Calculus and Differential Equations - Key Terms (EMATH 210)

Vocabulary flashcards covering Calculus, differential equations, and their real-world applications as presented in the notes.

Calculus

Branch of mathematics studying change and accumulation; etymology from Latin calx (stone) and Greek chalís (limestone); developed by Leibniz and Newton; includes differential calculus, integral calculus, calculus of variations, and differential equations.

Calx

Latin for stone; root meaning in the word calculus.

Chalis/Chalís

Greek term meaning limestone; part of calculus etymology.

Leibniz

Gottfried Wilhelm von Leibniz, cofounder of calculus.

Newton

Isaac Newton, cofounder of calculus.

Differential Calculus

Branch of calculus dealing with derivatives and rates of change.

Integral Calculus

Branch of calculus dealing with accumulation and integrals.

Calculus of Variations

Branch focusing on optimizing functionals; variations of functionals.

Differential Equation

An equation relating a function to its derivatives, showing how a quantity changes over time or space.

Ordinary Differential Equation (ODE)

A differential equation with one independent variable; involves derivatives of a function with respect to that variable.

Partial Differential Equation (PDE)

A differential equation involving two or more independent variables and partial derivatives.

General Solution

A solution that contains at least one arbitrary constant.

Particular Solution

A solution that contains no arbitrary constants.

Order (of a differential equation)

The highest order of derivative present in the differential equation.

Degree (of a differential equation)

The largest power (exponent) of the highest-order derivative present.

Heat transfer

Engineering application of differential equations to model heat transfer in machines.

Vibration

Modeling the vibration of structures and vehicles using differential equations.

Epidemiology

Study of the spread of disease in medicine and biology.

Population growth models

Models describing how populations grow over time.

Motion

Movement of objects; described by differential equations.

Electric circuits

Behavior of electrical circuits described by differential equations.

Interest rate growth

Modeling the growth of interest rates in banks.

Supply and Demand modeling

Economic models of market supply and demand.

Pollution spreading

Spread of pollutants in water or air.

Climate change models

Models that simulate climate change dynamics.