Functions Graphs and Limits
- Analysis of Graphs
- Use of Technology
- Limits of a Function
- The Limiting Process
- Use Algebra to Calculate Limits
- Estimate Limits from Graphs or Data Tables
|
Derivatives
- Concept of Derivative
- Graphic, Numerical and Analytical Presentation
- Instantaneous Rates of Change
- Limit of the Difference Quotient
- Relation Between Differentiability and Continuity
- Derivative as a Point
- Slope of a Curve at a Point
- Tangent Lines and Local Linear Approximation
- Instantaneous Rate of Change
- Approximate Rate of Change
- Derivative as a Function
- Corresponding Characteristics of graph of f and f'
- Increasing and Decreasing Behavior Relationship
- Mean Value Theorem and Geometric Consequences
- Equations Involving Derivatives
- Second Derivatives
- Corresponding Characteristics Between f, f' and f"
- Relationship Between the Concavity of f and the Sign of f"
- Points of Inflection Where Concavity Changes
- Applications of Derivatives
- Analysis of Curves: Monotonicity and Concavity
- Optimization: Global and Local
- Model Rates of Change
- Implicit Differentiation
- Interpretation of the Derivative as a Rate of Change
- Computation of Derivatives
- Derivatives of Basic Functions
- Basic Rules for the Derivative of Operations
- Chain Rule and Implicit Differentiation
- Slope Fields: Geometric Interpretations
|
Integrals
- Interpretations and Properties of Definite Integrals
- Computation of Riemann Sums
- Definite Integrals
- Basic Properties of Definite Integrals
- Applications of Integrals
- Fundamental Theorem of Calculus
- Use to Evaluate Definite Integrals
- Use to Represent Antiderivatives and Analyses of Functions
- Techniques of Antidifferentation
- Antiderivatives from Derivatives of Basic Functions
- Antiderivatives by Substitution of Variables
- Applications of Antidifferentation
- Find Specific Antidifferivatives USing Initial Conditions
- Solve Separable Differential Equations and Use in Modeling
- Numerical Approximations to Definite Integrals
- Use of Riemann and Trapezoidal Sum
|