CC Calculus I

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SubsectionB.1Calculus I

SubsubsectionPreCalculus Review

SubsubsectionChapter 1 Understanding the Derivative

Introduction to Continuity
Introduction to Limits
How do we Measure Velocity?
- Introduction
- Limits and Velocity
The Derivative of a Function at a Point
- Defining Derivatives at Points
- Approximating and Computing Derivatives at a Point
The Derivative Function
Interpreting, Estimating, and Using the Derivative
- Using the Derivative
The Second Derivative
Differentiability
- Definition and Graphical Examples
- Continuity and Differentiability

SubsubsectionChapter 2 Computing Derivatives

Elementary Derivative Rules
The Sine and Cosine Functions
- Derivative Rules
The Product and Quotient Rules
Derivatives of Other Trigonometric Functions
- Deriving Derivative of Tangent
- Deriving Derivative of Secant
The Chain Rule
Derivatives of Inverse Functions
Derivatives of Functions Given Implicitly
- Implicit Differentiation
- Implicit Differentiation Examples
Hyperbolic Functions
- Introduction to Hyperbolic Functions
- Extension to Hyperbolic Tangent
The Tangent Line Approximation
The Mean Value Theorem

SubsubsectionChapter 3 Using Derivatives

Using Derivatives to Identify Extreme Values
Global Optimization
Applied Optimization
Using Derivatives to Describe Families of Functions
- Families of Functions
Related Rates
Using Derivatives to Evaluate Limits
Parametric Equations

SubsubsectionChapter 4 The Definite Integral

Determining Distance Traveled from Velocity
Riemann Sums
The Definite Integral
The Fundamental Theorem of Calculus
- FTC
- FTC Examples

SubsubsectionChapter 5 Evaluating Integrals

Constructing Accurate Graphs of Antiderivatives
Antiderivatives from Formulas
Differential Equations
The Second Fundamental Theorem of Calculus
Integration by Substitution