|
課程名稱 |
微積分乙
Calculus (General Mathematics) (B) |
|
開課學期 |
113-1 |
|
授課對象 |
牙醫學系 |
|
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 |
|
|
核心能力關聯 |
核心能力與課程規劃關聯圖 |
|
課程大綱
|
|
為確保您我的權利,請尊重智慧財產權及不得非法影印
|
|
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% |
|
|
|
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 |
|