This course covers the learning outcomes and goals of understanding and solving differential equations. Students will learn skills such as separation of variables, integrating factors, exact equations, power series solutions, Laplace transforms, and solving linear models. The teaching method includes theoretical explanations, step-by-step examples, and problem-solving demonstrations. The intended audience for this course includes students and professionals interested in mastering differential equations and their applications in various fields.
Overview
Syllabus
Separation of Variables :: dy/dx + 2xy^2 = 0 :: y'+2xy^2=0.
Separation of Variables :: yln(x) dx/dy = ((y+1) /x)^2.
ODE:: y' + 2xy = x^3 :: Integrating Factor.
ODE :: y' - x/(x+1)y = x :: Integrating Factor for Linear Equations.
Exact Equations :: (1-3/y + x) dy/dx +y = 3/x-1.
Exact Differential Equation IVP:: ((y^3-t^2)/y^5)dy/dt = -t/(2y^4).
Linear Models:: Applications of Linear ODEs.
Radius of Convergence for Series Solution of a Differential Equation Including Complex Sing Pts.
ODE:: y'' - xy' + 2y=0 :: Power Series Solution about an Ordinary Point.
What are Regular Singular Points of Differential Equations?? With 3 Full Examples.
ODE :: xy'' + y' +2xy = 0 :: Method of Frobenius Series Solution about a Regular Singular Point.
Show sin(t) y'' + cos(t) y' +n(n+1) sin(t) y = 0 is a Legendre Equation.
The Definition of the Laplace Transform and Three Basic Examples.
Laplace Transform of a Piecewise Function Using the Definition.
Find the Laplace Transform of cos(kt) using the Definition.
Linearity Property of the Laplace Transform and 7 Useful Transforms to Know! Full Example..
Inverse Laplace Transform and Linearity of Inverse Laplace :: With Examples.
Shifting Laplace Transforms :: The First Translation Theorem for Laplace Transforms.
Inverse Laplace Transform :: Completing the Square :: First Translation Theorem in Reverse.
Inverse Laplace Partial Fraction Decomposition :: Overall Strategy.
Use Laplace Transform to Solve Initial Value Problem :: Full Example with Partial Fraction Decomp.
Laplace Transform With Unit Step Functions :: Second Shifting/Translation Theorem.
Proof of the Convolution Theorem :: Laplace Transforms.
Homogeneous System of Linear Differential Equations :: Real Distinct Eigenvalues.
Homogeneous System of Differential Equations :: Complex Eigenvalues.
Bernoulli DIfferential Equation || xy' -(1+x)y = xy^2.
(x^2+2y^2) dx/dy = xy || Homogeneous Substitution.
Taught by
Jonathan Walters
