The Great Calculus courses include the study and application of differentiation and integration; and graphical analysis, including limits, asymptotes, and continuity.

### Integrals

Antiderivative of a function

Interpretations

The area as a sum

Properties

Definite integrals and geometry

Indefinite integral

Rules of Integration

Physical Applications

The fundamental rule of Calculus

Average value

Net change theorem

Numerical approximations

Riemann Sums

Volume by Slicing

Discontinuity

### Limits

Analysis of graphs (predicting and explaining behaviour)

Limits of functions (one and two-sided)

Limits for piecewise functions

Continuity and types of discontinuity

One-sided limits

Infinite limits

Limits at infinity

Asymptotic and unbounded behaviour

Continuity over an interval

### Derivatives

Definition

Rules of Differentiation

At a point

As a function

Derivatives as a rate of change

Application to motion

Higher Order derivatives

Difference Quotient

Chain Rule and implicit differentiation

Physical Applications

Optimization

Maximum and minimum points, increasing and decreasing functions

Inflection points and concavity

Using derivatives to analyze graphs.

Related Rates

Mean Value Theorem

Tangent Lines

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