Paul's Online Math Notes
Calculus III (Practice Problems)   [Notes] [Practice Problems] [Assignment Problems]


On August 21 I am planning to perform a major update to the site. I can't give a specific time in which the update will happen other than probably sometime between 6:30 a.m. and 8:00 a.m. (Central Time, USA). There is a very small chance that a prior commitment will interfere with this and if so the update will be rescheduled for a later date.

I have spent the better part of the last year or so rebuilding the site from the ground up and the result should (hopefully) lead to quicker load times for the pages and for a better experience on mobile platforms. For the most part the update should be seamless for you with a couple of potential exceptions. I have tried to set things up so that there should be next to no down time on the site. However, if you are the site right as the update happens there is a small possibility that you will get a "server not found" type of error for a few seconds before the new site starts being served. In addition, the first couple of pages will take some time to load as the site comes online. Page load time should decrease significantly once things get up and running however.

August 7, 2018

Calculus III - Practice Problems

Here is a list of sections for which problems have been written. Sections for which problems have been written will have active links and those that do not yet have problems written will not have active links.


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


Partial Derivatives

Interpretations of Partial Derivatives

Higher Order Partial Derivatives


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 - Part I

Line Integrals - Part II

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

Calculus III (Practice Problems)    [Notes] [Practice Problems] [Assignment Problems]

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