# Krishna’s TB Solution B.Sc. Mathematics III , Edition

SYLLABUS- Solution B.Sc. MATHEMATICS-III, Advanced Algebra

B.A./B.Sc. III Semester–Paper-I

Rings: Rings, Various types of rings, Rings with unity, Rings without zero divisors,

Properties of rings, Sub rings.

Ideals: Ideals, Quotient rings, Principal ideals, Maximal ideals, Prime ideals, Principal

ideal domains, Characteristic of a ring.

Integral Domains and Fields: Integral domain, Field, Skew field etc., Field of

quotients of an integral domain, Embedding of an integral domain in a field,

Factorization in an integral domain, Divisibility, Units, Associates, Prime and irreducible

elements, Unique Factorisation Domain, Euclidean rings.

Polynomial Rings: Polynomials over a ring, Degree of a polynomial, Zero, Constant

and monic polynomials, Equality of polynomials, Addition and multiplication of

polynomials, Polynomial rings, Embedding of a ring R into R[x], Division algorithm,

Euclidean algorithm, Units and associates in polynomials, Irreducible polynomials.

Differential Equations

B.A./B.Sc. III Semester–Paper-II

Differential Equations: Introduction of Differential equations, Order and Degree of

Differential Equations, Complete primitive (general solution, particular solution and

singular solutions), Existence and uniqueness of the solution dy/dx= f(x,y).

First Order Differential Equations: Differential equations of first order and first

degree, Separation of variables, Homogeneous Equations, Exact Equations,

Integrating Factor, Linear Equation, Equation of First order but not of first degree,

Various methods of solution, Clairaut’s form, Singular solutions, Trajectory, Orthogonal

Trajectory, Self-Orthogonal family of Curves.

Linear Differential Equations: Linear equations with constant coefficients,

Complementary function, Particular integral, Working rule for finding solution,

Homogeneous linear equations.

Miscellaneous Equations: Simultaneous differential equations, Differential

equations of the form dx/P= dy/Q= dz/R where P, Q, R are functions of x, y, z. Exact

differential equations, Total differential equations, Series solutions of differential

equations, Linear differential equations of second order with variable coefficients.

Applications: Initial and boundary value problems, Simple applications of

differential equations of first order.

Mechanics

B.A./B.Sc. III Semester–Paper-III

Rectilinear motion: Newton’s Laws of Motion, velocity and acceleration, motion

under constant acceleration, motion under inverse square law, rectilinear motion with

variable acceleration, Simple Harmonic Motion.

Kinematics in two dimension: Angular velocity and angular acceleration,

Components of velocity and acceleration along coordinate axes, Radial and

transverse components of velocity and acceleration, tangential and normal

components of velocity and acceleration.

Motion in resisting medium, constrained motion and Central orbits:

Terminal Velocity, Motion in resisting medium in a straight line, Motion on vertical

circle, Cycloidal motion, Central Force, Central orbit, intrinsic equation, Pedal form,

apse and apsidal distance.

Statics: Coplaner Forces, Equilibrium of forces in three dimensions, Common

**Authors:** A.R Vasishtha

**Date:** 2021

**Upload Date:** 9/29/2021 9:59:30 AM

**Format:** pdf

**Pages:** 600

**OCR:**

**Quality:**

**Language:** English

**ISBN / ASIN:** B0931V61HT

**ISBN13:**

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