Contents of Calculus I

An Introduction to Limits

Properties of Limits: Techniques of Limit Computation

Continuity of Functions

Slope of a Curve, Velocity, and Rates of Change

Introduction to the Derivative of a Function

Techniques of Differentiation

The Product and Quotient Rules

Derivatives of Trigonometric Functions

The Chain Rule

Implicit Differentiation

Related Rates

Applications of the Derivative

Increasing/Decreasing and Concavity of Functions

Rolle's Theorem and Mean Value Theorem (Brief)

First Derivative Test

Second Derivative Test

Limits of Functions at Infinity

How to Sketch Graphs of Functions

Optimization: Max/Min Application Problems

An Introduction to the Indefinite Integral

Integration by Substitution

Area Under a Curve (Limits & Riemann Sums)

The Evaluation of Definite Integrals

The Fundamental Theorem of Calculus

Finding Area Between Two Curves

Volume by Disks and Washers

Volume by Cylindrical Shells

Arc Length of a Plane Curve

Calculus I

Limits, derivatives, and the beginnings of integration—this page is your structured path through the core ideas of single-variable calculus. Use the table of contents on the left to jump to any topic.

What you'll learn

Understand limits and continuity and how they underpin derivatives.
Compute derivatives efficiently (product/quotient/chain rules, trig, implicit) and apply them to real problems.
Analyze functions via monotonicity, concavity, and theorems (MVT), and sketch accurate graphs.
Start integration: antiderivatives, substitution, Riemann sums, definite integrals, and the Fundamental Theorem of Calculus.
Apply integrals to areas, volumes (disks/washers/shells), and arc length.