Construct and solve real-life examples using ordinary differential equations

What you'll learn:
Identify a differential equation's type, order, and linearity
Verify solutions to differential equations
Use initial conditions to solve initial-value problems
Construct and solve first-order ODEs as mathematical models
Solve a first-order ODE (eight methods of solutions)
Find the general solution of a homogeneous linear DE with constant coefficients
Find the general solution of a homogeneous Cauchy-Euler DE
Find the particular solution of a nonhomogeneous linear DEs using undetermined coefficients, variation of parameters, and Green's function
Evaluate some important integrals using the Gamma function
Evaluate the Laplace transforms of some basic functions, derivatives, integral, periodic functions, and Dirac delta functions
Evaluate the derivative and integral of Laplace transforms
Apply the first and second translation theorems (Laplace transforms)
Apply the convolution theorem
Solve an ODE using the Laplace transforms' method
Find the general solution of a homogeneous linear system with constant coefficients
Find a particular solution of a nonhomogeneous linear system using undetermined coefficients and variation of parameters

Requirements:
Calculus 3 (Multivariable Calculus)
Linear Algebra

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