the
Real Analysis appendices of
Why Slopes
and
More Math
Volume 3
Printed in Canada
ISBN 0-9697564-3-7
|
These Real Analysis appendices
continue the decimal
viewpoint of limits, continuity and convergence in chapter 14. and
this further lesson
A. What's Next
B. Pigeon Hole Principle
B. Bolzano-Weierstrass
C1. Triangle Inequality
C2. Triangle Inequality
C. More T.Inequality
D. Sets & Sequences
D. Monotone Sequences
E. Limits, Properties
E Limits & Error Control
F. Continuous Functions
F. Closed Range Thm
F. Intermediate Val. Thm
F. Compactness Thm
F. Equicontinuity Thm
F Extreme Value Thm
G. Rolle's Theorem etc
G. Mean Val. Thm.
G. Constant Difference Thm
G. Lipschitz Continuity I
PS: One Sided Range Theorems
G. Velocity Revisited
G. Sufficient Conditions
H. Riemann Sums Conv
H. Lipschitz Continuity II
Proofs of one-sided theorems could be of interest in the
study of 2D topology.
| |
Two References
First books on calculus typically leave a few theorems
unproven. If first books on calculus are not sufficiently
challenging for you then
- Advanced Calculus, 1968, by L. Loomis and S.
Sternberg. Revised Edition 1990 from Jones and Bartlett.
- Principles of Mathematical Analysis by W.
Rudin, McGraw-Hill 1964 (second edition).
may be of interest. These references are not first books on
calculus. Most, if not all theorems in these books are
proven. I found the first easier to read.
Remember these two books if you
concentrate in mathematics, electrical engineering,
physics or some other very mathematical discipline at the
university or college level. Or remember these references
if the next pages are of interest. These references may
provide perspectives on mathematics beyond and besides
those offered next.
About the Next Appendices
The following pages demonstrate the various kinds of
reasoning, direct and indirect, met by college students
specializing in mathematics. Since some of the proofs, as
written here, are hard or technical, your first objective
should be to visit the following appendices to see and
survey what can be easily understood. What is not
immediately understood can be left for later study or
postponed indefinitely. Mastering all the details could be a
project for high school or college math and science clubs.
The following appendices state the basic theorems of
calculus and give most proofs. In contrast to the initial
pages and chapters, the following appendices complement
first courses and first books in calculus at the advanced
instead of the elementary level. Proofs most likely to found
elsewhere are omitted.
| |
|
|
|
www.whyslopes.com
site
search
Parents: Help
your Child/Teen Learn covers Speaking
Skills, Reading
& Writing,
Preparing for Science &
Having Patience, etc
Math How-TOs
1. Arithmetic
2. Algebra
3. More
Algebra 4. Geometry
5 More
Geometry 6. Calculus
>> densely written
>> use as skill checklists
Online Volumes (orders)
1, Elements of Reason.
1996
1A. Pattern Based
Reason 1995
1B. Math
Curriculum Notes 1996
2. Three
Skills for Algebra 1995
3 .Why.Slopes.&.More.Math.1995
Skill &
Concept
Review or Development
1. Decimal
Arith - Video Based ]
2 Fractions
3. Fractions
with Units
3. Solving
Linear Equations -
making alg easier
4. Formulas
forwards & Backwards - unifying theme for Algebra
5. Proportionality,
Back- & For-wards - theme at work.
6. Logic
- Math Free, good for precision in work & studies
7. Euclidean-Geometry
(leanly)
8. Slopes
and Lines
9. Why
Study Slopes - a context
10. Quadratics
11 Polynomials
12 Factored
Polys - a context
13 Functions
- For-& Back -wards
14 Number Theory,
Richly
15. Exponents, Radicals
& logs.
16 Calculus
- Examples & Advice
17. Real
Analysis
18 Electric
Circuits Etc (So So)
19 Maps,
Similarity & Trig, (alt view)
20 Complex
numbers
21
Logic with Symbols+truth tables
22 Consistent
Story Telling
23. Even
More Logic
|
|