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