微積分(一)
Calculus I
學期
109-1
學分
0
學分
當期課號
A028
永久課號
A5185
開課單位
共同教育中心
授課教師
王禹超
校區
陽明
類別
必修
上課時間表
| 節 | 週三 |
|---|---|
1 08:00–08:50 | 微積分(一) YX406（陽明） 2 節連堂 |
2 09:00–09:50 |
* 根據陽明交大上課時間表所列
概述
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先修科目
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備註
無備註
教學方式
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課程大綱
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週次計畫
| 週次 | 主題 |
|---|---|
| 第 1 週 | Course introduction Review of high school mathCourse introduction Introduction to mathematical modeling |
| 第 2 週 | Functions Inverse functions Exponential functions and logarithmic functions Trigonometric functions and inverse trigonometric functionsReview of high school math Functions - Operation of functions |
| 第 3 週 | Discrete-time dynamical systems Cobwebbing: a graphical solution technique for discrete-time dynamical systems Equilibria of discrete-time dynamical systems Average/instantaneous rate of changeInverse functions Exponential functions and logarithmic functions Trigonometric functions and inverse trigonometric functions Discrete-time dynamical systems |
| 第 4 週 | Quiz 1 Limits of functions The squeeze theorem ContinuityCobwebbing: a graphical solution technique for discrete-time dynamical systems Equilibria of discrete-time dynamical systems Average/instantaneous rate of change Limits of functions |
| 第 5 週 | Computing derivatives Derivatives - Power rule - Sum rule, constant product rule, product rule, quotient rule - Chain rule Derivative of trigonometric functionsQuiz 1 The squeeze theorem Continuity Computing derivatives |
| 第 6 週 | Derivative of exponential functions Implicit differentiation Derivative of inverse trigonometric functionsComputing derivatives Derivatives - Power rule - Sum rule, constant product rule, product rule, quotient rule - Chain rule Derivative of trigonometric functions |
| 第 7 週 | Quiz 2 Derivative of inverse functions Derivative of logarithmic functions Higher derivatives Increasing / decreasing functions Maximum / minimumDerivative of exponential functions Implicit differentiation Derivative of inverse trigonometric functions |
| 第 8 週 | Midterm examQuiz 2 Derivative of inverse functions Derivative of logarithmic functions Higher derivatives Increasing / decreasing functions Maximum / minimum |
| 第 9 週 | Concavity Curve sketching Useful theorems for continuous/differentiable functions - Intermediate value theorem - Extreme value theorem - Rolle’s theorem - Mean value theorem Limits at infinity - L’Hopital’s ruleMidterm exam |
| 第 10 週 | Approximating functions Newton’s method: a numerical method to solve an equation Introduction to differential equations Euler’s method: a numerical method to solve differential equationsConcavity Curve sketching Useful theorems for continuous/differentiable functions - Intermediate value theorem - Extreme value theorem - Rolle’s theorem - Mean value theorem Limits at infinity - L’Hopital’s rule |
| 第 11 週 | Antiderivatives The definite integral全校運動大會(停課一天) |
| 第 12 週 | 全校運動大會(停課一天) Approximating functions Newton’s method: a numerical method to solve an equation Introduction to differential equations Euler’s method: a numerical method to solve differential equations |
| 第 13 週 | Quiz 3 The fundamental theorem of calculus Mean value theorem for definite integrals Antiderivatives The definite integral |
| 第 14 週 | Integration by substitution Integration by partsQuiz 3 The fundamental theorem of calculus Mean value theorem for definite integrals |
| 第 15 週 | Integration by partial fractionsIntegration by substitution Integration by parts |
| 第 16 週 | Final examIntegration by partial fractions |
| 第 17 週 | 彈性補充教學開國紀念日(放假一天) |
| 第 18 週 | 彈性補充教學Final exam |
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