# Welcome to Calculus 3

The following covers material commonly seen in a College level Calculus 3 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!

Vector Geometry – Vectors Introduction

Vector Geometry – Dot Product and Projections

Vector Geometry – Cross Product

Vector Geometry – Lines and Planes in 3 Space

Vector Geometry – Quadric Surfaces

Vector Geometry – Cylindrical and Spherical Coordinates

Vector Calculus – Vector Valued Functions

Vector Calculus – Differentiate and integrate Vector Valued Function

Vector Calculus – Arc Length and Speed

Vector Calculus – Frenet Frames

Vector Calculus – Motion in 3 Space

Multivariable Differentiation- Function of Several Variables

Multivariable Differentiation- Partial Derivatives

Multivariable Differentiation- Tangent Planes and Linear Approximation

Multivariable Differentiation- Chain Rule

Multivariable Differentiation- Directional Derivative and the Gradient

Multivariable Differentiation- Optimization

Multivariable Differentiation- Lagrange Multipliers

Multivariable Integration – Double Integral over Rectangular Regions

Multivariable Integration – Double Integral over Arbitrary Regions

Multivariable Integration – Triple Integrals

Multivariable Integration – Polar, Cylindrical, and Spherical Coordinates

Multivariable Integration – Applications

Multivariable Integration – Change Of Variables

Line and Surface Integrals – Vector Fields

Line and Surface Integrals – Line Integrals

Line and Surface Integrals – Conservative Vector Fields

Line and Surface Integrals – Surface Integrals of Scalar Functions

Line and Surface Integrals – Surface Integrals of Vector Fields

Fundamental Theorems of Vector Analysis – Green’s Theorem

Fundamental Theorems of Vector Analysis – Stokes’ Theorem

Fundamental Theorems of Vector Analysis – Divergence Theorem

Calculus 3 Summary and Formulas

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