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