# Joseph Kitchen's Calculus (reference)

I'm asking about one textbook: Kitchen's Calculus. I tried to get a copy in different libraries but nothing. I tried buying it and I cannot find it wherever I've been. I've heard that is an outstanding book, as good as Spivak or Apostol at the rigorous level, to say the two classics book of Calculus (introduction to real analysis).

Therefore, I ask the following questions: What happens with the book? The only conclusion for me is that it has been out of print for a long time (for some strange reason). Is there a place where it can get it? Is it as good as someone told me (at the theoretical level)? Does somebody know what is the the table of content?

With theoretical level, I'd like to say:

(The textbook should be rigorous, it should not state a major theorem without a detail proof, and also it should be primarily based on developing the theoretical foundations of calculus).

• More complete information about the book: Joseph Weston Kitchen (1936- ), Calculus of One Variable, Addison-Wesley Series in Mathematics, Addison-Wesley Publishing Company, 1968, xiv + 785 pages. [not reviewed by MR; Zbl 162.35302] Reviewed by: William Leonard Ferrar, Mathematical Gazette 53 #384 (May 1969), p. 186. – Dave L. Renfro Mar 29 '14 at 15:58
• Thank for the information @DaveL.Renfro do you have this book? Is worth to continue looking for it? – Jose Antonio Mar 29 '14 at 16:05
• The book is in the the university library near where I live, and it's on a list of books I've compiled (mainly in case anyone is interested) of books that I would classify as suitable for an honors level calculus course. However, I don't recall more specifically what merits it may or may not have over other such books. – Dave L. Renfro Mar 29 '14 at 17:42
• I have to leave now, but in case you or anyone else is interested in this list: Ralph Palmer Agnew's Calculus. Analytic Geometry and Calculus, with Vectors (1962), Apostol's Calculus, Colin Whitcomb Clark's The Theoretical Side of Calculus (1972), Courant/John's Introduction to Calculus and Analysis, Embry/Schell/Shomas' Calculus and Linear Algebra. An Integrated Approach (1972), Robert Clark James' University Mathematics (1963), Kazimierz Kuratowski's Introduction to Calculus (1961), Spivak's Calculus. – Dave L. Renfro Mar 29 '14 at 17:50
• @Dave A very good list indeed. To that list, I would add Charles McCluer's HONORS CALCULUS, Donald Estep's PRACTICAL ANALYSIS OF ONE VARIABLE, Kenneth Ross' ELEMENTARY ANALYSIS:THE THEORY OF CALCULUS. Of course,these are for single variable courses only-for honors MULTIVARIABLE calculus,there's a host of other beautiful textbooks recommended here: math.stackexchange.com/questions/14475/… – Mathemagician1234 Apr 3 '14 at 1:17

Let me steal the fame from Dave L. Renfro and Mathemagician, and just format this in a more usable form:

(Renfro -- I've added bibliographic information for some reviews of these books.)

Agnew reviewed by: Edwin George Eigel, Pi Mu Epsilon Journal 3 #8 (Spring 1963), 426; Eric John Fyfe Primrose, Mathematical Gazette 48 #363 (February 1964), 115-116; Robert C. Stewart, American Mathematical Monthly 71 #7 (Aug.-Sept. 1964), 810-811.

Apostol reviewed by: Volume 1 Frederic Cunningham, American Mathematical Monthly 69 #5 (May 1962), 449-451; Yvonne Germaine Marie Chislaine Cuttle, Canadian Mathematical Bulletin 6 #2 (May 1963), 306-307; Karl Menger, Scripta Mathematica 27 #3 (May 1965), 270-272; Ethan David Bolker, American Mathematical Monthly 77 #1 (January 1970), 88-89. Volume 2 Frederic Cunningham, American Mathematical Monthly 70 #5 (May 1963), 587-588.

• Colin Whitcomb Clark's The Theoretical Side of Calculus (1972): amazon link which is obviously a wrong link

Clark reviewed by: Robert Patrick Webber, American Mathematical Monthly 81 #7 (Aug.-Sept. 1974), 795-796; Jon [Arnold?] Reed, Nordisk Matematisk Tidskrift 27 #4 (1979), 164-165 (in Norwegian). Briefly mentioned in this article.

