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SYLLABUS
UNIT-I
Vector Calculus Vector Differentiation : Gradient – Directional Derivative – Divergence – Curl – Scalar Potential. Vector Integration : Line Integral – Work Done – Area – Surface and Volume Integrals – Vector Integral Theorems : Greens, Stokes and Gauss Divergence Theorems (Without Proof) and Problems on above Theorems.
UNIT-II
Laplace Transforms Laplace Transforms – Definition and Laplace Transforms of Some Certain Functions – Shifting Theorems – Transforms of Derivatives and Integrals – Unit Step Function – Dirac’s Delta Function – Periodic Function – Inverse Laplace Transforms – Convolution Theorem (Without Proof). Applications : Solving Ordinary Differential Equations (Initial Value Problems) Using Laplace Transforms.
UNIT-III
Fourier Series and Fourier Transforms Fourier Series : Introduction – Periodic Functions – Fourier Series of Periodic Function – Dirichlet’s Conditions – Even and Odd Functions – Change of Interval – Half-range Sine and Cosine Series. Fourier Transforms : Fourier Integral Theorem (Without Proof) – Fourier Sine and Cosine Integrals – Sine and Cosine Transforms – Properties – Inverse Transforms – Convolution Theorem (Without Proof) – Finite Fourier Transforms.
UNIT-IV
PDE of First Order Formation of Partial Differential Equations by Elimination of Arbitrary Constants and Arbitrary Functions – Solutions of First Order Linear (Lagrange) Equation and Nonlinear (Standard Types) Equations.
UNIT-V
Second Order PDE and Applications Second Order PDE : Solutions of Linear Partial Differential Equations With Constants Coefficients – Non-homogenous Term of the Type eax + by, sin(ax + by), cos(ax + by), xmyn . Applications of PDE : Method of Separation of Variables – Solution of One dimensional Wave, Heat and Two-dimensional Laplace Equation.
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CategoriesEngineering
Format PDF
TypeeBook