Course Content

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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