Derivatives & Differential Equations

 - The derivative

 - The Partial Derivative

 - Time Derivatives

 - Derivatives of Polynomials

 - Properties of the Derivative

 - Derivatives of Common Functions

 Some general terms used in the discussion of differential equations:

Order: The order of a differential equation is the highest power of derivative which occurs in the equation, e.g., Newton's second law produces a 2nd order differential equation because the acceleration is the second derivative of the position.

Linear and nonlinear: A differential equation is said to be linear if each term in the equation has only one order of derivative, e.g., no term has both y and the derivative of y with respect to time. Also, no derivative is raised to a power.

Homogeneous and nonhomogeneous: A differential equation is said to be homogeneous if there is no isolated constant term in the equation, e.g., each term in a differential equation for y has y or some derivative of y in each term.

 - Differential Equations

 - First Order Homogeneous DE

 - General Solution to a D.E.

 - Boundary Conditions

 - Uniqueness Theorem

 - Differential Equation Terminology