Beginner Guide to Differential Equation

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About Course

A differential equation is an equation involving an unknown function y = f(x) y = f (x) and one or more of its derivatives. A solution to a differential equation is a function y = f(x) y = f (x) that satisfies the differential equation when f f and its derivatives are substituted into the equation.

In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives.[1] In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such relations are common in mathematical models and scientific laws; therefore, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology.

The study of differential equations consists mainly of the study of their solutions (the set of functions that satisfy each equation), and of the properties of their solutions. Only the simplest differential equations are solvable by explicit formulas; however, many properties of solutions of a given differential equation may be determined without computing them exactly.

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What Will You Learn?

  • First order equations, including linear, separable, and Bernoulli equations.
  • Modeling with differential equations, including Euler's method, the logistic equation, exponential growth and decay, electrical series, spring and mass systems.
  • Laplace transforms, including Laplace and inverse Laplace transforms, the Second Shifting Theorem, Dirac delta functions, and convolution integrals.
  • Higher order equations, including nonhomogeneous equations, their Laplace transforms, systems of higher order equations, and their series solutions.
  • Partial differential equations, including separation of variables and boundary value problems, the heat equation, and Laplace's equation.
  • Second order equations, including homogeneous and nonhomogeneous equations, undetermined coefficients, and variation of parameters.
  • Series solutions, including power series solutions, nonpolynomial coefficients, and Frobenius' Theorem.
  • Systems of differential equations, including solving systems with real and complex Eigenvalues, trajectories and phase portraits, and the matrix exponential.
  • Fourier series, including periodic extensions, convergence of a Fourier series, Fourier cosine series and Fourier sine series, and piecewise functions

Course Content

Getting Started

  • Differential Equations made simple and easy
    13:43

First & Second Order Equation

Modelling with Differential Equations

Linear differential equation

Non-Linear differential Equation

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