Date

Topic 1

Topic 2

13-Jan-22

ODE

Formation,Integarting factors

PDE

Origin of PDE, Formation, (U,V) method

14-Jan-22

Problems on IF

15-Jan-22

Geometry interpretation, Application of ODE

Linear PDE of Order one
Lagrange Method- Type 1,2,3,4

16-Jan-22

Orthogonality

First Order Eqn : Solvable for p, x,y

Linear PDE Applications. Problems, Orthogonality

17-Jan-22

18-Jan-22

First Order Eqn : Claurait, Singular Soln

Charpit

19-Jan-22

LDE constant coefficient

20-Jan-22

ODE

PDE

Standard Forms I,II,III,IV

21-Jan-22

Cauchy Euler Eqn

Jacobians

22-Jan-22

Method of Variation of Parameter

23-Jan-22

Ordinary Simultaneous Eqns

PDE

Homogeneous Linear PDE

24-Jan-22

Linear Eqn of second Order
Reduction Method and Normal Form

Euler Cauchy eqns

25-Jan-22

26-Jan-22

Laplace Eqns

27-Jan-22

Canonical Form and Cauchy Strip

28-Jan-22

Inverse Laplace

29-Jan-22

30-Jan-22

Laplace in Solving ODE

Boundary Problems

30-Jan-22

31-Jan-22

ODE

Solve Previous Year Qns

PDE

Solve Previous Problems

1-Feb-22

Calculus and Real Analysis

Limits , Continuity

Calculus and Real Analysis

2-Feb-22

Differentiability

Sequences

3-Feb-22

Calculus and Real Analysis

4-Feb-22

Mean Value Theorem

Series

5-Feb-22

Indeterminate form Problems

6-Feb-22

Uniform Convergence

7-Feb-22

Improper Integrals

8-Feb-22

Several Variable Functions

9-Feb-22

Max/Min One and Two Variable Several, Lagrangian Method

10-Feb-22

Differentiation Under Integral Sign,

Asymptotes,

Definite Integral as Sum

11-Feb-22

Rieman Integrals

12-Feb-22

Jacobians

13-Feb-22

Calculus and Real Analysis

Calculus and Real Analysis

14-Feb-22

Partial Differentiations: Euler, Total Differentiations
 

Length of Arc, Areas,

Surfaces, Volumes

15-Feb-22

16-Feb-22

Beta Gamma Function : Application

17-Feb-22

Multiple Integrals

18-Feb-22

Calculus -Previous Year qns

Real Analysis
 Previous Year qns

19-Feb-22

20-Feb-22

21-Feb-22

3D Geometry

Basics: System of Coordinates

Analytic Geometry
Cosines and Projections

Numerical Analysis

solution of algebraic and transcendental equations of one variable by bisection, Regula-Falsi and Newton-Raphson methods

22-Feb-22

solution of system of linear equations by Gaussian elimination and Gauss-Jordan (direct), Gauss-Seidel(iterative) methods

23-Feb-22

Straight Lines ,

Planes
 

Lagrange’s interpolation

24-Feb-22

Trapezoidal rule, Simpson’s rules, Gaussian quadrature formula

25-Feb-22

Numerical solution of ordinary differential equations: Euler and Runge Kutta-methods.

26-Feb-22

27-Feb-22

Shortest Distance,

Skew Lines

28-Feb-22

1-Mar-22

2-Mar-22

Numerical Analysis

Number System,
Algorithms and flow charts for solving  problems

3-Mar-22

Analytic Geometry

4-Mar-22

Cones

Cylinders,

Spheres

5-Mar-22

6-Mar-22

Fluid Dynamics

Fluid Dynamics
Introduction, Various Coordinate Systems, Formulas
Kinematics of Fluid,

