| 週次 |
授課內容 |
| 第1週 |
課程介紹
Ch07S04: Integration of rational functions by partial fractions
Ch06S08: Indeterminate forms and L’hospital Rule
Ch07S08: Improper integrals
|
| 第2週 |
Ch05S01: Areas between curves
Ch05S02: Volumes
Ch05S03: Volumes by cylindrical shells
Ch05S05: Average of a function |
| 第3週 |
Ch08S01: Arc length
Ch08S02: Area of Surface of Revolution
Ch10S01: Curves Defined by Parametric Equations.
Ch10S02: Calculus with Parametric Curves. |
| 第4週 |
Ch10S03: Polar Coordinates.
Ch10S04: Calculus in Polar Coordinates.
Ch11S01: Sequences
Ch11S02: Series |
| 第5週 |
Ch11S03: The Integral Test and Estimates of Sums
Ch11S05: Alternating Series
Ch11S06: Absolute Convergence and the Ratio and Root Tests
Ch11S07: Strategy for Testing Series
|
| 第6週 |
Mid 1: 3/30
|
| 第7週 |
Ch11S08: Power Series
Ch11S09: Representations of Functions as Power Series
Ch11S10: Taylor and Maclaurin Series
Ch11S11: Applications of Taylor Polynomials |
| 第8週 |
Ch14S01: Functions of Several Variables
Ch14S02: Limits and Continuity
Ch14S03: Partial Derivatives |
| 第9週 |
Ch14S04: Tangent Planes and Linear Approximations
Ch14S05: The Chain Rule
Ch14S06: Directional Derivatives and the Gradient Vector |
| 第10週 |
Ch14S07: Maximum and Minimum Values
Ch14S08: Lagrange Multipliers
|
| 第11週 |
Mid 2 |
| 第12週 |
Ch15S01: Double Integrals over Rectangles
Ch15S02: Double Integrals over General Regions
Ch15S03: Double Integrals in Polar Coordinates |
| 第13週 |
Ch15S04: Applications of Double Integrals
Ch15S05: Surface Area
Ch15S06: Triple Integrals |
| 第14週 |
Ch15S07: Triple Integrals in Cylindrical Coordinates
Ch15S08: Triple Integrals in Spherical Coordinates
Ch15S09: Change of Variables in Multiple Integrals |
| 第15週 |
Final exam |
| 第16週 |
Self-directed learning |
自主學習
內容 |
Vector Fields, Line Integrals, and The Fundamental Theorem of Line Integrals
by videos on the internet
Green’s Theorem, Parametric Surfaces and Their Areas |