Lecture Engineering electromagnetics - Vector analysis presents the following content: Scalars and vectors, the rectangular coordinate system, the Dot product and the cross product, the circular cylindrical coordinate system, the spherical coordinate system.
In this volume I present some examples of line integrals, cf. also Calculus 2b, Functions of Several
Variables. Since my aim also has been to demonstrate some solution strategy I have as far as possible
structured the examples according to the following form
A Awareness, i.e. a short description of what is the problem.
D Decision, i.e. a reflection over what should be done with the problem.
I Implementation, i.e. where all the calculations are made.
C Control, i.e. a test of the result.
This is an ideal form of a general procedure of solution.
The purpose of this volume is to present some worked out examples from the theory of Functions in
Several Variables in the following topics:
1) Maximum and minimum of a function.
2) Integration in the plane and in the space.
3) Vector analysis.
As an experiment I shall here use the following generic diagram for solving problems:
A. For Awareness. What is the problem?
Try to formulate the problem in your own words, thereby identifying it.
D. For Decision. What are we going to do with it?
Are there any reasonable solution procedure available? If so, which one should be chosen?...
Lines and angles Triangles Isosceles and equilateral triangles Rectangles, squares, and parallelograms Circles Advanced circle problems Polygons Cubes and other rectangular solids Cylinders Coordinate signs and the four quadrants Defining a line on the coordinate plane Graphing a line on the coordinate plane Midpoint and distance formulas Coordinate geometry Summing it up
In this chapter, you’ll review the fundamentals involving plane geometry, starting with the following: • • • • • • Relationships among angles formed by intersecting lines Characteristics of any triangle Cha...