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Calculus I Syllabus and Course Structure Overview

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Introduction to Functions

Piecewise Functions

Properties of Functions

Common Functions

Transformations

Combining Functions

Exponential Functions

Logarithmic Functions

Properties of Logarithms

Exponential & Logarithmic Equations

Introduction to Limits

Finding Limits Algebraically

Continuity

Tangent Lines and Derivatives

Derivatives as Functions

Basic Rules of Differentiation

Product and Quotient Rules

The Chain Rule

Derivatives of Exponential & Logarithmic Functions

Logarithmic Differentiation

Intro to Extrema

Finding Global Extrema

The First Derivative Test

Concavity

The Second Derivative Test

Curve Sketching

Applied Optimization

Antiderivatives

Indefinite Integrals

Estimating Area with Finite Sums

Riemann Sums

Introduction to Definite Integrals

Fundamental Theorem of Calculus

Average Value of a Function

Substitution

Area Between Curves