Krishna’s – Solution B.Sc. Mathematics – III

English | 2021 | ASIN: B0931V61HT | 600 pages | PDF | 6.07 MB

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