dimensions

2 pages

Equation of Continuity

17 pages

Euler's Equation of Motion for Inviscid Flow

10 pages

Source and Sink

7 pages

Vortex Motion

15 pages

Navier-Stokes Equation for Viscous Flow

5 pages

Linear Algebra

Vector spaces over R and C

4 pages

Linear Dependence and Independence

2 pages

Subspaces, Bases, Dimensions & Rank

6 pages

Linear Transformations

15 pages

Rank and Nullity

6 pages

Matrix of Linear Transformations

5 pages

Algebra of Matrices

6 pages

Row Reduction

1 page

Echelon Form

2 pages

Congurence and Similarity of Triangles

2 pages

Inverse of a Matrix

3 pages

Eigenvalues and EigenVectors

4 pages

Cayley-Hamilton theorem

7 pages

Properties and Eigenvalues of Special Matrices

5 pages

Calculus

Limit (in one variable)

14 pages

Continuity(in one variable)

12 pages

Intermediate Value Property & its Theorems

5 pages

Taylor's theorem

2 pages

Maxima and Minima(In One Variable)

5 pages

Limit and Continuity

15 pages

Partial Derivatives

5 pages

Maxima and Minima (Two or three variable)

12 pages

Curve Tracing

1 page

Lagrange Method of Multipliers

5 pages

Riemann Integration (Definite Integrals and their Properties)

6 pages

Indefinite Integrals

3 pages

Infinite and Improper Integral

14 pages

Double and Triple Integrals

1 page

Mean value theorem

5 pages

Analytic Geometry

Cartesian and polar coordinates in three dimensions

2 pages

Reduction of Second Order Equation in Canonical Form

3 pages

Shortest Distance between two Skew Lines

3 pages

Conic Section

4 pages

Hyperboloid, Ellipsoid, Paraboloid

3 pages

Ordinary Differential Equations

Equations of First-Order Differential Equations

4 pages

Second and Higher Order Differential Equation

49 pages

Complementary Function

3 pages

Second Order Linear Differential Equations with Variable Coefficients

3 pages

Euler Cauchy Equation

3 pages

Laplace Transform

4 pages

Orthogonal Trajectories

7 pages

Dynamics & Statics

Dynamics of a Particle

140 pages

Statics

49 pages

Fluid Dynamics

63 pages

Mechanics

143 pages

Hydrostatics

60 pages

Rectilinear Motion

2 pages

SHM and Harmonic Motion

2 pages

Vector Analysis

Vector Analysis

109 pages

Gradient, Divergence and Curl in Cartesian Plane

8 pages

Vector Identities and Vector Equation

6 pages

Curves in Space

4 pages

Curvature and Torsion

6 pages

Gauss and Stokes Theorem

10 pages

Green's Identities

4 pages

Algebra

Algebra: Section - 1 (Groups)

95 pages

Algebra: Section - 2 (Rings)

31 pages

Algebra: Section - 3 (Fields)

53 pages

Groups

3 pages

Subgroups

3 pages

Cayleys Table & Cyclic Groups

4 pages

Lagrange Group

3 pages

Normal Subgroup

3 pages

Quotient Group

4 pages

Homomorphism and Isomorphism

5 pages

Permutation Group

3 pages

Cayley's Theorem

5 pages

Rings, Integral Domain & Field

6 pages

Subrings and Ideals

4 pages

Quotient Fields

4 pages

Eucleadian Domain and Unique Factorzation Theorem

3 pages

Real Analysis

Least Upper Bound Property

1 page

Series and Convergent Series

5 pages

Absolute and Conditional Convergenvce

5 pages

Continuity and Uniform Continuity of a Function

1 page

Fundamental Theorem of Calculus

5 pages

Continuity, Differentiability and Integrability for Sequences and Series of Functions

3 pages

Partial Derivatives

5 pages

Maxima and Minima (Two or three variable)

12 pages

Set theory and Sequence

16 pages

Cauchy Sequences

10 pages

Completeness Axiom

2 pages

Improper Integrals

2 pages

Complex Analysis

Analytic Function

2 pages

Cauchy’s integral formula

1 page

Power Series

10 pages

Laurent Series

3 pages

Taylor's theorem

2 pages

Zeroes and Singularities

4 pages

Contour Integration

13 pages

Cauchy Riemann Equations

3 pages

Cauchy’s theorem

4 pages

Linear Programming

Linear Programming

6 pages

Graphical Method and Simplex Method of Solution

5 pages

Duality

11 pages

Transportation and Assignment Problems

37 pages

Numerical Analysis and Computer programming

Gauss Elimination Method

2 pages

Computer Programming : Binary system; Arithmetic and Logical Operations on Numbers

