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 – Numerical and Graphical Evaluation
Differentiation – Introduction to Derivatives
Differentiation – Differentiation Rules and Higher Derivatives
Differentiation – Trigonometric Derivatives
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
Please send all comments, corrections, and requests to steve@ferrantetutoring.com