APPLIED MATHEMATICS (G105)
UNIT1-Numerical Analysis:
Interpolation :Introduction to interpolation.Lagrange’s interpolation formula.The operators and Relation between them.Difference Table.Newton’s forward and backward interpolation formula.Concept of extrapolation.Numerical Differentiation and Integration.Newton’s forward and backward difference formula for differentiation at any point Numerical Integration.Trapezoidal rule and Simpson’s 1/3 rule. Numerical Solution of Ordinary Differential Equation: Introduction.Runge Kutta’s 2nd and 4th order methods.
UNIT2-Differential Equations (ordinary):
Introduction.Order and degree of a differential equation.Formation of Differential Equations.Solution of a Differential Equation.Differential equation of the first order and first degree.Variables separable.Homogeneous Differential Equations.Linear Differential Equations.Equations reducible to linear form.Exact differential Equations. Equations reducible to the exact form.Linear Differential Equations of second order with constant coefficients.Complete solution = Complementary Function + Particular Integral.Method of finding Particular Integral.
UNIT3-Graph Theory:
Introduction.Basic Terminology.Simple Graph, Multigraph and Pseudo graph. Degree of a Vertex.Types of Graphs. Subgraphs and Isomorphic Graphs. Operations of Graphs. Paths, Cycles and Connectivity.Eulerian and Hamiltonian Graph. Shortest Path Problems using known Algorithm .
UNIT4-Discrete Mathematics:
The principle of Inclusion and Exclusion with examples. Generating Functions. Introductory examples. Definition and examples of Calculation Techniques. Recurrence Relations.First order linear recurrence relations.Second order linear homogeneous recurrence relations with constant coefficients. Non-homogeneous recurrence relations
REFERENCE BOOKS.
(1) Integral Calculus by B.C.Das and B.N.Mukherjee.
(2) Diploma Engineering Mathematics (Volume-II) by B.K.Pal.
(3) Applied Mathematics-I by Dr.J.S.Bindra and K.S.Gill.
(4) Applied Mathematics-II by Dr.J.S.Bindra and K.S.Gill.
(5) Applied Mathematics-III by Dr.J.S.Bindra.
(6) Engineering Mathematics (Volume-I, Volume-II & Volume-III). By S.Arumugam, A.ThangapandiIssac and A.Somsundaram.
(7) Discrete and Combinatorial Mathematics by Ralph P.Grimaldi.
(8) A TEXT BOOK OF DISCRETE MATHEMATICS by Swapan Kumar Sarkar.
(9) Mathematics for Polytechnic by S.P.Deshpande.
(10) Higher Engineering Mathematics by B.S.Grewal.
(11) Introductory Method of Numerical Analysis by S.S.Sastry.
(12) Calculus of Finite Difference and Numerical Analysis by Gupta-Malik.