what is going to be learned in Calculus 3?

Three Dimensional Space

The 3-D Coordinate System

Equations of Lines

Equations of Planes

Quadric Surfaces

Functions of Several Variables

Vector Functions

Calculus with Vector Functions

Tangent, Normal and Binormal Vectors

Arc Length with Vector Functions

Velocity and Acceleration

Cylindrical Coordinates

Spherical Coordinates

Partial Derivatives

Limits

Partial Derivatives

Interpretations of Partial Derivatives

Higher Order Partial Derivatives

Differentials

Chain Rule

Directional Derivatives

Applications of Partial Derivatives

Tangent Planes and Linear Approximations

Gradient Vector, Tangent Planes and Normal Lines

Relative Minimums and Maximums

Absolute Minimums and Maximums

Lagrange Multipliers

Multiple Integrals

Double Integrals

Iterated Integrals

Double Integrals over General Regions

Double Integrals in Polar Coordinates

Triple Integrals

Triple Integrals in Cylindrical Coordinates

Triple Integrals in Spherical Coordinates

Change of Variables

Surface Area

Area and Volume Revisited

Line Integrals

Vector Fields

Line Integrals

Line Integrals of Vector Fields

Fundamental Theorem for Line Integrals

Conservative Vector Fields

Green’s Theorem

Curl and Divergence

Surface Integrals

Parametric Surfaces

Surface Integrals

Surface Integrals of Vector Fields

Stokes’ Theorem

Divergence Theorem

Basically calculus 3 covers very similar topics you learn in calculus 1 and 2, but rather in 3 dimensions. (In this class you'll be using an x, y, and z axis for your functions). For example, you'll learn how to take derivatives of functions that contain 2 or more variables (partial derivatives- which are pretty straightforward and simple), applications of derivatives in 3 dimensions (such as optimization problems and related rates). The only part that is really tricky about calc 3 is when you get to triple and double integration, where rather than setting your limits of integration as constants, they will be functions or surfaces in 2 and 3 dimensional space. It's some pretty weird stuff at first but you get the hang of it after a while.

Calc 3 is mostly just going over everything you've already learned and applying it in higher dimensions so it generally begins with going over vectors. Just try to find a calc 3 website from your school that is still up and see exactly what they cover at the beginning of the semester if you want to get a jump start on things.