Math 21C
COURSE SYLLABUS
AND
SUPPLEMENTARY CLASS HANDOUTS

Last Update: June 1, 2005
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• ..... Math 21C Course Syllabus .....
  
  
  
• ..... Determining Equation for Surface of Revolution .....
  
  
  
• ..... Precice Epsilon Delta Definition of Limit in 3D-Space .....
  
  
  
• ..... A Geometric Interpretation of Partial Derivatives .....
  
  
  
• ..... Exact Change, Differential , and Chain Rule
  
  
  
• ..... Finding the Second Partial Derivative Using the Chain Rule .....
  
  
  
• ..... The Second Derivative Test for Partial Derivatives to Find and Classify Critical Points.....
  
  
  
• ..... Integrating a Function of Two Variables Over a Region R in the Plane .....
  
  
  
• ..... Evaluating a Double Integral Using Rectangular Coordinates .....
  
  
  
• ..... Moments and Center of Mass .....
  
  
  
• ..... Applications of Double Integrals .....
  
  
  
• ..... Evaluating a Double Integral Using Polar Coordinates .....
  
  
  
• ..... Evaluating a Triple Integral Using Rectangular Coordinates .....
  
  
  
• ..... Applications of Triple Integrals .....
  
  
  
• ..... An Example (Moment of Inertia) of a Triple Integral Using Rectangular Coordinates .....
  
  
  
• ..... The Differential of Volume for Spherical Coordinates .....
  
  
  
• ..... A Brief Summary of Multiple Integration and Coordinate Systems .....
  
  
  
• ..... The Definition of an Infinite Series Using the Sequence of Partial Sums Test .....
  
  
  
• ..... The Geometric Series Test for Infinite Series .....
  
  
  
• ..... The Integral Test for Infinite Series and Problems Using (*) and (*)(*) from the Integral Test Handout and Solutions .....
  
  
  
• ..... Subtle and Important Facts About Infinite Series .....
  
  
  
• ..... The Comparison and Limit Comparison Tests for Infinite Series .....
  
  
  
• ..... The Ratio Test for Infinite Series .....
  
  
  
• ..... The Alternating Series Test for Infinite Series .....
  
  
  
• ..... The Absolute Convergence Test for Infinite Series .....
  
  
  
• ..... A List of Tests for Convergence/Divergence of Infinte Series .....
  
  
  
• ..... Taylor Series and Taylor Polynomials .....
  
  
  
• ..... Examples of Maclaurin Series .....
  
  
  
• ..... An Example Using the Lagrange Form of the Taylor Remainder .....
  
  
  
• ..... A Introduction to Complex Numbers .....
  
  
  
• ..... Complex Numbers and Taylor Series .....