Chapter Preface Introduction to Physics Introduction to vectors Introduction to calculus(微积分)
Chapter 1Chapter 1 Measurment ➢ Introduction to Physics ➢ Introduction to Vectors ➢ Introduction to Calculus(微积分) Chapter 0 Preface
Chapter 0 Preface Introduction to Physics (See动画库力学夹绪论exe) 1) Objects studied in physics 2) Methodology for studying physics 3)Some other key points
Chapter 1Chapter 1 Measurment Chapter 0 Preface ➢ Introduction to Physics 1) Objects studied in physics 2) Methodology for studying physics 3) Some other key points (See 动画库\力学夹\绪论.exe)
Chapter 0 Preface Introduction to vectors A scalar is a simple physical quantity that does not depend on direction mass, temperature, volume, work A vector is a concept characterized by a magnitude and a direction force, displacement, velocity
Chapter 1Chapter 1 Measurment Chapter 0 Preface ➢ Introduction to Vectors A scalar is a simple physical quantity that does not depend on direction. mass, temperature, volume, work… A vector is a concept characterized by a magnitude and a direction. force, displacement, velocity…
Chapter 0 Preface 1)Representation of vectors (See动画库力学夹0-4矢量运算exe) 2) Addition and subtraction of vectors (See动画库力学夹0-4矢量运算exe) 3)Dot and cross products
Chapter 1Chapter 1 Measurment Chapter 0 Preface 1) Representation of vectors 2) Addition and subtraction of vectors 3) Dot and cross products (See 动画库\力学夹\0-4矢量运算.exe) (See 动画库\力学夹\0-4矢量运算.exe)
Chapter 0 Preface 31) Dot product: A·B=A|·|B|cos(O) B B Bcos(0) B No problem Bib>兀 /6
Chapter 1Chapter 1 Measurment θ A B θ A B ? ? Chapter 0 Preface A B | A| | B| cos(θ) 3.1) Dot product: = θ A B θ A B Bcos() ) ( Acos No problem， if θ
Chapter 0 Preface A·B=B.A AA=A Prove it? A(B+C)=A·B+AC A=A2+4+Ak) A·B=? B=Bi+Bj+Bk A·B=(A1i+A1j+Ak)·(B,i+B,j+Bk) AB+AB+aB AB=AB+A,B+A
Chapter 1Chapter 1 Measurment Chapter 0 Preface A A i A j A k x y z = + + B B i B j B k x y z = + + AB = ? A B (A i A j A k) (B i B j B k) x y z x y z = + + + + = Ax Bx + Ay By + Az Bz A B = Ax Bx + Ay By + Az Bz A B B A = 2 2 A A = A| = A | A B C A B A C ( + ) = + Prove it?
Chapter 0 Preface 3. 2)Cross product: AxB= ABsin(e)n The length of A X B can be interpreted as the area of the parallelogram having A and B as sides n is a unit vector perpendicular to both a and B A,B, and n also becomes a right handed system. AxBb≤兀 AB,A×B=0 B A⊥B,|AxB=AB 0 Scalar triple product A(B×C) B×A=-4×B
Chapter 1Chapter 1 Measurment Chapter 0 Preface 3.2) Cross product: A B ABsin n = () is a unit vector perpendicular to both and . , , and also becomes n a right handed system. n The length of × can be interpreted as the area of the parallelogram having A and B as sides. A B A B A B A B A B n B A -A B = θ If A B,| A B| AB If A//B, A B 0 ⊥ = = Scalar triple product: A(BC) = ?
Chapter 0 Preface A=Ai+A,j+Ak A×B=? B=Bi+Bi+Bk A×B=(41i+A+A)×(B1+B,j+B2k) (A, B.-AB)i+(AB-AB).j +(ABy-A B k 7k|=(A,B:-AB,)元 A×B=A.A,A +(A B-A B.j Br By B+(ABy-A, B)k
Chapter 1Chapter 1 Measurment Chapter 0 Preface A A i A j A k x y z = + + B B i B j B k x y z = + + A B = ? A B (A i A j A k) (B i B j B k) x y z x y z = + + + + A B A B i A B A B j y z z y z x x z = ( − ) + ( − ) A B A B k x y y x + ( − ) x y z x y z B B B A A A i j k A B = A B A B j z x x z + ( − ) A B A B k x y y x + ( − ) A B A B i y z z y = ( − )
Chapter 0 Preface Introduction to calculus(微积分) 1)Limit of a function lin f(x-L Cose to zes estd b x→>c making x sufficiently close to c The limit of f of X, as X approaches C, is L Note that this statement can be true even if f(c)* lor f(x) is not defined at c EXample: f(x) imf(x)=x+1|1=1=2 x-1
Chapter 1Chapter 1 Measurment Chapter 0 Preface ➢ Introduction to Calculus(微积分) 1) Limit of a function f x L x c = → lim ( ) ƒ(x) can be made to be as close to L as desired by making x sufficiently close to c. “The limit of ƒ of x, as x approaches c, is L." Note that this statement can be true even if f (c) L or ƒ(x) is not defined at c. 1 1 ( ) 2 − − = x x Example: f x lim ( ) 1| 1 2 1 = + = = → x x f x x
Chapter 0 Preface 2) Derivative of a function(函数的导数) Motion with constant Motion with changing velocity speed 2 v() S(2)-s(41) v()2 S(2)-S(1) t2-t1
Chapter 1Chapter 1 Measurment Chapter 0 Preface 2) Derivative of a function(函数的导数) • Motion with constant velocity t s t1 t2 2 1 2 1 ( ) ( ) ( ) t t s t s t v t − − = t s t1 t2 • Motion with changing speed 2 1 2 1 ( ) ( ) ( ) t t s t s t v t − − ? =