5 pages

Octal and Hexadecimal Systems

2 pages

Conversion to and from Decimal Systems; Algebra of Binary Numbers

7 pages

Concept of Memory

7 pages

Basic Logic of Gates

3 pages

Basic Logic of Truth Table

2 pages

Bollean Algebra

5 pages

Unsigned and Signed Integers

4 pages

Gaussian Elimination and Gauss-Jorden (direct), Gauss-Seidel (iterative) Methods

3 pages

Newton’s (forward and backward) and interpolation, Lagrange’s Interpolation

4 pages

Numerical integration: Trapezoidal rule, Simpson’s rule, Gaussian quadrature Formula

2 pages

Numerical Solution of Ordinary Differential Equations: Eular and Runga Kutta Methods

5 pages

Difference Between Single and Double Precision

3 pages

Mechanics and Fluid Dynamics

D’Alembert’s principle and Lagrange’s equations

4 pages

Hamilton Equations

3 pages

Generalised coordinates

3 pages

Motion of Rigid Bodies in Two Dimension

4 pages

Class 6 Mathematics

NCERT Textbook: Knowing Our Numbers

18 pages

NCERT Textbook: Whole Numbers

5 pages

NCERT Textbook: Playing with Numbers

22 pages

NCERT Textbook: Basic Geometrical Ideas

13 pages

NCERT Textbook: Understanding Elementary Shapes

24 pages

NCERT Textbook: Integers

20 pages

NCERT Textbook: Fractions

30 pages

NCERT Textbook: Decimals

9 pages

NCERT Textbook: Data Handling

11 pages

NCERT Textbook: Mensuration

16 pages

NCERT Textbook: Algebra

8 pages

NCERT Textbook: Ratio & Proportion

17 pages

NCERT Textbook: Symmetry

13 pages

NCERT Textbook: Practical Geometry

19 pages

Class 7 Mathematics

NCERT Textbook: Integers

19 pages

NCERT Textbook: Fractions & Decimals

24 pages

NCERT Textbook: Data Handling

15 pages

NCERT Textbook: Simple Equations

15 pages

NCERT Textbook - The Triangle and its Properties

20 pages

NCERT Textbook: Lines & Angles

14 pages

NCERT Textbook: Congruence of Triangles

20 pages

NCERT Textbook: Comparing Quantities

16 pages

NCERT Textbook: Rational Numbers

20 pages

NCERT Textbook: Practical Geometry

12 pages

NCERT Textbook: Perimeter & Area

16 pages

NCERT Textbook: Algebraic Expressions

10 pages

NCERT Textbook: Exponents & Powers

16 pages

NCERT Textbook: Symmetry

12 pages

NCERT Textbook: Visualising Solid Shapes

16 pages

Class 8 Mathematics

NCERT Textbook: Rational Numbers

14 pages

NCERT Textbook: Linear Equations in One Variable

6 pages

NCERT Textbook: Understanding Quadrilaterals

16 pages

NCERT Textbook- Practical Geometry

12 pages

NCERT Textbook: Data Handling

14 pages

NCERT Textbook- Squares and Square Roots

20 pages

NCERT Textbook: Cubes & Cube Roots

8 pages

NCERT Textbook: Comparing Quantities

14 pages

NCERT Textbook: Algebraic Expressions and Identities

10 pages

NCERT Textbook- Visualising Solid Shapes

16 pages

NCERT Textbook: Mensuration

18 pages

NCERT Textbook: Exponents & Powers

8 pages

NCERT Textbook- Direct and Inverse Proportions

16 pages

NCERT Textbook- Factorisation

12 pages

NCERT Textbook- Introduction to Graphs

14 pages

NCERT Textbook- Playing with Numbers

12 pages

Class 9 Mathematics

NCERT Textbook: Number System

24 pages

NCERT Textbook - Polynomials

14 pages

NCERT Textbook: Coordinate Geometry

12 pages

NCERT Textbook: Linear Equations in Two Variables

5 pages

NCERT Textbook - Introduction to Euclid's Geometry

9 pages

NCERT Textbook: Lines & Angles

14 pages

NCERT Textbook: Triangles

21 pages

NCERT Textbook: Quadrilaterals

12 pages

NCERT Textbook- Areas of Parallelograms

16 pages

NCERT Textbook: Circles

15 pages

NCERT Textbook- Constructions

9 pages

NCERT Textbook: Heron's Formula

6 pages

