Vector Analysis: An Introduction to Vector-methods and Their Various Applications to Physics and Mathematics (Google eBook)

Front Cover
J. Wiley & Sons, 1911 - Vector analysis - 262 pages
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Contents

Equation of a Plane
16
Condition that Four Vectors Terminate in a Plane
18
Relations Independent of the Origin General Condition
21
Exercises and Problems
22
Scalar or Dot Product Laws of the Scalar Product
28
LineIntegral of a Vector
31
SurfaceIntegral of a Vector
32
Vector or Cross Product Definition
34
Distributive Law of Vector Products Physical Proof
35
Cartesian Expansion of the Vector Product
38
ART PAQB
39
Possible Combinations of Three Vectors
48
Third Proof
54
Line through End of b Parallel to a
60
CHAPTER IV
70
Curvature Osculating Plane Tortuosity Geodetic Lines
78
ART PASS 39 Equations of Surfaces Curvilinear Coordinates Ortho gonal System
79
Integration with Respect to a Scalar Variable Orbit of a Planet Harmonic Motion Ellipse
83
art paob
85
Hodograph and Orbit under Newtonian Forces
87
Partial Differentiation Origin of the Operator V
90
Exercises and Problems
91
CHAPTER V
94
Scalar and Vector Functions of Position Mathematical and Physical Discontinuities
95
Potential Level or Equipotential Surfaces Relation between Force and Potential
100
applied to a Scalar Function Gradient Independence of Axes Fouriers Law
102
applied to Scalar Functions Effect of V on Scalar Product
104
The Operator S i V or Directional Derivative Total Deriva tive
106
Directional Derivative of a Vector V applied to a Vector PointFunction
107
Divergence The Operator V
109
The Divergence Theorem Examples Equation of Flow of Heat
112
Equation of Continuity Solenoidal Distribution of a Vector
116
Curl The Operator V Example of Curl
117
Motion of Rotation without Curl Irrotational Motion
119
Differentiation of rm by V
135
Exercises and Problems
136
CHAPTER VI
138
Gausss Theorem Solid Angle Gausss Theorem for the Plane Second Proof
141
The Potential Function Poissons and Laplaces Equations Harmonic Function
147
Greens Theorems
148
Solution of Poissons Equation The Integrating Operator pot rrr dv
152
VectorPotential
153
Separation of a VectorFunction into Solenoidal and Lamellar Components Other Systems of Units
155
Energy in Terms of Potential
156
Energy in Terms of Field Intensity
157
Surface and Volume Density in Terms of Polarization
159
ElectroMagnetic Field Maxwells Equations
160
Equation of Propagation of ElectroMagnetic Waves
163
Poyntings Theorem Radiant Vector
164
Magnetic Field due to a Current
165
Mechanical Force on an Element of Current
167
Theorem on Line Integral of the Normal Component of a Vector Function
168
Electric Field at any Point due to a Current
170
Mutual Energy of Circuits Inductance Neumanns Integral
171
VectorPotential of a Current Mutual Energy of Systems of Conductors Integration Theorem
173
Mutual and SelfEnergies of Two Circuits
175
EXKHCIHKS AND PROBLKMS
176
Linear VectorFunction Instantaneous Axis
182
Geometrical Representation of the Motion Invariable
191
Transformation of Equations of MotionCentrifugal Couple
199
Lagranges Generalized Equations of Motion The Oper
205
Transformations of the Equations of Motion
211
Exercises and Problems
217
Various Notations in Use
221
Formulae
228
Linear Vector Function
237
Frenets Formulae for a Space Curve
244
Proof of Gausss Theorem
251

Common terms and phrases

Popular passages

Page 22 - A person travelling eastward at the rate of 4 miles per hour, finds that the wind seems to blow directly from the north; on doubling his speed it appears to come from the north-east; find the direction of the wind and its velocity.
Page 44 - The sum of the squares of the diagonals of a parallelogram is equal to the sum of the squares of its four Dem. Let ABCD be the a.
Page viii - Poinsot has brought the subject under the power of a more searching analysis than that of the calculus, in which ideas take the place of symbols, and intelligible propositions supersede equations".
Page 24 - ... intersection of corresponding sides lie on a line, then the lines joining the corresponding vertices pass through a common point and conversely. 5. Given a quadrilateral in space. Find the middle point of the line which joins the middle points of the diagonals. Find the middle point of the line which joins the middle points of two opposite sides. Show that these two points are the same and coincide with the center of gravity of a system of equal masses placed at the vertices of the quadrilateral....
Page 44 - The squares of the sides of any quadrilateral exceed the squares of the diagonals by four times the square of the line which joins the middle points of the diagonals.
Page 44 - P meet in a point and are directed along the diagonals of the three faces of a cube meeting at the point. Determine the magnitude of their resultant.
Page 113 - A through a closed surface S is equal to the volume integral of the divergence of the vector field over the region enclosed by S.
Page 46 - The triangle formed by joining the middle point of one of the nonparallel sides of a trapezoid to the extremities of the opposite side, is equivalent to one-half the trapezoid.
Page iii - Vector analysis; an introduction to vector-methods and their various applications to physics and mathematics. Ed.2. 1911. Wiley. "Bibliography,
Page 27 - I is the center of its inscribed circle. Show that the resultant of the vectors a AD, b BD, c CD is (a + b + c) ID, where a, b, c are the lengths of the sides of the triangle. 10. ABCD, A'B'C'D' are two parallelograms in the same plane.

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