| 週次 |
授課內容 |
| 第1週 |
6.1 Inverse Functions
6.2* The Natural Logarithmic Function
6.3* The Natural Exponential Function
|
| 第2週 |
6.4* General Logarithmic and Exponential Functions
6.2 Exponential Functions and Their Derivatives
6.3 Logarithmic Function |
| 第3週 |
6.4 Derivatives of Logarithmic Function
6.6 Inverse Trigonometric Functions
|
| 第4週 |
6.7 Hyperbolic Functions
6.8 Indeterminate Forms and l’Hospital’s Rule
7.1 Integration by Parts |
| 第5週 |
7.2 Trigonometric Integrals
7.3 Trigonometric Substitution
7.4 Integration of Rational Functions by Partial Fractions |
| 第6週 |
7.7 Approximate Integration
7.8 Improper Integrals
11.1 Sequences
11.2 Series |
| 第7週 |
11.3 The Integral Test and Estimates of Sums
11.4 The Comparison Tests
11.5 Alternating Series
|
| 第8週 |
期中考 |
| 第9週 |
11.6 Absolute Convergence and the Ratio and Root Tests
11.7 Strategy for Testing Series
11.8 Power Series
|
| 第10週 |
11.9 Representations of Functions as Power Series
11.10 Taylor and Maclaurin Series
11.11 Applications of Taylor Polynomials |
| 第11週 |
14.1 Functions of Several Variables
14.2 Limits and Continuity
14.3 Partial Derivatives |
| 第12週 |
14.4 Tangent Planes and Linear Approximations
14.5 The Chain Rule
14.6 Directional Derivatives and the Gradient Vector |
| 第13週 |
14.7 Maximum and Minimum Values
14.8 Lagrange Multipliers
15.1 Double Integrals over Rectangles |
| 第14週 |
15.2 Iterated Integrals
15.3 Double Integrals over General Regions
15.4 Double Integrals in Polar Coordinates
|
| 第15週 |
15.5 Applications of Double Integrals
15.6 Triple Integrals
15.7 Triple Integrals in Cylindrical Coordinates |
| 第16週 |
期末考 |
| 第17週 |
自主學習(研習教師指定的教材) |
| 第18週 |
自主學習(研習教師指定的教材) |