| 週次 |
授課內容 |
| 第1週 |
Integration by Parts
Trigonometric Integrals |
| 第2週 |
Trigonometric Substitution
Integration of Rational Functions by Partial Fractions |
| 第3週 |
Improper Integrals
Sequences |
| 第4週 |
Series
The Integral Test and Estimates of Sums |
| 第5週 |
Quiz#1 |
| 第6週 |
The Comparison Tests
Alternating Series and Absolute Convergence |
| 第7週 |
The Ratio and Root Tests
Strategy for Testing Series |
| 第8週 |
Power Series
Representations of Functions as Power Series |
| 第9週 |
Taylor and Maclaurin Series
Application of Taylor Polynomials |
| 第10週 |
Functions of Several Variables
Limits and Continuity
Partial Derivatives |
| 第11週 |
Quiz#2 |
| 第12週 |
Tangent Planes and Liner Approximations
The Chain Rule |
| 第13週 |
Directional Derivatives and the Gradient Vector
Maximum and Minimum Values |
| 第14週 |
Lagrange Multipliers
Double Integrals over Rectangles |
| 第15週 |
Double Integrals over General Regions
Double Integrals over Polar Coordinates |
| 第16週 |
Final exam
|
自主學習
內容 |
自主學習，多重積分教學開放課程。
自主學習，微分方程教學開放課程。 |