Boundary Problems

7-Mar-22

Analytic Geometry

Central Conicoids

8-Mar-22

9-Mar-22

10-Mar-22

Generating Lines,

Paraboloid

Fluid Dynamics
Kinematics: Streamline, Vorticity

11-Mar-22

12-Mar-22

3D-PYQ

13-Mar-22

Fluid Dynamics

Equation of Motion,

Bernauli Eqns

14-Mar-22

Mechanics

Moment of Inertia,

D alambert

15-Mar-22

16-Mar-22

17-Mar-22

Lagrangian Eqns

Source, Sink

18-Mar-22

19-Mar-22

Irrotational Motion
 

20-Mar-22

Hamiltonian Eqns

21-Mar-22

Vortex Motion,

Navier Stoke : 4 Qns

22-Mar-22

23-Mar-22

Mechanics

Fixed Axis,

Energy Conservation
Important Qns

24-Mar-22

Fluid Dynamics

Motion of Cylinder and Sphere

30-Mar-22

31-Mar-22

Linear Algebra

Introduction: Algebra of Matrices; Row and column reduction, , congruence’s and similarity; Symmetric, skew- Hermitian, skew- orthogonal and unitary matrices. Rank of a matrix, Echelon form, Normal Form,  Inverse of a matrix,

Complex Analysis

Analytic Functions , Cauchy Reiman Eqns: Definition and Problems, Limit ,Continuity

1-Apr-22

2-Apr-22

Eigenvalues and eigenvectors, characteristic polynomial,

 Cayley Hamilton Theorem

Taylor’s series; Laurent’s series formula

3-Apr-22

Linear Algebra

Solution of system of linear equations

Complex Analysis

4-Apr-22

Cauchy’s theorem, Cauchy’s integral formula

5-Apr-22

Diagnosable

6-Apr-22

Vector spaces Definition and problems

Subspaces, Bases, Dimension

7-Apr-22

,

Calculus of Residue

8-Apr-22

Linear transformations, rank and nullity ,

LT Bases, Singular, Inveribles

Power Series and Misc Topics like Convergence

9-Apr-22

Matrix Formations

10-Apr-22

Linear Algebra

Previous Year Problems

Complex Analysis

Previous Year Problems Complex Analyisis
 

11-Apr-22

12-Apr-22

Dynamics

Central Forces

Statics

Virtual work

13-Apr-22

Inverse Square Law

14-Apr-22

Common Catenary

15-Apr-22

Projectile

16-Apr-22

17-Apr-22

SHM

Equilibrium Stable/Unstable

18-Apr-22

19-Apr-22

Work Energy

Friction
 

20-Apr-22

21-Apr-22

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

Modern Algebra

Binary Operations, Groups, Order, Properties

22-Apr-22

23-Apr-22

Subgroup,

Cyclic Group,

Permutation Group

Normal Group

24-Apr-22

Gauss Theorem

Stoke Theorem

25-Apr-22

Homomorphism

Cayley Theorem

26-Apr-22

Green Theorem

Ring Theory and Properties,

Integral Domain,

Field

27-Apr-22

28-Apr-22

Differential Geometry : Basics

Serret Frenet

Curvature, Torsion

Ideals,

Ring Homomorphism,

Quotient Ring

29-Apr-22

30-Apr-22

1-May-22

Imbedding of Rings,

Maximal,Prime Ideals, PID

2-May-22

Vector Analysis

Vector Analysis PYQ

3-May-22

4-May-22

Modern Algebra

ED, Polynomial Rings

UFD, Primitive,

Irreducible Polynomial

SYLLABUS COMPLETE ONCE

5-Jun-22

UPSC PRELIMS 2022 Exam

6-Jun-22

7-Jun-22

19-Jun-22

Mini Test Paper 1

Part A

Mini Test Paper 2

Part A

26-Jun-22

Mini Test Paper 1

Part B

Mini Test Paper 2

Part B

3-Jul-22

10-Jul-22

Full Length Test 1

Paper 1

Full Length Test 1

Paper 2

17-Jul-22

31-Jul-22

Full Length Test 2

Paper 1

Full Length Test 2

Paper 2

7-Aug-22

14-Aug-22

Grand Full Length Test 1

Paper 1

Grand Full Length Test 1

Paper 2

21-Aug-22

28-Aug-22

Grand Full Length Test 2

Paper 1

Grand Full Length Test 2

Paper 2

4-Sep-22

11-Sep-22

12-Sep-22

UPSC MAINS EXAM STARTS