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Mathematical Methods

Mathematical Methods

Published by uLektz

Course Code:R15103


University: Jawaharlal Nehru Technological University, Hyderabad (JNTUH)


Categories:Engineering Mathematics

Format : ico_bookePUB3 (DRM Protected)

Type :eBook

Rs.354 Rs.177 Rs.50% off

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Description :Mathematical Methods

Note : No printed book. Only ebook. Access eBook using uLektz apps for Android, iOS and Windows Desktop PC.

UNIT – I: Interpolation and Curve fitting

1.1 Introduction- Errors in Polynomial Interpolation

1.2 Finite differences- Forward Differences- Backward differencesCentral differences Symbolic relations and separation of symbols-

1.3 Difference Equations -Differences of a polynomial-Newton’s formulae for interpolation - Central difference interpolation Formulae -Gauss Central Difference Formulae

1.4 Interpolation with unevenly spaced points-Lagrange’s Interpolation formula. B. Spline interpolation -Cubic spline.

1.5 Fitting a straight line-Second degree curve-exponential curve-power curve by method of least squares.

UNIT – II : Numerical techniques

2.1 Introduction -Graphical interpretation of solution of equations.The Bisection Method

2.2 The Method of False Position -The Iteration Method-Newton-Raphson Method.

2.3 Solving system of non-homogeneous equations by L-U Decomposition method(Crout’s Method)Jacobi’s and Gauss- Seidel Iteration method

2.4 Numerical differentiation, Numerical integration -Trapezoidal rule, Simpson’s 1/3rd and 3/8 Rule , Generalized Quadrature.

2.5 Solution by Taylor’s series method-Picard’s Method of successive Approximation-

2.6 Single step methods-Euler’s Method-Euler’s modified method,

2.7 Runge-Kutta Methods ,Predictor –corrector methods(Milne’s Method and Adams-Bashforth methods only).

UNIT – III: Fourier series and Fourier Transforms

3.1 Definition of periodic function. Fourier expansion of periodic functions in a given interval of length 2 -Determination of Fourier coefficients

3.2 Fourier series of even and odd functions -Fourier series in an arbitrary interval -Even and odd periodic continuation -Half-range Fourier sine and cosine expansions.

3.3 Fourier integral theorem, Fourier sine and cosine integrals

3.4 Fourier transforms, Fourier sine and cosine transforms, Properties, Inverse transforms, Finite Fourier transforms

UNIT-IV: Partial differential equations

4.1 Introduction and Formation of partial differential equation by elimination of arbitrary constants and arbitrary functions

4.2 Solutions of first order linear (Lagrange) equation and non-linear equations (Charpit’s method)

4.3 Method of separation of variables for second order equations

4.4 Applications of Partial differential equations-Two dimensional wave equation, Heat equation

UNIT – V Vector Calculus

5.1 Scalar point function and vector point function, Gradient- Divergence- Curl and their related properties, Laplacian operator, Line integral – work done, Surface integrals -Volume integral

5.2 Green’s Theorem, Stoke’s theorem and Gauss’s Divergence Theorems (Statement & their Verification)

5.3 Solenoidal and irrotational vectors, Finding Potential function