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## SubsectionB.1Calculus I

### SubsubsectionPreCalculus Review

• Functions

• Exponential and Logarithmic Functions

• Trigonometric Functions

### SubsubsectionChapter 1 Understanding the Derivative

• Introduction to Continuity

• Introduction to Limits

• How do we Measure Velocity?

• The Derivative of a Function at a Point

• The Derivative Function

• Interpreting, Estimating, and Using the Derivative

• The Second Derivative

• Differentiability

### SubsubsectionChapter 2 Computing Derivatives

• Elementary Derivative Rules

• The Sine and Cosine Functions

• The Product and Quotient Rules

• Derivatives of Other Trigonometric Functions

• The Chain Rule

• Derivatives of Inverse Functions

• Derivatives of Functions Given Implicitly

• Hyperbolic Functions

• 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

• 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

### SubsubsectionChapter 5 Evaluating Integrals

• Constructing Accurate Graphs of Antiderivatives

• Antiderivatives from Formulas

• Differential Equations

• The Second Fundamental Theorem of Calculus

• Integration by Substitution