B.Sc 2nd Year Syllabus Kashmir University

I want the syllabus of Integral Calculus and Theory of Equations of B.Sc 2nd Year of Kashmir University so can you provide me?

[shikha]

Ok, here I am providing you the syllabus of Integral Calculus and Theory of Equations of B.Sc 2nd Year of Kashmir University.

Kashmir University B.Sc 2nd Year Integral Calculus and Theory of Equations syllabus

Integral Calculus

Unit I

Integration by substitution and by parts, integration of algebraic rational functions, integration of algebraic rational functions by substitution, integration of irrational functions, reduction formulae for the integrals of circular functions and for the integrals of sinmx cosnx, cosmx cosnx, xm cosnx, Definite integral as the limit of a sum, summation of series with the help of definite integrals, Quaderature, area of a region bounded by a curve, x-axis (y-axis) and two ordinates (abscissa), sectorial areas bounded by a closed curve, Lengths of plane curves, volumes and surface of revolution.

Differential Equations

Unit II

Homogeneous equations, Linear equations and equations reducible to linear form, Bernoulli’s equations, Exact differential equations, Symbolic operators. Linear differential equations with constant coefficients, differential equations of the forms f (D) y = sin bx, eax V, where V is any functions of x, Homogeneous linear equations.

Unit III

Miscellaneous forms of differential equations. First order higher degree equations solvable for x,y,z,p, Equations from which one variable is explicitly absent, Clairut’s form, equations reducible to Clairut’s form, Legendre polynomials, Recurrence relation and differential equation satisfied by it, Bessel functions, recurrence relation and differential equation.

THEORY OF EQUATIONS

Unit IV

General properties of equations, synthetic division, relation between the roots and the coefficients of an equation, transformation of equations, diminishing the roots of an equation by a given number, removal of terms of an equation, formation of equations whose roots are functions of the roots of a given equation, equations of squared differences, Symmetric functions, Newton’s method of finding the sum of powers of the roots of an equation, Cardan’s solution of the cubic, nature of the roots of a cubic, Descarte’s solution of a biquadratic, Descarte’s rule of signs, rational roots of an integral polynomial, location of roots of an equation (simple cases).

Text Books Recommended:

1. S. D. Chopra and M.L. Kochhar, Integral Calculus.

2. Schaum Series, Differential Equations.

3 A.Aziz, N.A.Rather & B.A.Zargar, Theory of Equations, KBS.

4 Ordinary Differential Equations, M.D.Raisinghania. Suggested Readings: 1. T. M. Apostol, Calculus-I. 2. Samuel Borofsky, Elementary theory of Equations. 3. H.T.H. Piaggio, Differential Equations.

Contact-

University of Kashmir
Hazratbal, Srinagar, Jammu and Kashmir 190006