This Course Made for specially GTU (Gujarat Technological University) students, based on that we have covered the full course of GTU Maths-3.

The topics cover are as below,

1.First Order (ODE)

2.Higher-Order (O.D.E)

3.Laplace

4.Power Series

5.Fourier Series

6.Partial Differential Equation (PDE)

Ordinary Differential Equations and Applications: First order differential equations: basic concepts, Geometric meaning of y’ = f(x,y) Direction fields, Exact differential equations, Integrating factor, Linear differential equations, Bernoulli equations, Modeling, Orthogonal trajectories of curves.Linear differential equations of second and higher-order: Homogeneous linear differential equations of second order, Modeling: Free Oscillations, Euler- Cauchy Equations, Wronskian, Non-homogeneous equations, Solution by undetermined coefficients, Solution by variation of parameters, Modeling: free Oscillations resonance and Electric circuits, Higher order linear differential equations, Higher-order homogeneous with constant coefficient, Higher-order non-homogeneous equations. Solution by [1/f(D)] r(x) method for finding particular integral.

Fourier Series and Fourier integral: Periodic function, Trigonometric series, Fourier series, Functions of any period, Even and odd functions, Half-range Expansion, Forced oscillations, Fourier integral

Series Solution of Differential Equations: Power series method, Theory of power series methods, Frobenius method.

Laplace Transforms and Applications: Definition of the Laplace transform, Inverse Laplace transform, Linearity, Shifting theorem, Transforms of derivatives and integrals Differential equations, Unit step function Second shifting theorem, 09 15 Dirac’s delta function, Differentiation, and integration of transforms, Convolution and integral equations, Partial fraction differential equations, Systems of differential equations

Partial Differential Equations and Applications: Formation PDEs, Solution of Partial Differential equations f(x,y,z,p,q) = 0, Nonlinear PDEs first order, Some standard forms of nonlinear PDE, Linear PDEs with constant coefficients, Equations reducible to Homogeneous linear form, Classification of second-order linear PDEs.Separation of variables use of Fourier series, D’Alembert’s solution of the wave equation, Heat equation: Solution by Fourier series and Fourier integral

we have also added Basic Of Differentiation and basic Integration for a better understanding of Basics Mathematics.