Mathematics-II | 3110015 | Computer Engineering | Study Materials | GTU Medium

Mathematics-II | Computer Engineering | SEM 1 & 2

Mathematics-II (3110015) Syllabus :

Syllabus

1 Vector Calculus

Parametrization of curves. Arc length of curve in space. Line Integrals, Vector fields and applications as Work, Circulation and Flux. Path independence. potential function, piecewise smooth. connected domain, simply connected domain, fundamental theorem of line integrals. Conservative fields, component test for conservative fields, exact differential forms, Div, Curl, Green's theorem in the plane (without proof). Parametrization of surfaces. surface integrals. Stoke's theorem (without proof), Divergence Theorem (without proof).

2 Laplace Transform

Laplace Transform and inverse Laplace transform, Linearity. First Shifting Theorem (s-Shifiing). Transforms of Derivatives and Integrals. ODEs. Unit Step Function (Heaviside Function). Second Shifting Theorem (t-Shifting). Laplace transform of periodic functions. Short Impulses, Dime's Delta Function, Convolution. Integral Equations, Differentiation and Integration of Transforms. ODEs with Variable Coefficients, Systems of ODEs.

3 Fourier Integral

Fourier Integral, Fourier Cosine Integral and Fourier Sine Integral.

 

4 First order ordinary differential equations

First order ordinary differential equations. Exact, linear and Bernoulli's equations, Equations not of first degree: equations solvable for p, equations solvable for y. equations solvable for x and Clairaut's type.

5 Ordinary differential equations

Ordinary differential equations of higher orders, Homogeneous Linear ODEs of Higher Order. Homogeneous Linear ODEs with Constant Coefficients. Euler-Cauchy Equations, Existence and Uniqueness of Solutions. Linear Dependence and Independence of Solutions. Wronskian, Nonhomogeneous ODEs, Method of Undetermined Coefficients. Solution by Variation of Parameters.

6 Series Solutions of ODEs

Series Solutions of ODEs. Special Functions. Power Series Method, Legendre's Equation, Legendre Polynomials. Frobenius Method, Bessel's Equation. Bessel functions of the first kind and their properties.

Syllabus	Download
Mathematics-II	Click Here

Mathematics-II - IMP Question :

Material	Download
Laplace Transform (IMP Questions)	Click Here
First Order Differential Equation (IMP Questions)	Click Here
Higher Order Differential Equation (IMP Questions)	Click Here
Mathematics-II - IMP Question By L.J College	Click Here
All Subject (IMP SEM 2)	Click Here
Mathematics-II (IMP Question & Answers)	Click Here

Chapter-Wise PPTs/Notes :

Units	Download
Mathematics-II (Darshan Notes)	Click Here
Mathematics-II (Handwritten Notes)	Click Here
Engineering-Mathematics-II	Click Here

Mathematics-II Old Papers :

Year(Winter/Summer)	Question Paper
Winter 2019	Click Here
Winter 2018	Click Here
Summer 2020	Click Here
Summer 2019	Click Here
Summer 2018	Click Here

Mathematics-II Books :

Books	Download
Mathematics-II By A.Ganesh And G.Balasubrmanian	Click Here
Engineering Mathematics	Click Here
Mathematics-II By Darshan Institute	Click Here
Engineering Mathematics-II	Click Here

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