Calculus

Calculus is concerned with change and motion; it deals with the quantities that approach other quantities.

Sir Isaac Newton invented his version of calculus in order to explain the motion of planets around the sun. Today, calculus is used in calculating the orbits of satellites and spacecrafts, in predicting population sizes, in estimating how fast prices rise, in forecasting weather, in calculating life insurance premiums, and in many other areas.

Differential Calculus

The study of differential calculus is concerned with how one quantity changes in relation to another quantity. The central concept of differential calculus is the derivative.

The Limits of a Function (with videos) – Definition and Techniques to find Limits

Derivatives (with videos) – Definition and Slope of Tangent

Power Rule (with videos) – Constant Multiple Rule, Sum Rule, Difference Rule

Product Rule (with videos) – Find the derivative of the product of two functions

Quotient Rule (with videos) - Find the derivative of the quotient of two functions

Chain Rule (with videos) - Find the derivative of composite functions

Derivative Rules (with videos) - Product Rule, Quotient Rule, Chain Rule, Power Rule, Exponential and Logarithmic Functions, Trigonometric Functions, Inverse Trigonometric Functions, Hyperbolic Functions and Inverse Hyperbolic Functions

Trigonometrc Derivatives (with videos) - Derivatives of sin, cos, tan, scs, sec, cot

Inverse Trigonometric Derivatives (with videos) - Derivatives of the inverse of sin, cos, tan, scs, sec, cot

Derivatives of Exponential Functions (with videos) - Derivatives of e^x, a^x, a^g(x)

Derivative of the Natural Log (with videos) - Derivatives of ln(x), ln[g(x)]

Implicit Differentiation (with videos) - Find the derivatives of non-functions

Second Derivative and Higher Derivatives (with videos) - Find the derivatives of derivatives and their applications

Maxima and Minima (with videos) - Maximum amd Minimum Values, Fermat's Theorem, Critical Number, Extreme Value Theorem, Closed Interval Method

Derivative Test (with videos) - First Derivative Test, Second Derivative Test, Minima, Maxima, Increasing/Decreasing Test

Mean Value Theorem (with videos) - What is Mean Value Theorem?

Asymptotes (with videos) - Vertical Asymptote, Horizontal Asymptote, Oblique Asymptote

Hyperbolic Functions (with videos) - Hyperbolic Identities, Derivatives of Hyperbolic Functions and Derivatives of Inverse Hyperbolic Functions

Integral Calculus

Antiderivative (with videos) - Formulas for powers of x, trigonometric functions, exponential functions

Definite Integral (with videos) - Area, Riemann Sum, Properties of Definte Integral

The Fundamental Theorem of Calculus (with videos) - What is the Fundamental Theorem of Calculus?

Indefinite Integrals (with videos) - Integral Notation, Integral Formulas

Integration by Parts (with videos) - Formula and Examples

Trigonometric Integrals (with videos) - Integration of the Powers of Sine, Cosine, Tangent and Secant

Integral Test (with videos) - To determine whether a series is convergent or divergent

Area under a Curve (with videos) - Calculate area under a curve and between two curves.

Videos

Calculus I in 20 minutes - Professor Edward Burger gives an in-depth review of Calculus I.

Calculus in 20 minutes - Professor Edward Burger gives an in-depth review of differential and integral Calculus.

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