Partial Differential Equations in Engineering
( 25 Modules )

Module #1
Introduction to PDEs in Engineering
Overview of PDEs, importance in engineering, and types of PDEs

Module #2
Classification of PDEs
Classification of PDEs into parabolic, hyperbolic, and elliptic types

Module #3
Physical Laws and PDEs
Derivation of PDEs from physical laws (conservation of mass, momentum, energy)

Module #4
Mathematical Preliminaries
Review of vector calculus, differential equations, and linear algebra

Module #5
First-Order PDEs
Introduction to first-order PDEs, characteristics, and integration

Module #6
Quasi-Linear First-Order PDEs
Quasi-linear first-order PDEs, method of characteristics, and examples

Module #7
Linear First-Order PDEs
Linear first-order PDEs, integrating factor method, and applications

Module #8
Higher-Order PDEs
Introduction to higher-order PDEs, classification, and reduction to first-order systems

Module #9
Heat Equation
Derivation, solution, and applications of the heat equation

Module #10
Wave Equation
Derivation, solution, and applications of the wave equation

Module #11
Laplaces Equation
Derivation, solution, and applications of Laplaces equation

Module #12
Poissons Equation
Derivation, solution, and applications of Poissons equation

Module #13
Separation of Variables
Method of separation of variables for PDEs, applications, and examples

Module #14
Fourier Transform Method
Application of Fourier transform to solve PDEs

Module #15
Laplace Transform Method
Application of Laplace transform to solve PDEs

Module #16
Numerical Methods for PDEs
Introduction to numerical methods for PDEs, finite difference method

Module #17
Finite Element Method
Introduction to finite element method, applications, and examples

Module #18
Boundary Value Problems
Boundary value problems, types, and solution methods

Module #19
Initial Boundary Value Problems
Initial boundary value problems, types, and solution methods

Module #20
Dimensionless Form of PDEs
Scaling and dimensionless form of PDEs, benefits and examples

Module #21
PDEs in Fluid Mechanics
PDEs in fluid mechanics, Navier-Stokes equations, and applications

Module #22
PDEs in Heat Transfer
PDEs in heat transfer, heat equation, and applications

Module #23
PDEs in Mass Transport
PDEs in mass transport, diffusion equation, and applications

Module #24
PDEs in Electromagnetics
PDEs in electromagnetics, Maxwells equations, and applications

Module #25
Course Wrap-Up & Conclusion
Planning next steps in Partial Differential Equations in Engineering career

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