Math 21C Class Handouts
Sequences with Example
Sequence of Partial Sums Test
Geometric Series Test
The Integral Test
Two Examples Using (*) and (*)(*)
Subtle Facts About Infinite Series
The Comparison and Limit Comparison Tests for Series
The Ratio and Root Tests for Series
The Alternating Series Test
The Absolute Convergence Test for Series
Taylor Series and Taylor Polynomials, Lagrange Form of the Remainder
Some Well-Known Maclaurin Series
Plan of Attack on Series
Introduction to Three-Dimensional Space
Vectors
An Explanation of the Right Hand Rule for the Cross Product
Parallelepipeds and the Triple Scalar Product
Definition of Lines and Planes
Determining Equation for Surface of Revolution
Precice Epsilon Delta Definition of Limits in 3D-Space
A Geometric Interpretation of Partial Derivatives
Finding the Second Partial Derivatives Using the Chain Rule
Directional Derivatives and Gradient Vectors
The Second Derivative Test for Partial Derivatives to Find and Classify Critical Points
Extrema on Restricted Domain Example
General Procedure for Lagrange Multipliers