微積分(一)

Course introduction Review of high school mathCourse introduction Introduction to mathematical modeling

Functions Inverse functions Exponential functions and logarithmic functions Trigonometric functions and inverse trigonometric functionsReview of high school math Functions - Operation of functions

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

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

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

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

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

Midterm examQuiz 2 Derivative of inverse functions Derivative of logarithmic functions Higher derivatives Increasing / decreasing functions Maximum / minimum

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

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

Antiderivatives The definite integral全校運動大會(停課一天)

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

Quiz 3 The fundamental theorem of calculus Mean value theorem for definite integrals Antiderivatives The definite integral

Integration by substitution Integration by partsQuiz 3 The fundamental theorem of calculus Mean value theorem for definite integrals

Integration by partial fractionsIntegration by substitution Integration by parts

Final examIntegration by partial fractions

彈性補充教學開國紀念日(放假一天)

彈性補充教學Final exam