User:Prime.mover/Source Work Progress

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Progress

I reckon it's about time I started on another item of displacement activity, that is: documenting how far I have got with the task of transferring the contents of the works on my bookshelf into pages on $\mathsf{Pr} \infty \mathsf{fWiki}$.

This will of course be an ongoing task.


In chronological order of works:

Early

1921

1922

Redo from start

1924

1926

1927

1932

1933

Most of the examples are to be missed, as they are minimally instructive.

Building up common material, so starting from Next:

1934

1935

1936

1937

Revisit

1938

1939

1941

1944

Starting on : Chapter $\text {II}$: Integration of Elementary Functions: $\S 7$ with Next:

1945

From Next:

1946

1947

Note that there is considerable refactoring needed around the Combination Theorem for Limits of Functions.

1951

1952

1953

From Next:
From Next:
From Next:
From Next:
From Next:
From Next:
From Next:
From the start:

1954

1955

Going around again. Closer look needed at the axioms underlying the definition of Ordering.

1956

Redo from start

1957

From Next:

From start:

1958

1959

Second pass
Plenty of discursive and historical material omitted from here on in

1960

Discussion of how Parallelogram Law is equivalent to Euclidean nature of space into which it is embedded.
Starting from Next

1961

Revisit from $\S 2.2$: confusion over definition of piecewise differentiable.
Exercises for Chapter $1$ section $\S 2$ have been ignored because they are tedious and repetitive.

1962

1963

To be revisited

1964

From Next:

Much missed out from Table $1.1$, although there is room for adding some of them

Some proofs in the above still incomplete or just not done.

Starting from Next:

Redo from start
Some gaps to fill just before here
From here on in there is much work to do on Axiom:Axiom of Choice.
Starting on Chapter $\text I$ with Next:
$1$-based exposition of Peano structure to be embarked upon.

1965

Also from Next:

Missing result just before this:
Don't forget this:
Revisit this section:


Filling out exercises and examples (the worthwhile ones -- plenty are just makework):


1966

Exercises not done. Redoing from start.
Go through it again because the examples are not all done.

1967

Revisiting from start:
Exercises after this point not all done
Starting from Next:


1968

Complete but for some improved solutions.

Redoing from start:
Discussion on difference between disjunction and exclusive-or to be analysed
Redoing from start:

Murray R. Spiegel: Mathematical Handbook of Formulas and Tables

Published $\text {1968}$, Schaum

ISBN 0-07-060224-7


Contents

Preface

Part $\text I$: Formulas

The Greek Alphabet
1. Special Constants
2. Special Products and Factors
3. The Binomial Formula and Binomial Coefficients
4. Geometric Formulas
5. Trigonometric Functions
6. Complex Numbers
7. Exponential and Logarithmic Functions
8. Hyperbolic Functions
9. Solutions of Algebraic Equations
10. Formulas from Plane Analytic Geometry
11. Special Plane Curves
12. Formulas from Solid Analytic Geometry
13. Derivatives
14. Indefinite Integrals
15. Definite Integrals
16. The Gamma Function
17. The Beta Function
18. Basic Differential Equations and Solutions
19. Series of Constants
20. Taylor Series
21. Bernoulli and Euler Numbers
22. Formulas from Vector Analysis
23. Fourier Series
24. Bessel Functions
25. Legendre Functions
26. Associated Legendre Functions
27. Hermite Polynomials
28. Laguerre Polynomials
29. Associated Laguerre Polynomials
30. Chebyshev Polynomials
31. Hypergeometric Functions
32. Laplace Transforms
33. Fourier Transforms
34. Elliptic Functions
35. Miscellaneous Special Functions
36. Inequalities
37. Partial Fraction Expansions
38. Infinite Products
39. Probability Distributions
40. Special Moments of Inertia
41. Conversion Factors


