微積分(一)

週次計畫

週次	主題
第 1 週	Course introduction Introduction to mathematical modeling 2019/09/11
第 2 週	Review of high school math Functions - Operation of functions 2019/09/18
第 3 週	Inverse functions Exponential functions and logarithmic functions Trigonometric functions and inverse trigonometric functions Discrete-time dynamical systems 2019/09/25
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 functions 2019/10/02
第 5 週	Quiz 1 The squeeze theorem Continuity Computing derivatives 2019/10/09
第 6 週	Computing derivatives Derivatives - Power rule - Sum rule, constant product rule, product rule, quotient rule - Chain rule Derivative of trigonometric functions 2019/10/16
第 7 週	Derivative of exponential functions Implicit differentiation Derivative of inverse trigonometric functions 2019/10/23
第 8 週	Quiz 2 Derivative of inverse functions Derivative of logarithmic functions Higher derivatives Increasing / decreasing functions Maximum / minimum 2019/10/30
第 9 週	Midterm exam 2019/11/06
第 10 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 rule 2019/11/13
第 11 週	全校運動大會(停課一天) 2019/11/20
第 12 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 equations 2019/11/27
第 13 週	Antiderivatives The definite integral 2019/12/04
第 14 週	Quiz 3 The fundamental theorem of calculus Mean value theorem for definite integrals 2019/12/11
第 15 週	Integration by substitution Integration by parts 2019/12/18
第 16 週	Integration by partial fractions 2019/12/25
第 17 週	開國紀念日(放假一天) 2020/01/01
第 18 週	Final exam 2020/01/08