Type of Credit: Required
Credit(s)
Number of Students
Calculus is a basic, unversity-entrance level mathematics course which is needed as a prerequiste for the majority of the other university-level mathematics courses. The main goal of the course is to expose students to the fundamentals of calculus as well as provide rigorous training in analytic thinking and (mathematical) problem solving. The course of this semester will continue the calculus course of the previous semester, starting from the integral of the length of the curve to the application of integral in polar coordinates.
能力項目說明
Students will learn important calculus concepts such as the calculation of the arc length of curves, the integral of functions in polar coordinates, the application of sequences and series, the calculus of vector functions, Taylor expansion and its applications.
| 教學週次Course Week | 彈性補充教學週次Flexible Supplemental Instruction Week | 彈性補充教學類別Flexible Supplemental Instruction Type |
|---|---|---|
|
週次 Week |
課程主題 Topic
|
課程內容與指定閱讀
Content and Reading Assignment |
教學活動與作業
Teaching Activities and Homework |
學習投入時間 Student workload expectation |
|
|
課堂講授 In-class Hours |
課程前後 Outside-of-class Hours |
||||
|
1 |
Arc length and calculus of parametric curves |
1 |
Selected Exercises |
3 |
5 |
|
2 |
Calculus of polar curves |
2 |
Selected Exercises |
3 |
5 |
|
3 |
Sequences, Series |
2 |
Selected Exercises |
3 |
5 |
|
4 |
The Integral Test and estimates of sums, The comparison test |
3 |
Selected Exercises |
3 |
5 |
|
5 |
Alternative series, Absolute convergence and ratio and root tests |
3 |
Selected Exercises |
3 |
5 |
|
6 |
Power series, Representation of functions as power series |
4 |
Selected Exercises |
3 |
5 |
|
7 |
Taylor and Maclaurin series, |
4 |
Selected Exercises |
3 |
5 |
|
8 |
Vector functions, Functions of several variables. |
|
Selected Exercises |
3 |
5 |
|
9 |
Midterm Exam |
|
Selected Exercises |
2 |
6 |
|
10 |
Limits and continuity, Partial derivatives and differentiability for multivariable function. |
5 |
Selected Exercises |
3 |
5 |
|
11 |
The chain rule, Directional derivatives and the gradient vector. |
5 |
Selected Exercises |
3 |
5 |
|
12 |
Maximum and minimum values, Lagrange multipliers. |
5 - 6 |
Selected Exercises |
3 |
5 |
|
13 |
Double integrals. |
6 |
Selected Exercises |
3 |
5 |
|
14 |
Double integrals in polar coordinates and applications. |
7 |
Selected Exercises |
3 |
5 |
|
15 |
Trigonometric Substitution and Integration by Partial Fractions |
7 |
Selected Exercises |
3 |
5 |
|
16 |
Check up |
7 |
Selected Exercises |
2 |
6 |
|
17 |
Final Exam |
|
|
3 |
5 |
|
18 |
|
|
|
|
8 |
小考（含指定作業）40%，期中考30%，期末考30%
James Stewart, Daniel Clegg, Saleem Watson. Calculus, Early Transcendentals, Metric Version, Ninth Edition