Foreword
Preface
I VECTOR CALCULUS
1 Introduction and Basic Definitions
2 The Scalar Product
3 Component Representation of a Vector
4 The Vector Product (Axial Vector)
5 The Triple Scalar Product
6 Application of Vector Calculus
Application in mathematics:
Application in physics:
7 Differentiation and Integration of Vectors
8 The Moving Trihedral (Accompanying Dreibein)--the Frenet Formulas
Examples on Frenet's formulas:
9 Surfaces in Space
10 Coordinate Frames
11 Vector Differential Operations
The operations gradient, divergence, and curl (rotation)
Differential operators in arbitrary general (curvilinear) coordinates
12 Determination of Line Integrals
13 The Integral Laws of Gauss and Stokes
Gauss Law:
The Gauss theorem:
Geometric interpretation of the Gauss theorem:
Stokes law:
14 Calculation of Surface Integrals
15 Volume (Space) Integrals
II NEWTONIAN MECHANICS
16 Newton's Axioms
17 Basic Concepts of Mechanics
Inertial systems
Measurement of masses
Work
Kinetic energy
Conservative forces
Potential
Energy law
Equivalence of impulse of force and momentum change
Angular momentum and torque
Conservation law of angular momentum
Law of conservation of the linear momentum
Summary
The law of areas
Conservation of orientation
18 The General Linear Motion
19 The Free Fall
Vertical throw
Inclined throw
20 Friction
Friction phenomena in a viscous medium