MATHEMATICS IV
RESOURCES AVAILABLE FOR MATHEMATICS IV :
- SYLLABUS
- TEXT BOOK - B.S GREWAL
- PREVIOUS PAPERS
SYLLABUS :
Unit-I : VECTOR CALCULUS-1
Differentiation of vectors, curves in space, velocity and acceleration, relative velocity and relative acceleration, scalar and vector point functions, vector operator Ñ applied to scalar point functions- gradient, Ñ applied to vector point functions- divergence and curl. Physical interpretation of , Ñ applied twice to point functions, Ñ applied to products of two functions; Irrotational and Solenoidal fields.
Unit-II : VECTOR CALCULUS-2
Integration of vectors, line integral, circulation, work done, surface integral-flux, Green’s theorem in the plane, Stoke’s theorem, volume integral, Gauss Divergence theorem.
Introduction of orthogonal curvilinear coordinates, cylindrical and spherical polar coordinates
Unit-III : INTRODUCTION OF PARTIAL DIFFERENTIAL EQUATIONS
Formation of partial differential equations, solutions of partial differential equations- equations solvable by direct integration, linear equations of first order: Lagrange’s Linear equation, non-linear equations of first order, Charpit’s method.
Homogeneous linear equations with constant coefficients- rules for finding the complementary function, rules for finding the particular integral (working procedure), non- homogeneous linear equations.
Unit-IV : APPLICATIONS OF PARTIAL DIFFERENTIAL EQUATIONS
Method of separation of variables, One dimensional wave equation-vibrations of a stretched string, one dimensional Heat equation, Two dimensional heat flow in steady state - solution of Laplace’s equation in Cartesian and polar coordinates (two dimensional).
Unit-V : INTEGRAL TRANSFORMS
Introduction, definition, Fourier integral, Sine and Cosine integrals, Complex form of Fourier integral, Fourier transform, Fourier Sine and Cosine transforms, Finite Fourier Sine and Cosine transforms, properties of Fourier transforms, Convolution theorem for Fourier transforms, Parseval’s identity for Fourier transforms, Fourier transforms of the derivatives of a function, simple applications to Boundary value problems.
TEXT BOOKS:
Scope and treatment as in “Higher Engineering Mathematics”, by Dr. B.S.Grewal, 43rd Edition, Khanna Publishers.
REFERENCE BOOKS:
- A text book of Engineering Mathematics by N.P. Bali and Dr. Manish Goyal, Lakshmi Publications.
- Mathematical Methods of Science & Engineering aided with MATLAB by Kanti B.Dutta, Cengage Learning India Pvt. Ltd.
- Advanced Engineering Mathematics by Erwin Kreyszig.
- Higher Engineering Mathematics by B. V. Ramana, Tata McGraw Hill Company.
- Advanced Engineering Mathematics by H.K.Dass. S.Chand Company.
TEXT BOOK :
PREVIOUS PAPERS :