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課程名稱 |
微積分乙
Calculus (General Mathematics) (B) |
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開課學期 |
110-1 |
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授課對象 |
醫學系 |
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授課教師 |
林太家 |
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課號 |
MATH1209 |
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課程識別碼 |
201 101B0 |
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班次 |
01 |
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學分 |
3.0 |
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全/半年 |
半年 |
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必/選修 |
必帶 |
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上課時間 |
星期二3,4(10:20~12:10)星期四6,7(13:20~15:10) |
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上課地點 |
普101普101 |
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備註 |
大二以上限20人。
限本系所學生(含輔系、雙修生)
總人數上限：165人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1101MATH1209_01 |
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課程簡介影片 |
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核心能力關聯 |
核心能力與課程規劃關聯圖 |
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課程大綱
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為確保您我的權利,請尊重智慧財產權及不得非法影印
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課程概述 |
學習微積分及其在生理醫學相關主題的應用 |
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課程目標 |
學習內容包括：
1. Differentiation: Functions of single variable, Definition (limit, continuity, derivative), Rule (product, chain rules), Applications of derivatives (Optimization problems, L’Hospital Rule), Transcendental functions (log, exp, sin,sinh, etc)
2. Integration: Antiderivative, Techniques of Integration (substitution method, integration by part), Improper Integral, Taylor’s formula and theorem
3. Applications of integration, Differential equations
4. Partial Derivative: Functions of multi-variables, Critical points, Lagrange multiplier
5. Multiple Integrals: Definition (Polar coordinates, cylinder coordinates, spherical coordinates), Fubini theorem
Application I: The law of mass action
Application II: Fourier Transform and Signal Analysis (Filter of signals)
Application III: Ion channels, Hodgkin-Huxley equations and Poisson-Nernst-Planck equations
Application IV Radon (X-ray) transform
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課程要求 |
採課前預習、上課討論的上課方式。修課學生需每週在Ceiba下載PDF檔和在NTU COOL下載MP4檔預習當週課程內容，於上課時參與討論。PDF與MP4檔僅提供修課學生個人使用，請勿外傳。另外因NTU COOL提供的記憶體容量有限，可能無法同時儲存所有的MP4檔，將以每週上課有關內容為主，請大家儘早下載MP4檔。 |
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預期每週課後學習時數 |
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Office Hours |
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指定閱讀 |
在Ceiba的PDF檔和在NTU COOL的MP4檔 |
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參考書目 |
1. Thomas’ Calculus, 11th edition
2. Thomas’ Calculus: Early Transcendentals
3. Modeling Differential Equations in Biology, C. Taubes, 2008 Cambridge
University Press
4. J. Keener and J. Sneyd, Mathematical Physiology, 1998 Springer |
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評量方式
(僅供參考) |
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No. |
項目 |
百分比 |
說明 |
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1. |
作業 |
60% |
每週作業與上課表現 |
2. |
報告ㄧ |
10% |
Read the assigned paper and write a five-page ppt (or pdf) file for your report. |
3. |
報告二 |
10% |
Read the assigned paper and write a five-page ppt (or pdf) file for your report. |
4. |
期末報告 |
20% |
Select chapter(s) of J.Keener's book "Mathematical Physiology" and write a ten-page ppt (or pdf) file for your report. |
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週次 |
日期 |
單元主題 |
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第1週 |
9/23 |
Introduction |
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第2週 |
9/28,9/30 |
Limit, Continuity, Derivative |
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第3週 |
10/05,10/07 |
Rules, Implicit Differentiation |
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第4週 |
10/12,10/14 |
Extreme values of functions |
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第5週 |
10/19,10/21 |
L'Hospital's rule, Newton's method, Antiderivative (see 2intl1.pdf) |
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第6週 |
10/26,10/28 |
Definite Integral, Taylor's expansion |
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第7週 |
11/02,11/04 |
substitution rule, natural logarithm function, exponential function |
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第8週 |
11/09,11/11 |
Inverse functions, Integration by parts |
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第9週 |
11/16,11/18 |
11/18公布報告ㄧ, Integration of Rational Functions, Trigonometric integrals, Improper integrals, Numerical integration |
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第10週 |
11/23,11/25 |
Differential Equation 1 (Modeling in the Biological Sciences, Application on Biochemical Reactions) |
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第11週 |
11/30,12/02 |
11/30報告一上傳截止日，Limits and Continuity in higher dimensions, Partial Derivatives, Hodgkin-Huxley model and action potential
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第12週 |
12/07,12/09 |
Second-Order Partial Derivatives, Chain Rule, Directional Derivatives and Gradient Vectors, Fourier series |
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第13週 |
12/14,12/16 |
12/16公布報告二，Tangent planes and Differentials, Maximum values, Lagrange multipliers, Fourier transform 1 |
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第14週 |
12/21,12/23 |
12/22公布期末報告, Differential Equation 2 (Advection, Diffusion, Application on ion channels) |
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第15週 |
12/28,12/30 |
12/28報告二上傳截止日，Double integrals, Polar coordinates, Fourier transform 2,3 |
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第16週 |
1/04,1/06 |
1/4 上課(10:20AM), Triple integrals, Cylindrical coordinates, Spherical coordinates, Radon transform |
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第17週 |
1/11,1/13 |
1/11 期末報告上傳截止日 |
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