Differential Equations In Depth

Description

This course has everything you need to learn and understand Differential Equations. Differential equations are a class of equation that involves the use of differentials (derivatives) in their construction. Differential equations are used in many areas of science, particularly in physics, where they are used to model real-world phenomena such as the propagation of waves.

This course covers: 

• Ordinary differential equations (ODEs) - first and second order

• Laplace Transform and Fourier Series

• Partial differential equations (PDEs) - including common equations such as the Wave Equation and the Heat Conduction Equation

• Numeric solutions of differential equations - e.g., Euler's Method, Runge-Kutta

• Modeling and solving differential equations using MATLAB and Maple.

Course pre-requisites:

• Fundamental understanging of differentiation and integration

• Knowledge of common integration operations (integration by parts, integration by substitution)

• Basic understanding of numerical computing (required for numerical methods)

• Access and basic knowledge of common CAS packages such as MATLAB, Maple, Mathematica, etc.

This course is presented as a series of hand-written lectures where we discuss the relevant topics. I also present approaches to using CAS (Computer-aided Algebra Systems) to solving differential equations either analytically or symbolically.

It is recommended that you augment your study of differential equations on this course with a good textbook on differential equations.

This course will continue to evolve and improve based on feedback from the course participants.  Please leave feedback!

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