微積分甲（二）授課大綱

◆ 標示之章節，由老師依課程內容完整度決定是否講授

• Sequences, Series, and Power Series

  1. 1. Sequences Series 

     2. The Ratio and Root Tests 

     3. Power Series 

     4. Representations of Functions as Power Series 

     5. Taylor and Maclaurin Series 

     6. Applications of Taylor Polynomials

• Partial Derivatives

  1. 1. Functions of Several Variables and Level Curves

     2. Limits and Continuity 

     3. Partial Derivatives 

     4. Tangent Planes and Linear Approximations 

     5. The Chain Rule 

     6. Directional Derivatives and the Gradient Vector 

     7. ◆Maximum and Minimum Values 

     8. ◆Lagrange Multipliers

• Multiple Integrals

  1. 1. Double Integrals over Rectangles 

     2. Double Integrals over General Regions 

     3. Double Integrals in Polar Coordinates 

     4. ◆Surface Area 

     5. Triple Integrals 

     6. ◆Triple Integrals in Cylindrical Coordinates 

     7. ◆Triple Integrals in Spherical Coordinates 

     8. ◆Change of Variables in Multiple Integrals