微積分(一)
Calculus I
學期
107-1
學分
2
學分
當期課號
A494
永久課號
A5186
開課單位
生命科學系暨基因體科學研究所
授課教師
王禹超
類別
必修
上課時間表
| 節 | 週三 |
|---|---|
1 08:00–08:50 | 微積分(一) 2 節連堂 |
2 09:00–09:50 |
* 根據陽明交大上課時間表所列
週次計畫
| 週次 | 主題 |
|---|---|
| 第 1 週 | Course introduction Introduction to mathematical modeling |
| 第 2 週 | Review of high school math Functions - Operation of functions |
| 第 3 週 | Inverse functions Exponential functions and logarithmic functions Trigonometric functions and inverse trigonometric functions Discrete-time dynamical systems Inverse functions Exponential functions and logarithmic functions Trigonometric functions and inverse trigonometric functions |
| 第 4 週 | Cobwebbing: a graphical solution technique for discrete-time dynamical systems Equilibria of discrete-time dynamical systems Average/instantaneous rate of change Limits of functionsDiscrete-time dynamical systems Analysis of discrete-time dynamical systems - Cobwebbing - Solving for equilibria - Stable and unstable equilibria Average and instantaneous rates of change |
| 第 5 週 | 國慶日(放假一天) |
| 第 6 週 | Quiz 1 The squeeze theorem Continuity Computing derivativesQuiz 1 Limits of functions The squeeze theorem Continuity |
| 第 7 週 | Computing derivatives Derivatives - Power rule - Sum rule, constant product rule, product rule, quotient rule - Chain rule Derivative of trigonometric functions Computing derivatives Derivatives - Power rule - Sum rule, constant product rule, product rule, quotient rule - Chain rule - Derivative of trigonometric functions - Derivative of exponential functions |
| 第 8 週 | Derivative of exponential functions Implicit differentiation Derivative of inverse trigonometric functions Derivatives - Implicit differentiation - Derivative of inverse trigonometric functions - Derivative of inverse functions - Derivative of logarithmic functions |
| 第 9 週 | Midterm exam |
| 第 10 週 | Derivative of inverse functions Derivative of logarithmic functions Higher derivatives Increasing / decreasing functions Maximum / minimumThe second derivative Increasing / decreasing functions Local maximum / minimum Global maximum / minimum Concavity |
| 第 11 週 | 全校運動大會(停課一天) |
| 第 12 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 ruleIntermediate value theorem Extreme value theorem Rolle’s theorem Mean value theorem Limits at infinity L’Hopital’s rule |
| 第 13 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 equationsApproximating functions - Tangent line approximation - Quadratic approximation - Taylor polynomial Newton’s method Introduction to differential equations |
| 第 14 週 | Quiz 2 AntiderivativesQuiz 2 Euler’s method Antiderivatives - power rule - constant product rule - sum rule Solving polynomial differential equations Integrals of special functions |
| 第 15 週 | The definite integral The fundamental theorem of calculus Mean value theorem for definite integrals Definite integrals - Partition - Riemann sum - Signed area Properties of definite integrals Fundamental theorem of calculus part 1 |
| 第 16 週 | Integration by substitution Integration by parts Fundamental theorem of calculus part 2 Integration by substitution Integration by parts |
| 第 17 週 | Quiz 3 Integration by partial fractionsQuiz 3 Integration by parts (continued) Integration by partial fractions |
| 第 18 週 | Final exam |