!Integral Calculus, Ordinary and Partial Differential Equations, and Series Solutions

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Syllabus

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Integral Calculus: Definitions of integration: Integration by the method of substitutions: Integration by parts: Standard integrals: Integration by the method of successive reduction, Definite integrals and its properties and use in summing series: Walli formula, Improper integrals, Beta function, and Gamma function; Area under a plane curve in cartesian and polar co-ordinates: Area of the region enclosed by two curves in cartesian and polar co-ordinates; Trapezoidal rule, Simpson rule. Are lengths of curves in cartesian and polar coordinates. parametric and pedal equations, Intrinsic equation: Volume of solids of revolution; Volume of hollow solids of revolution by shell method. Area of the surface of revolution: Jacobian, multiple integrals and their application. Ordinary Differential Equation (ODE): Degree and order of ordinary differential equations; Formation of differential equations: Solution of first-order differential equations by various methods: Solution of first-order but higher degree ordinary differential equations: Solution of general linear equations of second and higher orders with constant coefficients: Solution of homogeneous linear equations and its applications: Solution of differential equations of higher order when dependent and independent variables are absent: Solution of differential equation by the method based on factorization of operators. Partial Differential Equations (PDE): Four rules for solving simultaneous equations of the form: Lagrangeâ€TMs method of solving PDE of order one: Integral surfaces passing through a given curve: Nonlinear PDE of order one (complete, particular, singular, and general integrals): standard forms f(p,q) - 0,2 px + 4y + f(p.9), f(p.q.z) = 0, fAl(x,p) = 12cy, q); Charpit method: Second order PDE: its nomenclature and classifications to canonical (standard)- parabolic, elliptic, hyperbolic: Solution by separation of variables. Linear PDE with constant coefficients. Series Solution: Solution of differential equations in series by the method of Frobenius; Bessel functions, Legendre polynomials, and their properties.

Books

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> Differential Equations

Shepley L. Ross;

View PDF [3rd Edition]

Lecture Slides

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(According to Barishal University)

7th Batch

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