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MatheMagician @UCEjpRpZSjy6mkwKqzeTeVrQ@youtube.com

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My name is Bernard Meulenbroek; I am a assistant professor a

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The inverse laplace transform and initial value problems - example two

The phase space - complex eigenvalues

Taylor polynomials for functions of two variables

Solution strategy for x'=Ax, A diagonalizable

The Wronskian for systems of differential equations

Superposition of solutions

Linear and homogeneous systems of differential equations

Conversion into a system of differential equations

Step functions and shifting functions

Partial fractions - example

Partial fractions - introduction

The Laplace transform and initial value problems - example one

The factorial - introduction

Improper integrals of type one

Fourier series of even and odd functions

Integration of even and odd functions

Even and odd functions

The Wronskian - examples

The Wronskian - introduction

Solving PDEs using separation of variables

How can we find a trial solution?

Integration by parts - examples

Integration by parts - introduction

The substitution rule - examples

The substitution rule - introduction

Solving quadratic equations - completing the square

The derivative - chain rule

The derivative - product rule

The derivative - notation and rules

Homogeneous DEs with constant coefficients - a double root

Solving DEs by direct integration

What is a differential equation?

The wave equation - example two

The wave equation - example one

Solving the wave equation - procedure

The motion of a string and the wave equation

The motion of a string - derivation of the governing equation

The motion of a string - introduction

Solving the heat equation using separation of variables - example two

Solving the heat equation using separation of variables - example one

The heat equation - inital conditions and boundary conditions

The heat equation - introduction and derivation

Even and odd extensions - example

Even and odd extensions of a function

Does the Fourier series of a function f(x) converge to the original function - example

Does the Fourier series of a function f(x) converge to the original function?

Determining the Fourier coefficients of a Fourier series - example

How to determine the Fourier coefficients of a Fourier series

Orthogonality of eigenfunctions

Introduction to Fourier series

Properties of eigenvalues and eigenfunctions

Boundary value problems and eigenvalue problems

Boundary value problems - introduction

The components of a tensor - example

Analyzing a nonlinear predator-prey model

How can we determine whether a nonlinear system is locally linear?

Relation between a nonlinear system and its local linearizations

Characterizing the equilibrium points of a nonlinear system - example

How can we analyze the equilibrium points of nonlinear systems?