Mathematics - iii (Differential Calculus) - Vol 2 | 4. First-Order PDEs by Abraham | Learn Smarter
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4. First-Order PDEs

First-order partial differential equations (PDEs) are essential in the mathematical modeling of various physical phenomena, capturing first derivatives with respect to multiple independent variables. The chapter explores the formation, solutions, and classifications of first-order PDEs, detailing methods such as Lagrange's and Charpit's approaches for linear and non-linear equations. A clear understanding of types of solutions—complete, particular, singular, and general—enables better categorization and application in complex problem-solving scenarios.

Sections

  • 4

    Partial Differential Equations

    This section introduces first-order Partial Differential Equations (PDEs), their formation, and methods for solving them.

    Learning Practice

  • 4.1

    Formation Of First-Order Pdes

    This section outlines how first-order partial differential equations (PDEs) are formed from functions by eliminating arbitrary constants and functions.

    Learning Practice

  • 4.1.1

    From A Function

    This section explains how first-order Partial Differential Equations (PDEs) can be formed by eliminating arbitrary constants or functions from given functions.

    Learning Practice

  • 4.2

    General Form Of First-Order Pde

    First-order partial differential equations (PDEs) can be represented in a general form involving two independent variables and a dependent variable.

    Learning Practice

  • 4.3

    Linear First-Order Pdes: Lagrange’s Method

    This section focuses on solving linear first-order partial differential equations (PDEs) using Lagrange’s method, including the auxiliary equations and the formation of general solutions.

    Learning Practice

  • 4.3.1

    Standard Form

    This section introduces first-order linear partial differential equations (PDEs) in standard form and discusses Lagrange’s method for solving them.

    Learning Practice

  • 4.3.2

    Lagrange’s Auxiliary Equations

    Lagrange’s Auxiliary Equations are a method for solving first-order linear PDEs, focusing on the relationships between derivatives of functions.

    Learning Practice

  • 4.4

    Non-Linear First-Order Pdes

    Non-linear first-order partial differential equations (PDEs) are equations that do not exhibit a linear relationship in the first derivatives of the dependent variable.

    Learning Practice

  • 4.4.1

    Charpit’s Method (For Non-Linear Equations)

    Charpit's Method is an advanced technique used to solve non-linear first-order partial differential equations (PDEs).

    Learning Practice

  • 4.5

    Types Of Solutions

    This section covers the different classifications of solutions to first-order partial differential equations (PDEs).

    Learning Practice

References

Unit_2_ch4.pdf

Class Notes

Memorization

What we have learnt

  • First-order PDEs involve on...
  • They can be formed by elimi...
  • Lagrange’s method is effect...

Final Test

Revision Tests