1. Chapter 1 Chapter 1 Measurment  Introduction to Physics  Introduction to Vectors  Introduction to Calculus( 微积分 ) Chapter 0 Preface

2. Chapter 1 Chapter 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)

3. Chapter 1 Chapter 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…

4. Chapter 1 Chapter 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)

5. Chapter 1 Chapter 1 Measurment ? ? Chapter 0 Preface 3.1) Dot product: No problem ， if

6. Chapter 1 Chapter 1 Measurment Chapter 0 Preface Prove it?

7. Chapter 1 Chapter 1 Measurment Chapter 0 Preface 3.2) Cross product: is a unit vector perpendicular to both and.,, and also becomes a right handed system. The length of × can be interpreted as the area of the parallelogram having A and B as sides. Scalar triple product:

8. Chapter 1 Chapter 1 Measurment Chapter 0 Preface

9. Chapter 1 Chapter 1 Measurment Chapter 0 Preface  Introduction to Calculus( 微积分 ) 1) Limit of a function 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 or ƒ(x) is not defined at c. Example:

10. Chapter 1 Chapter 1 Measurment Chapter 0 Preface 2) Derivative of a function( 函数的导数 ) Motion with constant velocity t s t1t1 t2t2 t s t1t1 t2t2 Motion with changing speed ?

11. Chapter 1 Chapter 1 Measurment Chapter 0 Preface How to find the instantaneous speed at t 1 ? Motion with changing speed Derivative of s

12. Chapter 1 Chapter 1 Measurment Chapter 0 Preface For general function, its derivative is defined as: x f(x)f(x) x1x1 x2x2 A A’ tangent The meaning of derivative of a function:

13. Chapter 1 Chapter 1 Measurment How big is an infinitesimal?... is infinitesimal.

14. Chapter 1 Chapter 1 Measurment Chapter 0 Preface

15. Chapter 1 Chapter 1 Measurment Chapter 0 Preface Example: Some basic formulae:

16. Chapter 1 Chapter 1 Measurment Some basic rules: Chapter 0 Preface For a vector:,C is a const.

17. Chapter 1 Chapter 1 Measurment Chapter 0 Preface 3) Differential of a function ( 函数的微分 ) If f ( x ) has its derivative at point x, then f ’( x )d x is its differential at that point. Differential of the function Differential of the variable So f ’( x ) is also called differential quotient ( 微商 )

18. Chapter 1 Chapter 1 Measurment Chapter 0 Preface,C is a const. Operation rule is the same as that for derivative: One application of differential

19. Chapter 1 Chapter 1 Measurment Chapter 0 Preface Example: Following approximate formulae often used in physics ( ) :

20. Chapter 1 Chapter 1 Measurment Chapter 0 Preface 4) Integrals ( 积分 ) Motion with constant velocity Motion with changing speed t v t0t0 0 S t v t0t0 0 S How to find S?

21. Chapter 1 Chapter 1 Measurment Chapter 0 Preface t v t0t0 0 i …… In general, the integral from a to b of f(x) with respect to x is expressed as: definite integral indefinite integral

22. Chapter 1 Chapter 1 Measurment Chapter 0 Preface How to find an integral of a function? If function f(x) is continuous on the interval [a, b] and if on the interval (a, b), then

23. Chapter 1 Chapter 1 Measurment Chapter 0 Preface Example: Basic integral formulae: k,C: const.