Journey Through Calculus (Software)

1. A SURVEY OF LIMITS.

Definition of Limits.
Slopes.
Tangent Problems.
Approaching Limits, Right and Left Hand Limits.

2. LIMITS OF FUNCTIONS.

Rates of Change.
Tangent and Velocity Problems.
Calculating Limits Using the Limit Laws.

3. DERIVATIVES.

Velocity, Average and Instantaneous.
Definition of Derivatives.
Increasing and Decreasing Velocity.
Concavity Linear Approximation.
Limits at Infinity.

4. DERIVATIVE CALCULATION.

Polynomial Calculations, Derivatives of Trigonometric Functions.
The Chain Rule. Product and Quotient Rules.
Implicit Logs. Exponential Models.

5. DERIVATIVE APPLICATIONS.

Newton's Method, Maximum and Minimum.
Visualizing Newton's Method.

6. INTEGRATION.

Area, The Fundamental Theorem of Calculus Differential Equations.
Improper Integrals.
Trigonomic Integrals.

7. INTEGRATION APPLICATIONS.

Differential Equations. Moment and Centers of Mass.
Hydrostatic Pressure.
Using Tables and Computer Algebra Systems for Integration.