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Calculus I Syllabus: Key Topics and Study Guide

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Properties of Functions

Exponential Functions

Logarithmic Functions

Introduction to Trigonometric Functions

Inverse Trigonometric Functions

Introduction to Limits

Finding Limits Algebraically

Continuity

Tangent Lines and Derivatives

Basic Rules of Differentiation

Product and Quotient Rules

Derivatives of Trig Functions

The Chain Rule

Implicit Differentiation

Derivatives of Exponential & Logarithmic Functions

Derivatives of Inverse Trigonometric Functions

Related Rates

Intro to Extrema

The First Derivative Test

Concavity

The Second Derivative Test

Curve Sketching

Applied Optimization

Linearization

Differentials

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

Kinematics