The Aim of this Course Learn Advanced Mathematics OWhat is advanced mathematics OWhat is advanced mathematics doing OHow is mathematical thinking ●Learn English OWhat is saying in English about advanced mathematics
The Aim of this Course ⚫Learn Advanced Mathematics What is advanced mathematics What is advanced mathematics doing How is mathematical thinking ⚫Learn English What is saying in English about advanced mathematics
Calculus -Advanced Mathematics Different from High School Mathematics OCalculate v.s Analysis OStatic v.s Dynamic Different from Social Science OPhilosophy v.s Arts OLogical v.s Image
Calculus – Advanced Mathematics ⚫Different from High School Mathematics Calculate v.s Analysis Static v.s Dynamic ⚫Different from Social Science Philosophy v.s Arts Logical v.s Image
Method of Studying Advanced Mathematics o Understanding deeply ●Deduce step by step ● Exercise
Method of Studying Advanced Mathematics ⚫Understanding deeply ⚫Deduce step by step ⚫Exercise
Part Two ●Functions ●Limites ●Derivatives ●Integration o Differential Equations
Part Two ⚫Functions ⚫Limites ⚫Derivatives ⚫Integration ⚫Differential Equations
Functions ●Vhat is a function? OHow does a function play in Calculus? oWhat is any difference between the function in Calculus and the Mathematics in the Middle School?
Functions ⚫What is a function? ⚫How does a function play in Calculus? ⚫What is any difference between the function in Calculus and the Mathematics in the Middle School?
Basic Concepts ●Variables:x,y ●Value or image oRelation ●Determination ●Region
Basic Concepts ⚫Variables: x,y ⚫Value or image ⚫Relation ⚫Determination ⚫Region
Definition of Function If a variable y depends on a variablex in a such way that each value of x determines exactly one value of y,then we say thaty is a function ofx. OA function fis a rule that associates a unique output with each input.If the input is denoted by x,then the output is denoted byfx)(read“fofx")
Definition of Function ⚫If a variable y depends on a variable x in a such way that each value of x determines exactly one value of y, then we say that y is a function of x. ⚫A function f is a rule that associates a unique output with each input. If the input is denoted by x, then the output is denoted by f(x) (read “f of x”)