微積分(一)

Course introduction Introduction to mathematical modeling

Review of high school math Functions - Operation of functions

Inverse functions Exponential functions and logarithmic functions Trigonometric functions and inverse trigonometric functions

中秋節(放假一天)

Discrete-time dynamical systems Analysis of discrete-time dynamical systems - Cobwebbing - Solving for equilibria - Stable and unstable equilibria Average and instantaneous rates of change

Quiz 1 Limits of functions The squeeze theorem Continuity

Computing derivatives Derivatives - Power rule - Sum rule, constant product rule, product rule, quotient rule - Chain rule - Derivative of trigonometric functions - Derivative of exponential functions

Derivatives - Implicit differentiation - Derivative of inverse trigonometric functions - Derivative of inverse functions - Derivative of logarithmic functions

Midterm exam

The second derivative Increasing / decreasing functions Local maximum / minimum Global maximum / minimum Concavity

全校運動大會(停課一天)

Intermediate value theorem Extreme value theorem Rolle’s theorem Mean value theorem Limits at infinity L’Hopital’s rule

Approximating functions - Tangent line approximation - Quadratic approximation - Taylor polynomial Newton’s method Introduction to differential equations

Quiz 2 Euler’s method Antiderivatives - power rule - constant product rule - sum rule Solving polynomial differential equations Integrals of special functions

Definite integrals - Partition - Riemann sum - Signed area Properties of definite integrals Fundamental theorem of calculus part 1

Fundamental theorem of calculus part 2 Integration by substitution Integration by parts

Quiz 3 Integration by parts (continued) Integration by partial fractions

Final exam