长江大学大学物理双语教学前言.pptVIP

? ? ? Conclusion: Theorem 1. Theorem 2. Theorem 3. Theorem 4. Examples: ? ? ? ? ? ? ? ? ? 2.Integral calculus Example: ? Distance ? When time interval is small enough, is uniform and dt Work ?(F=Const) When F is not constant, Summation: Given f(x), is called definite integral of function f(x) with respect to x f(x): integrand discrete a: lower limit b: upper limit Distance: Work: How to calculate definite integral? Theorem: If integrand f(x) is the derivative of certain function i.e: then Proof: *Method: Indefinite integral (anti derivative for f(x) is not unique) ? Need guess ”Factoring” Indefinite integral table If Then ---------------------------- Theorem Example: ? ? ? set ? ? ? ? ? ? Definite integral Example: ? ? Application: ? ? Work-energy theorem 3.Vector Scalar Vector Definition geometric analytic axiomatic 2-D vector. magnitude—length unit vector: basis vector: Vector: Defined by its Algebra.(operation) *Analytical representation. Basic method to describe vector is Cartesian coordinate system. ? Property 3-D vector. Basis vector . ? Addition and subtraction of vectors N—D vector It can be regard as Commutative law Associative law Distributive law ? Is equivalent to parallelism rule. ? Scalar product(“Dot” product) Commutative law Geometric Definition Typical e