Part $\text {II}$: Tables

Sample Problems
1. Four Place Common Logarithms
2. Four Place Common Antilogarithms
3. $\operatorname{Sin} x$ ($x$ in degrees and minutes)
4. $\operatorname{Cos} x$ ($x$ in degrees and minutes)
5. $\operatorname{Tan} x$ ($x$ in degrees and minutes)
6. $\operatorname{Cot} x$ ($x$ in degrees and minutes)
7. $\operatorname{Sec} x$ ($x$ in degrees and minutes)
8. $\operatorname{Csc} x$ ($x$ in degrees and minutes)
9. Natural Trigonometric Functions (in radians)
10. $\log \sin x$ ($x$ in degrees and minutes)
11. $\log \cos x$ ($x$ in degrees and minutes)
12. $\log \tan x$ ($x$ in degrees and minutes)
13. Conversion of radians to degrees, minutes and seconds or fractions of a degree
14. Conversion of degrees, minutes and seconds to radians
15. Natural or Napierian Logarithms $\log_e x$ or $\ln x$
16. Exponential functions $e^x$
17. Exponential functions $e^{-x}$
18a. Hyperbolic functions $\sinh x$
18b. Hyperbolic functions $\cosh x$
18c. Hyperbolic functions $\tanh x$
19. Factorial $n$
20. Gamma Function
21. Binomial Coefficients
22. Squares, Cubes, Roots and Reciprocals
23. Compound Amount: $\paren {1 + r}^n$
24. Present Value of an Amount: $\paren {1 + r}^{-n}$
25. Amount of an Annuity: $\dfrac {\paren {1 + r}^n - 1} r$
26. Present Value of an Annuity: $\dfrac {1 - \paren {1 + r}^{-n}} r$
27. Bessel functions $\map {J_0} x$
28. Bessel functions $\map {J_1} x$
29. Bessel functions $\map {Y_0} x$
30. Bessel functions $\map {Y_1} x$
31. Bessel functions $\map {I_0} x$
32. Bessel functions $\map {I_1} x$
33. Bessel functions $\map {K_0} x$
34. Bessel functions $\map {K_1} x$
35. Bessel functions $\map {\operatorname{Ber} } x$
36. Bessel functions $\map {\operatorname{Bei} } x$
37. Bessel functions $\map {\operatorname{Ker} } x$
38. Bessel functions $\map {\operatorname{Kei} } x$
39. Values for Approximate Zeros of Bessel Functions
40. Exponential, Sine and Cosine Integrals
41. Legendre Polynomials $\map {P_n} x$
42. Legendre Polynomials $\map {P_n} {\cos \theta}$
43. Complete Elliptic Integrals of First and Second Kinds
44. Incomplete Elliptic Integrals of the First Kind
45. Incomplete Elliptic Integrals of the Second Kind
46. Ordinates of the Standard Normal Curve
47. Areas under the Standard Normal Curve
48. Percentile Values for Student's $t$ Distribution
49. Percentile Values for the Chi Square Distribution
50. $95$th Percentile Values for the $F$ Distribution
51. $99$th Percentile Values for the $F$ Distribution
52. Random Numbers
Index of Special Symbols and Notations
Index


Next


Click here for errata

Further Editions


Source work progress

<onlyinclude>* By chapters (work in progress):

From Next to end

1969

1970

From Next:

From Next:

From Next:

From start:

1971

Table of Integrals, starting with Next:

Exercises not all done

1972

Integrals:

Revisiting this book

From start:


redo from start

1973

Much of Chapter $3$ has been skipped.

1974

Working through the derivatives:

Working through the integrals:

1975

Chapter $2$ complete up to here. Section $7$ exercises have not been done, and Section $8$ has been completely missed out.
Chapter $2$ exercises still needing to be completed:
Redoing from start:
Chapter $5$ in progress -- exercises to do:

1976

(Chapters consisting of nothing but detailed calculation have not been implemented. Exercises also not done.)


From Next:

From start:

From Next:

From Next:

From Next:

From Next:

1977

1978

1979

Not all exercises are covered.

1980

Exercises to be completed:

1981

Undergoing a second pass to fill in the exercises, as follows:

1982

Second pass through:
Starting on Appendix $1$ with Next:
Check it, make sure nothing has been missed

1983

List of standard integrals done, starting from Next:
The full documentation of both $0$ and $1$ has been skipped, through laziness.

1985

1986

Redoing from start: examples and exercises to be covered

1987

1988

Second pass under way:

1989

In-depth discussion about partial functions and enumerations which needs attention

1990

From Next:
From Next:

1991

Redo from start

1992

1993

1994

$1$: Introduction:
$1.1$ Four Important Practical Problems:
$1.1.1$ Forecasting Time Series

Starting on Section $1.2$ with Next:

$1$: Introduction:
$1.2$ Stochastic and Deterministic Dynamic Mathematical Models
$1.2.1$ Stationary and Nonstationary Stochastic Models for Forecasting and Control: Nonstationary models

Starting on Section $1.3$ with Next:

Part $\text {I}$: Stochastic Models and their Forecasting:
$2$: Autocorrelation Function and Spectrum of Stationary Processes:
$2.1$ Autocorrelation Properties of Stationary Models:
$2.1.4$ Autocovariance and Autocorrelation Functions
Redo from start

1996

A complexity raised here which needs to be resolved:
Redo from start
Redoing Appendix $\text A$ from Next: lots of examples missed, and some fine detail ignored

1997

From Next:

From start:

Mostly complete up to this point. Much of the detailed work on algorithms has been left undone.

1998

Starting on Section $4.3$ with Next:

Bogged down in exactly what the product of linear operators means.
Analysis starts at chapter $2$. Chapter $1$ still to be addressed.

1999

to be reviewed

2000 and onward

to be reviewed
From Next:

Generally following 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.).

From start:


From Next:
From Next:
From Next:
From Next:


More or less complete

Section $39$ has been omitted as it is a discursion with an imprecise structure.
The bulk of the exercises (all collected at the end) remain to be documented.
except for a number of sundry results in section $142,857$
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