課程資訊
課程名稱
微積分乙
Calculus (General Mathematics) (B) 
開課學期
113-1 
授課對象
醫學系  
授課教師
林太家 
課號
MATH1209 
課程識別碼
201 101B0 
班次
01 
學分
3.0 
全/半年
半年 
必/選修
必帶 
上課時間
星期二3,4(10:20~12:10)星期四6,7(13:20~15:10) 
上課地點
普101普101 
備註
限本系所學生(含輔系、雙修生)
總人數上限:180人 
 
課程簡介影片
 
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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 

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
 
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NTU COOL下載MP4檔預習當週課程內容,於上課時參與討論。MP4檔僅提供修課學生個人使用,請勿外傳。 
預期每週課後學習時數
 
Office Hours
 
指定閱讀
NTU COOL的MP4檔 
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 
評量方式
(僅供參考)
 
No.
項目
百分比
說明
1. 
作業 
60% 
每週作業與上課表現 
2. 
期中考 
15% 
 
3. 
期末考 
25% 
 
 
課程進度
週次
日期
單元主題
第1週
9/3  Introduction  
第2週
9/10  Limit, Continuity, Derivative, Rules (1Diff1-1~1Diff1-4.ecm) HK1 
第3週
9/19  Implicit Differentiation, Extreme values of functions (1Diff2-1.ecm~1Diff2-4.ecm)
9/17放假,9/19上課 
第4週
9/24  Concavity, L'Hospital rule, Newton's method, (1Diff3-1.ecm~1Diff3-3.ecm) HK2 
第5週
10/1  Antiderivative, Definite Integral, Taylor's expansion (2Intl1-1~2intl1-3) HK3 
第6週
10/8  substitution rule, natural logarithm function, exponential function, ion channels (2intl2-1.ecm~2intl2-3.ecm) HK4 
第7週
10/15  Inverse functions, Integration by parts (2intl3-1.ecm~2intl3-3.ecm) HK5 
第8週
10/22  Integration of Rational Functions, Trigonometric integrals, Improper integrals, Numerical integration (2intl4-1.ecm~2intl4-3.ecm) HK6 
第9週
10/29  Differential Equation 1 (Modeling in the Biological Sciences, Application on Biochemical Reactions) (3DE1-1.ecm~3DE1-3.ecm)
Hodgkin-Huxley model and action potential, HK7
10/31 期中考 
第10週
11/5  Limits and Continuity in higher dimensions, Partial Derivatives (4PD1-1.ecm~4PD1-3.ecm) HK 8 
第11週
11/12  Second-Order Partial Derivatives, Chain Rule, Directional Derivatives and Gradient Vectors, Fourier series (4PD2-1.ecm~4PD2-3.ecm) HK9 
第12週
11/19  Tangent planes and Differentials, Maximum values, Lagrange multipliers, Fourier transform 1 (4PD3-1.ecm~4PD3-3.ecm) HK10 
第13週
11/26  Double integrals, Polar coordinates, Fourier transform 2,3 (6MI1-1.ecm~6MI1-3.ecm) HK11 
第14週
12/3  Triple integrals, Cylindrical coordinates, Spherical coordinates, Radon transform (6MI2-1.ecm~6MI2-3.ecm) HK12 
第15週
12/10  Differential Equation 2 (Advection, Diffusion, Application on ion channels) (5PDE1-1.ecm~5PDE1-3.ecm)  
第16週
  12/19期末考