*PAPER1- REAL ANALYSIS*

**NAME OF CHAPTER AND THEIR SYLLABUS **

*Unit-I*

Modulus, Intervals, Definition of a sequence, Theorems on limit of sequence, nested interval theorem, Cauchy’s sequence, convergence.

*Unit-II*

Convergence of series (Comparison; D’Alembert’s ratio, Cauchy’s nth root, Raabe’s, Gauss, Logarithmic, ETC.) Abel’s and Dirichlet’s tests.

*Unit-III*

Limit point of a set, Bolzano-Weierstrass theorem. Closed set.

*Unit-IV*

Definition of limit, Continuity of a function – Cauchy’s and Heine’s definitions, Differentiability, Rolle’s theorem, Lagrange’s and Cauchy’s mean value theorems. Taylor’s theorem, Darboux’s intermediate value theorem for derivatives.

LIMIT, CONTINUITY, DIFFEREN. NOTES IN HINDI

**Unit-V**

Riemann integral, Mean value theorems of integral calculus, The fundamental theorem of integral calculus. Improper integrals and their convergence comparison tests.

IMPROPER INTEGRAL AND RIEMANN NOTES IN ENGLISH

RIEMANN INTEGRAL NOTES IN HINDI

## PAPER2- DIFFERENTIAL EQUATION

**NAME OF CHAPTER AND THEIR SYLLABUS **

* Unit-I*

Differential equations of first order and first degree, variables separable, homogeneous equations. Exact differential equations.

* Unit-II *

Linear differential equations with constant coefficients, Homogeneous linear differential equations, Total differential equations.

*Unit-III*

Linear differential equations of second order. Exact differential equations.

*Unit-4*

Partial differential equations of first order, Lagrange’s solution. Charpit’s general method of solution.

**Unit-V **

Partial differential equations of second and higher orders. Homogeneous and non-homogeneous equations. Partial differential equations with constant coefficients.

## ** ***PAPER3- MECHANICS*

*PAPER3- MECHANICS*

**NAME OF CHAPTER AND THEIR NOTES LINK**

`STATICS`

*UNIT 1:*

Analytical Conditions of equilibrium of a rigid body under coplanar forces. Friction.

COPLANAR FORCES NOTES IN HINDI

*UNIT 2:*

Center of Gravity, Common Catenary

`DYNAMICS`

*UNIT 3:*

Simple harmonic motion. Motion under earth’s attraction. Hooke’s Law, Rectilinear motion in a resisting medium.

RECTILINEAR MOTION NOTES IN ENGLISH

UNIT 3, 4,5 COMPLETE DYNAMICS NOTES IN HINDI

*UNIT 4:*

Velocity and acceleration along radial and transverse directions and along tangential and normal directions.

VEL. AND ACCN. NOTES IN ENGLISH

*UNIT 5:*

Direct and oblique impact. Constrained Motion- Circular and Cycloidal.

Work, Energy and Impulse