Math 21C (Thomas)

SUPPLEMENTARY CLASS HANDOUTS

Last Update: November 24, 2017
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• SUPPLEMENTARY HANDOUTS
  
  
  • ..... The Formal Definition of the Limit of a Sequence .....
    
    
  • ..... The Limit of a Particular Factorial Sequence Form .....
    
    
  • ..... The Sequence of Partial Sums Test for Infinite Series .....
    
    
  • ..... The Geometric Series Test for Infinite Series .....
    
    
  • ..... The Integral Test and P-Series Test for Infinite Series .....
    
    
  • ..... Two Examples Using (*) and (*)(*) .....
    
    
  • ..... Subtle Facts About Infinite Series .....
    
    
  • ..... The Comparison and Limit Comparison Tests for Infinite Series .....
    
    
  • ..... The Ratio and Root Tests for Infinite Series .....
    
    
  • ..... The Alternating Series Test for Infinite Series .....
    
    
  • ..... The Absolute Convergence Test for Infinite Series .....
    
    
  • ..... HERE IS A SUMMARY OF TESTS FOR CONVERGENCE/DIVERGENCE OF INFINITE SERIES .....
    
    
  • ..... Taylor Series and Taylor Polynomials, Lagrange Form of the Taylor Remainder .....
    
    
  • ..... Some Well-Known Maclaurin Series .....
    
    
  • ..... Using Maclaurin Series to Estimate the Value of Pi .....
    
    
  • ..... An Introduction to Three-Dimensional Space .....
    
    
  • ..... An Introduction to Plane Vectors and Space Vectors .....
    
    
  • ..... Two Examples Using Vectors to Solve Problems .....
    
    
  • ..... An Explanation of the Right Hand Rule for the Cross Product .....
    
    
  • ..... Parallelepipeds and the Triple Scalar Product .....
    
    
  • ..... Problem Solving Tools for Problems Using Vectors, Dot Products, and Cross Products .....
    
    
  • ..... Examples Using Dot Products, Cross Products, and Projections .....
    
    
  • ..... Graphing Using Level Curves .....
    
    
  • ..... Determining Equation for Surface of Revolution .....
    
    
  • ..... Precice Epsilon Delta Definition of Limit of Function of Two Variables .....
    
    
  • ..... Examples of Limits of Functions of Two Variables .....
    
    
  • ..... A Geometric Interpretation of Partial Derivatives .....
    
    
  • ..... Exact Change, Differential , and Chain Rule for z=f(x,y) .....
    
    
  • ..... Finding the Second Partial Derivative Using the Chain Rule .....
    
    
  • ..... Directional Derivatives and Gradient Vectors .....
    
    
  • ..... An Alternate form of the Differential for z=f(x,y) Using a Directional Derivative .....
    
    
  • ..... Why Gradient Vectors are Normal to Level Curves .....
    
    
  • ..... The Second Derivative Test for Partial Derivatives to Find and Classify Critical Points .....