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Calculus I: Limits, Derivatives, Integrals, and Applications – 4-Week Study Guide

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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

Higher Order Derivatives

Intro to 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

Exponential Functions

Logarithmic Functions

Properties of Logarithms

Exponential & Logarithmic Equations

Integrals of Exponential Functions

Integrals Involving Logarithmic Functions

Inverse Trigonometric Functions

Integrals Involving Inverse Trigonometric Functions

Integrals of Trig Functions

Basics of Differential Equations