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
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