NCERT Textbook: Surface Area & Volumes

14 pages

NCERT Textbook: Statistics

16 pages

NCERT Textbook: Probability

15 pages

Class 10 Mathematics

NCERT Textbook: Real Numbers

9 pages

NCERT Textbook - Polynomials

14 pages

NCERT Textbook: Pair of Linear Equations in Two Variables

14 pages

NCERT Textbook: Quadratic Equation

11 pages

NCERT Textbook: Arithmetic Progressions

24 pages

NCERT Textbook: Triangles

26 pages

NCERT Textbook: Coordinate Geometry

14 pages

NCERT Textbook: Introduction to Trigonometry

20 pages

NCERT Textbook: Some Applications in Trigonometry

11 pages

NCERT Textbook: Circles

10 pages

NCERT Textbook: Constructions

7 pages

NCERT Textbook: Areas Related to Circles

7 pages

NCERT Textbook: Surface Areas & Volumes

10 pages

NCERT Textbook: Statistics

31 pages

NCERT Textbook: Probability

16 pages

Class 11 Mathematics

NCERT Textbook: Sets

23 pages

NCERT Textbook - Relations and Functions

19 pages

NCERT Textbook: Trigonometric Functions

33 pages

NCERT Textbook: Principle of Mathematical Induction

11 pages

NCERT Textbook: Complex Numbers & Quadratic Equations

13 pages

NCERT Textbook - Linear Inequalities

11 pages

NCERT Textbook: Permutations and Combinations

26 pages

NCERT Textbook: Binomial Theorem

9 pages

NCERT Textbook: Sequences and Series

16 pages

NCERT Textbook: Straight Lines

25 pages

NCERT Textbook: Conic Sections

32 pages

NCERT Textbook: Three Dimensional Geometry

9 pages

NCERT Textbook: Limits and Derivatives

40 pages

NCERT Textbook: Mathematical Reasoning

26 pages

NCERT Textbook: Statistics

32 pages

NCERT Textbook: Probability

25 pages

Class 12 Mathematics

NCERT Textbook - Relations and Functions

17 pages

NCERT Textbook: Inverse Trigonometric Functions

16 pages

NCERT Textbook: Matrices

42 pages

NCERT Textbook: Determinants

28 pages

NCERT Textbook: Continuity and Differentiability

43 pages

NCERT Textbook: Application of Derivatives

40 pages

NCERT Textbook: Integrals

67 pages

NCERT Textbook: Application of Integrals

8 pages

NCERT Textbook: Differential Equations

38 pages

NCERT Textbook: Vector Algebra

39 pages

NCERT Textbook: Three Dimensional Geometry

17 pages

NCERT Textbook - Linear Programming

12 pages

NCERT Textbook: Probability

33 pages

2024

Mathematics Optional Paper 1 - 2024

8 pages

Mathematics Optional Paper 2 - 2024

12 pages

2023

Mathematics Optional Paper 1 - 2023

8 pages

Mathematics Optional Paper 2 - 2023

8 pages

2022

Mathematics Optional Paper 1 - 2022

9 pages

Mathematics Optional Paper 2 - 2022

8 pages

2021

Mathematics Optional Paper 1 - 2021

7 pages

Mathematics Optional Paper 2 - 2021

7 pages

2020

Mathematics Optional Paper 1 - 2020

8 pages

Mathematics Optional Paper 2 - 2020

8 pages

2019

Mathematics Optional Paper 1 - 2019

11 pages

Mathematics Optional Paper 2 - 2019

8 pages

2018

Mathematics Optional Paper 1 - 2018

7 pages

Mathematics Optional Paper 2 - 2018

8 pages

Mathematics Optional Notes for UPSC

396 videos|308 docs

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Revision notes for Mathematics Optional Notes for UPSC 2025 is part of UPSC CSE exam preparation. The notes have been prepared according to the UPSC CSE exam syllabus. The revision notes, tests & MCQs are made for UPSC CSE 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests here.

Notes of Mathematics Optional Notes for UPSC in English & Hindi are available as part of UPSC CSE exam. Download more important topics, notes, lectures and mock test series for UPSC CSE Exam by signing up for free.

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