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Calculus I: Functions, Limits, Continuity, and Differentiation – Structured Study Notes

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Introduction to Limits

Finding Limits Algebraically

Continuity

Tangent Lines and Derivatives

Derivatives as Functions

Basic Rules of Differentiation

Product and Quotient Rules

Derivatives of Trig Functions

The Chain Rule

Implicit Differentiation

Linearization

Antiderivatives

Indefinite Integrals

Fundamental Theorem of Calculus

Substitution

Integration by Parts

Exponential Functions

Derivatives of Exponential & Logarithmic Functions

Logarithmic Differentiation

Logarithmic Functions

Properties of Logarithms

Exponential & Logarithmic Equations

Derivatives of Inverse Trigonometric Functions

Introduction to Trigonometric Functions

Inverse Trigonometric Functions

Related Rates

Intro to Extrema

Finding Global Extrema

The First Derivative Test

Concavity

The Second Derivative Test

Curve Sketching

Applied Optimization

Indefinite Integrals