Basic Calculus
Instructor: Wei-Liang Sun (Department of Mathematics, NTNU)
Office Location: M404, Math Building, NTNU
Teaching Asistant (TA): Jun-Wei Ruan
Time: 13:20 - 16:20 every Thursday
Class Room: S603 at Gongguan campus, NTNU
Syllbus: Here
Moodle: Here
Textbook: J. Stewart and T. Day, Biocalculus: Calculus for the Life Sciences, (2014) Cengage Learning
Reference: C. Neuhauser and M. L. Roper, Calculus for Biology and Medicine, (2018) Pearson Education, Inc.
Resources: WolframAlpha, GeoGebra, Paul's Online Notes , Koch snowflake
Section 1.4: 24, 30 (a)(b)(c)
Section 2.1: 15, 16, 17, 18, 21, 22, 25, 35*, 38
35*
(b): Write Q_{n+1} = a Q_n + b and find a, b.
(d): What is the limit of Q_n as n goes to infinity?
Exercise 3 (9/21): Solution
Section 2.2: 10, 17, 19, 31
Section 2.3: 6 (i)(j), 7 (h), 29, 30, 44
Section 2.4: 1 (e), 2 (a)(b), 32, 39
Exercise 4 (9/28): Solution
Section 2.5: 4, 12 (c)(d), 13, 30, 39, 40, 51 (此題不用交，看看它神秘的結論)
Section 3.1: 6, 11, 30
Section 3.2: 3 (b)(c)
Section 3.3: 23, 27, 45
Exercise 5 (10/5): Solution
Section 3.3: 13, 16, 18, 30, 48
Section 3.4: 8, 24, 49 (c), 58 (a) (58(b)不用交，請自行使用工具(WolframAlpha, GeoGebra, ...等等)去理解題目的意思)
Section 3.5: 9, 18, 31, 51
Section 3.7: 3, 4
Exercise 6 (10/12): Solution
Section 3.8: 12
Section 4.1: 3*, 41*
Section 4.2: 45, 47
Section 4.3: 7, 9, 10, 29, 47, 51
3*: absolute maximum/minimum (絕對極大/極小值) 指的就是整個圖形的最大/最小值
41*: [提示] 發生在端點之外的 absolute maximum/minimum 亦為 local maximum/minimum
Exercise 7 (11/2): Solution
Section 4.6: 14, 23, 41
Section 5.3: 39, 41
Section 5.4: 4, 5, 12, 16, 18
Section 5.5: 3, 4, 21
Section 5.6: 5, 17
Exercise 8 (11/9): Solution
Section 5.2: 27(d), 28(c), 30, 31, 38, 42
Section 5.3: 10, 19, 20, 29, 58
Section 5.4: 39, 40
Section 5.5: 13, 24*
Section 5.6: 8, 15
Section 5.8: 9, 15, 33
24*: [Hint] sin(2t) = 2 sin(t) cos(t)
Exercise 9 (11/16): Solution
Section 5.8: 11, 14, 18
Section 6.1: 1, 2, 3*, 4*, 9, 10, 25
Section 6.4*: 1, 2, 4, 5, 7, 8
3*, 4*: 題目說的 typical approximating rectangle 不用畫
6.4*: 善用資源 (如上方的 WolframAlpha, GeoGebra) 嘗試畫畫看題目所表達的意思來輔助計算
Exercise 10 (11/23): (善用網路資源) Solution
Section 9.1: 7, 26*, 41*-46*, 49, 51, 53, 57
26*, 41*-46*: 可固定一個 x 的值後看圖形為何 (即圖形與平面 x=k 的截面輪廓)，也可固定 y 的值做同樣的事，或是假設 x=y 後圖形為何 (即圖形與平面 x=y 的截面輪廓)