SYLLABUS

 

 

1st Week: Infinite Sequences and Series,

The Integral Test, Comparison Tests, Ratio and Root Tests

 

2nd Week: Alternating Series, Absolute and Conditional Convergence

Power Series, Taylor and Maclaurin Series,

 

3rd Week: Convergence of Taylor Series, Applications, 

Polar Coordinates, Vectors

 

4th Week:  Lines and Planes in Space, Cylinders and Quadric Surfaces

Limits and Continuity in Higher Dimensions

 

5th Week:  Partial Derivatives, The Chain Rule, Directional Derivatives

Tangent Planes, Extreme Values and Saddle Points

 

6th Week:  Lagrange Multipliers, Double Integrals 

Double Integrals in Polar Form

 

7th Week: Triple Integrals in Rectangular Coordinates

Substitutions in Double Integrals