Monthly Archives: February 2012

Calculus II

Here are review sheets for (Applied) Calculus II

Approximation of Higher Degrees

Arc Length

Differential Equations

Improper Integration

Integration by Parts

Linear Approximations

More Integral Properties

Newton’s Method

Numerical Integration

Partial Fractions

Physical Applicatoins


Regions Between Curves

Symmetric Integration

Trig Substitutions

Velocity and Net Change

Volumes by Integration


Alternating Series

Infinite Series

Sequences and Series Overview


The Divergence and Integral Tests

The Ratio and Comparison Tests

The following notes are not created by me, but I think you might find them helpful if you’re in need of them. They are made by Paul Dawkins of “Paul’s Online Math Notes,” and they are of stellar quality. You can download the PDF for the entire course here:,2,N

For some more basic review material, you can check out my AP Calculus BC Review Sheets at

Calculus III

Calculus: Early Transcendentals by Briggs and Cochran

Chapter 11 – Vectors and Vector-Valued Functions


11.1 – Vectors in the Plane, 11.2 – Vectors in Three Dimensions, 11.3 – Dot Products, 11.4 – Cross Products, 11.5 – Lines and Curves in Space, 11.6 – Calculus of Vector-Valued Functions, 11.7 – Motion in Space, and 11.8 – Length of Curves

Chapter 12 – Functions of Several Variables


12.1 – Planes and Surfaces, 12.2 – Graphs and Level Curves, 12.4 – Partial Derivatives, 12.5 – The Chain Rule, 12.6 – Directional Derivatives and the Gradient, 12.7 – Tangent Planes and Linear Approximations, 12.8 – Maximum/Minimum Problems, 12.9 – Lagrange Multipliers

Chapter 13 – Multiple Integration


13.1 – Double Integrals over Rectangular Regions, 13.2 – Double Integrals over General Regions, 13.3 – Double Integrals in Polar Coordinates, 13.4 – Triple Integrals, 13.5 – Triple Integrals in Cylindrical and Spherical Coordinates

Chapter 14, Part I – Vector Fields


14.1 – Vector Fields and Integrals, 14.2 – Line Integrals, 14.3 – Conservative Fields

Chapter 14, Part II – Vector Calculus – Part II


14.4 – Green’s Theorem, 14.5 – Divergence and Curl, 14.6 – Surface Integrals, 14.7 – Stokes’ Theorem, 14.8 – Divergence Theorem

This is an excellent Calc III review sheet made by my friend Tyler Silber, a student at the University of Connecticut. You can find it here:

Calc III Review by Tyler

Also, this will help you with computing double integrals. It’s a Wolfram|Alpha widget to easily find the answer to a double integral. It can be found at:

This review sheet is created by Paul Dawkins of “Paul’s Online Math Notes.” You can download a PDF of his Calc III review sheets at the following domain of his:,11,N