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Norm Prokup
Limits and Continuity
Limits and Continuity explores the numerical and graphical approaches of one-sided and infinite limits. This unit also demonstrates how to evaluate limits algebraically and their end behavior. Topics include:
The Derivative
The Derivative is one of the key concepts in Calculus. This unit explores the definitions of the derivative plus the derivatives of various types of functions. Topics include:
- Average Velocity
- Average Rate of Change
- Instantaneous Velocity
- Instantaneous Rate of Change
- The Definition of the Derivative
- The Derivative Function
- Derivative Notation
- Derivatives of Linear Functions
- Derivatives of Power Functions
- Derivatives of Polynomial Functions
- An Important Limit
- Derivatives of Exponential Functions
- Derivatives of Logarithmic Functions
Techniques of Differentiation
Techniques of Differentiation explores various rules including the product, quotient, chain, power, exponential and logarithmic rules. Topics include:
Applications of the Derivative
Applications of the Derivative identifies was that this concept is used in everyday life such as determining concavity, curve sketching and optimization. Topics include:
- Intervals of Increase and Decrease
- Critical Points
- Relative Maxima and Minima
- The First Derivative Test for Relative Maximum and Minimum
- Concavity and Inflection Points
- The Second Derivative Test for Relative Maximum and Minimum
- Curve Sketching with Derivatives
- Optimization Using the Closed Interval Method
- Optimization Using the First Derivative Test
- Optimization Using the Second Derivative Test
- Economics: Cost & Revenue
- Economics: Marginal Cost & Revenue
- Optimization Problems: Applications to Economics
Antiderivatives and Differential Equations
Antiderivatives and Differential Equations explores antidifferentiation, exponential growth and decay, logistic growth and indefinite integrals. Topics include:
- Definition of Antiderivatives
- Antidifferentiation
- Definition of Indefinite Integrals
- Indefinite Integrals
- Complicated Indefinite Integrals
- The Method of Substitution
- Simple Substitutions
- Substitutions Involving e^x or ln(x)
- Tricky Substitutions Involving Radicals
- Differential Equations
- Position, Velocity and Acceleration
- The Differential Equation Model for Exponential Growth
The Definite Integral
The Definite Integral unit identifies how to use the definite integral to approximate area, the average value of a function and how to compute it using substitution. Topics include:
