B.SC II YEAR math Syllabus

BMG: 201 Max Marks: 50

Elementary Analysis, Differential Equations and Vector Calculus

Unit-I

Real –Valued functions, Equivalence, Countability, Real numbers, Least upper

bound,Sequence of real numbers, Series of real numbers.

Infinite series: Introduction, Alternating series with Leibnitz test, P-series test for

positive terms, Comparison test for positive terms, D’Alembert’s ratio test , Cauchy’s

root test , Raabe’s test , Logarithmic test,

Open sets, closed sets on R, Derivatives, Rolle ’s Theorem, The law of the mean.

Unit-II

Ordinary differential equation of the first order and first degree, Clairaut’s form of

differential equations, Orthogonal trajectories, Linear differential equations with constant

coefficient, Homogeneous linear differential equations.

Unit-III

Linear differential equation of second order with constant coefficients.

Unit-IV

Scalar and Vecor product of three vectors, Product of four vectors , Reciprocal vectors,

Vector differentiation, Directional derivatives, Gradient, Divergence and Curl.

Unit-V

Vector integration, Theorems of Gauss,Green,Stokes and problems based on these.

BOOKS SUGGESTED

1. R.R.Goldberg Methods of Real Analysis

2. Gorakh Prasad Integral Calculus

3. Shanti Narayan A text –Book of Vector Calculus

(S. Chand & Co. New Delhi)

4.G.F.Simmons Differential Equations

5. Murray R. Spiegel Vector Analysis, Schaum Pub. Company New york

6 S.L.Ross Ordinary Differential Equations

7 H.L.Royden Real Analysis

BMG: 202 Linear Algebra Max Marks: 50

Unit-I

Vector Space: Field, Vector space, Subspaces, Base and dimension, Coordinates,

Summary of rows equivalence, Computations concerning subspaces.

Unit-II

Linear Transformations: Linear transformations and their algebra. Isomorphism,

Representation of transformations by matrices.

Linear functionals, Double dual, Transpose of linear transformations.

Unit-III

Polynomials: Algebra of polynomials, Polynomial ideals, Determinant functions and

simple properties.

Unit-IV

Canonical Form: Characteristic values and Characteristic vectors, Annihilating

polynomials, Examples of invariant subspaces.

Diagonalization, Orthogonal diagonalization, Applications to differential equations.

Unit-V

Quadratic forms: Quadratic forms in two and n variables, Cross-product terms of the

quadratic form. Positive definite Quadratic form, Diagonalization of quadratic forms,

Application to conic sections.

Books Recommended:

1. H.Anton Elementary Linear Algebra , John Wiley & Sons.

2. Chatles W.Curtis(C.W.Curtis) Elementary Linear Algebra

BMG: 203 Mechanics Max Marks: 50

Unit-I

Virtual Works: Equilibrium of strings and chains (common catanary and catanary of

uniform strength),Stable and Unstable equilibrium, Moments and couples, Varignon’s

theorem of moments

Unit-II

Equiblirium of forces in three dimensions, central axis, Wrench and Screw, Pitch of the

wrench.

Unit-III

Kinematics, Motion in a straight line and a plane, Radial and transverse velocities and

accelerations.

Unit-IV

Angular velocity and acceleration, Tangential and normal velocities and acceleration,

Rectilinear motion with constant acceleration.

Unit-V

Simple harmonic motion, Hook’s law, Repulsion from a fixed point varying as the

distance from the point, Constrained motion on a smooth plane (Vertical circle and

cycloid) , Projection.

Books Recommended:

1.R.S.Verma Statics

2.S.L.Loney Statics

3.M.Ray Dynamics