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Calculus,
Introduction
Instructional Objective
Students
will be able to do the following upon the completion
of each of the units.
Unit 1 - Prerequisites
for Calculus
1.
Coordinates and Graphs in the Plane
2.
Slope, and Equations for Lines
3.
Relations, Functions, and Their Graphs
4.
Geometric Transformations: Shifts, Reflections, Stretches,
and Shrinks
5.
Solving Equations and Inequalities Graphically
6.
Relations, Functions and Their Inverses
7.
A Review of Trigonometric Functions
Unit 2 - Limits
and Continuity
1.
Limits
2.
Continuous Functions
3.
The Sandwich Theorem and (sin 0)/0
4.
Limits Involving Infinity
5.
Controlling Function Outputs: Target Values
6.
Defining Limits Formally with Epsilons and Deltas
Unit 3 - Derivatives
1.
Slopes, Tangent Lines, and Derivatives
2.
Numerical Derivatives
3.
Differentiation Rules
4.
Velocity, Speed, and Other Rates of Change
5.
Derivatives of Trigonometric Functions
6.
The Chain Rule
7.
Implicit Differentiation and Fractional Powers
8.
Linear Approximations and Differentials
Unit 4 - Applications
for Derivatives
1.
Maxima, Minima, and the Mean Value Theorem
2.
Predicting Hidden Behavior
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