Welcome to Calculus 1

The following covers material commonly seen in a College level Calculus 1 course or a high school AP Calculus AB course.  I attempted to provide comprehensive introductions to each topic, as well as some example problems.  In some cases I give additional material to help provide deeper insight.  I suggest reading through the introduction material before looking at the examples.  The best way to have long term success in calculus is to understand the concepts.  Any particular example problem may still be challenging, but a sound understanding of the concepts should be the main goal for learning the material.  Enjoy, and always feel free to reach out for questions, corrections, or private tutoring!

Precalculus Review – Functions

Precalculus Review – Exponentials and Logarithms

Precalculus Review – Trigonometry

Limits – Motivation

Limits – Numerical and Graphical Evaluation

Limits – Basic Limit Laws

Limits – Continuity

Limits – Algebraic Evaluation

Limits – Trigonometric Limits

Limits – Limits at Infinity

Differentiation – Introduction to Derivatives

Differentiation – Differentiation Rules and Higher Derivatives

Differentiation – Trigonometric Derivatives

Differentiation – Chain Rule

Differentiation – Implicit Differentiation

Differentiation – Derivatives of Exponentials and Logarithms

Differentiation Applications – Related Rates

Differentiation Applications – Linear Approximation

Differentiation Applications – L’Hopital’s Rule

Differentiation Applications – Extreme Values

Differentiation Applications – Function Behavior and Graph Sketching

Differentiation Applications – Applied Optimization

Integration – The Area Problem

Integration – The Definite Integral

Integration – The Indefinite Integral

Integration – The Fundamental Theorem of Calculus

Integration – The Substitution Method

Integral Applications – Net Change as Integral of Rate of Change

Integral Applications – Area Between Curves

Integral Applications – Setting up Integrals: Volume, Density, Average Value

Integral Applications – Volumes of Revolution: Disk Method

Integral Applications – Volumes of Revolution: Shell Method

Calculus 1 Summary and Formulas

Please send all comments, corrections, and requests to steve@ferrantetutoring.com