MATHEMATICS â?? II
UNIT â?? I: Solution of Algebraic and Transcendental Equations and Interpolation
Solution of Algebraic and Transcendental Equations: Introduction â?? Graphical interpretation of solution of equations .The Bisection Method â?? The Method of False Position â?? The Iteration Method â?? Newton-Raphson Method .
Interpolation: Introduction-Errors in polynomial interpolation-Finite differences- Forward Differences- Backward differences â??Central differences â?? Symbolic relations and separation of symbols-Differences of a polynomial-Newtonâ??s formulae for interpolation â?? Central difference interpolation Formulae â?? Gauss Central Difference Formulae â?? Interpolation with unevenly spaced points-Lagrangeâ??s Interpolation formula.
UNIT â?? II : Numerical techniques and Curve Fitting
Numerical integration: Generalized Quadrature-Trapezoidal rule, Simpsonâ??s 1/3rd and 3/8th Rule.
Numerical solution of Ordinary Differential equations: Solution by Taylorâ??s series method â??Picardâ??s Method of successive Approximation- single step methods-Eulerâ??s Method-Eulerâ??s modified method, Runge-Kutta Methods.
Curve fitting: Fitting a straight line â??Second degree curve-exponential curve-power curve by method of least squares.
UNIT â?? III: Fourier series
Definition of periodic function. Fourier expansion of periodic functions in a given interval of length 2ð???. Determination of Fourier coefficients â?? Fourier series of even and odd functions â?? Half-range Fourier sine and cosine expansions-Fourier series in an arbitrary interval .
UNIT-IV: Partial differential equations
Introduction -Formation of partial differential equation by elimination of arbitrary constants and arbitrary functions, solutions of first order linear (Lagrange) equation and non-linear equations (Charpitâ??s method), Method of separation of variables for second order equations.
UNIT â?? V : Vector Calculus
Introduction- Scalar point function and vector point function, Gradient- Divergence- Curl and their related properties - Laplacian operator, Line integral â?? work done â?? Surface integrals -Volume integral. Greenâ??s Theorem,Stokeâ??s theorem and Gaussâ??s Divergence Theorems (Statement & their Verification).
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