Her you can download the VTU CBCS 2018 Scheme notes, Study materials of Transform Calculus, Fourier Series, and numerical techniques.
University
Visvesvaraya Technological University, Belagavi
Branch Name
Common to all branches
Subject Name
Transform Calculus, Fourier Series, and Numerical Techniques
Subject Code
18MAT31
Module – 1
Laplace Transforms Definition and Laplace transform of elementary functions. Laplace transforms of Periodic functions and unit-step function – problems. Inverse Laplace Transforms: Inverse Laplace transform – problems, Convolution theorem to find the inverse Laplace transform (without proof) and problems, solution of linear differential equations using Laplace transforms.
Module – 2
Fourier Series: Periodic functions, Dirichlet’s condition. Fourier series of periodic functions period 2 and arbitrary period. Half range Fourier series. Practical harmonic analysis, examples from the engineering field.
Module – 3
Fourier Transforms: Infinite Fourier transforms, Fourier sine, and cosine transforms. Inverse Fourier transforms. Simple problems. Difference Equations and Z-Transforms: Difference equations, basic definition, z-transform-definition, Standard z-transforms, Damping, and shifting rules, initial value, and final value theorems (without proof) and problems, Inverse z-transform. Simple problems.
Module – 4
Numerical Solutions of Ordinary Differential Equations (ODE’s): Numerical solution of ODE’s of the first order and first degree- Taylor’s series method, Modified Euler’s method. Range – Kutta method of fourth-order, Milne’s and Adam-Bashforth predictor and corrector method (No derivations of formulae), Problems.
Module – 5
Numerical Solution of Second Order ODE’s: Runge -Kutta method and Milne’s predictor and corrector method.(No derivations of formulae). Calculus of Variations: Variation of function and functional, variational problems, Euler’s equation, Geodesics, hanging chain, problems.
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