Begin2.DVI

Introduction to Calculus Volume II by J.H. Heinbockel ...

The regular solids or regular polyhedra are solid geometricfigures with the same identical regular polygon on each face. There a ...

Introduction to Calculus Volume II by J.H. Heinbockel Emeritus Professor of Mathematics Old Dominion University ...

©cCopyright 2012 by John H. Heinbockel All rights reserved Paper or electronic copies for noncommercial use may be madefreely wi ...

Preface This is the second volume of an introductory calculus presentation intended for future scientists and engineers. Volume ...

Table of Contents Introduction to Calculus Volume II Chapter 6 Introduction to Vectors...................................... 1 V ...

Table of Contents Chapter 8 Vector Calculus II................................................ 173 Vector Fields, Divergence of ...

Table of Contents Chapter 11 Introduction to Probability and Statistics... 381 Introduction, Simulations, Representation of Data ...

Chapter Introduction to Vectors Scalars are quantities with magnitude only whereas vectors are those quantities having both a ma ...

2. The magnitude of a vector is a nonnegative scalar quantity. The magnitude of a vector B
is denoted by the symbols B or |B
|. ...

If F
=A
−B
denotes the difference of two vectors A
and B,
then F
is determined by the above rule for vector addition by wri ...

Definition (Linear dependence and independence of vectors) Two nonzero vectors A
and
Bare said to be linearly dependent if it ...

Example 6-1. Show that the medians of a triangle meet at a trisection point. Figure 6-4. Constructing medians of a triangle Solu ...

and a triangle would not exist. By equating to zero the scalar coefficients in these equations, there results the simultaneous s ...

been represented by a variety of notations. Some of the more common notations employed in various textbooks to denote rectangula ...

The physical interpretation of projection can be assigned to the dot product as is illustrated in figure 6-6. In this figure A
...

A
·eˆ 1 =A 1 A
·ˆe 2 =A 2 A
·ˆe 3 =A 3 (6 .10) represent respectively, the components or projections of the vector A
onto the x ...

Any numbers proportional to the direction cosines of a line are called the di- rection numbers of the line. Show for a:b:cthe di ...

and this product can be expanded utilizing the distributive and commutative laws to obtain A
·B
=A 1 B 1 ˆe 1 ·eˆ 1 +A 1 B 2 ˆe ...

Let C
=A
−B
denote the directed line segment from (B 1 ,B 2 ,B 3 )to (A 1 ,A 2 ,A 3 ).The length of this vector is found to be ...