Courant/John reviewed by: (Volume 1) Robert Alexander Rankin, Mathematical Gazette 51 #376 (May 1967), 164-165.

• Embry/Schell/Thomas' Calculus and Linear Algebra. An Integrated Approach (1972): amazon link

Embry/Schell/Thomas reviewed by: Norman Schaumberger, Mathematics Teacher 65 #6 (October 1972), 547; Rodney Tabor Hood, American Mathematical Monthly 80 #4 (April 1973), 453-454.

Hille reviewed by: (Volume I) Joseph Leo Doob, Science (N.S.) 147 #3662 (5 March 1965), 1135-1136; (Volume I) Donald Everett Richmond, American Mathematical Monthly 73 #1 (January 1966), 100-101; (Volume II) Judith Molinar Elkins, American Mathematical Monthly 76 #3 (March 1969), 319-320.

James reviewed by: Joseph Buffington Roberts, Mathematics Magazine 38 #1 (January 1965), 48-49; Arthur Louis Gropen, Pi Mu Epsilon Journal 4 #2 (Spring 1965), 83.

• Kazimierz Kuratowski's Introduction to Calculus (1961): amazon link (with discussion that doing OCR on the 1923 book was not the greatest idea), PDF online

Kuratowski reviewed by: Frans Martin Djorup, Pi Mu Epsilon Journal 3 #8 (Spring 1963), 420; Raymond Charles Mjolsness, American Mathematical Monthly 71 #1 (January 1964), 111-112.

Spivak reviewed by: Graham S. Smithers, Mathematical Gazette 52 #380 (May 1968), 181-182; David Marius Bressoud, American Mathematical Monthly 120 #6 (June-July 2013), 577-580 (simultaneous review with 4 other honors or otherwise distinctive texts).

• Thanks, Dave. I think the best evidence of performance of a given book is what kind of classes a student can take if they (i) had this as a required textbook in a calculus class, but did not put any effort, to (ii) put in an honest effort and learned everything this given book can teach, while being limited to but this book being the only one in their disposal. – StasK Jun 21 '14 at 18:15

1. Preliminaries

• Sets and set operations
• The real numbers as a field
• The order axioms
• Absolute values
• Quantifiers
• Logical connectives
• Negation of quantified statements
• The principle of finite induction
• A deeper look at induction
2. Analytic Geometry of Straight Lines and Curves

• A synopsis of basic formulas
• Distance and point of division; circles
• Equations of straight lines
• Slopes of lines
• Applications to plane geometry
3. Limits

• Functions
• Operations with functions
• The limit concept for sequences
• Proofs of the limit theorems
• Limits of functions of a continuous variable
• Continuity
4. Techniques of Differentiation

• Definition of a derivative
• Tangents to curves
• The differentiation of some basic functions
• Differentiation of sums, products, and quotients
• The chain rule
• Operators and higher-order derivatives
• Implicit differentiation
5. Completeness of the Real Numbers

• The least upper bound axiom and the Archimedean ordering property
• The intermediate value theorem
• Some theorems on sequences
• The theorem on extreme values
• Uniform continuity
6. Mean-Value Theorems and Their Applications

• A necessary condition for relative maxima and minima
• The mean-value theorem
• Significance of the first derivative
• Sufficient conditions for relative extrema
• The sign of the second derivative
• Convexity
• Approaches to infinity
7. Antidifferentiation and its Applications

• Antiderivatives
• Finding antiderivatives
• The Newton integral
• Areas in rectangular coordinates
• Areas in polar coordinates
• Volumes
• Path length
• Moments and centroids
• Miscellaneous applications to physics
8. The Riemann Integral

• Definite integrals and Riemann integrability
• The Riemann integral as a limit of sums
• Further properties of Riemann integrals
• The fundamental theorem of calculus
• A deeper look at areas
• Necessary and sufficient conditions for Riemann integrability
9. Transcendental Functions

• General theory of inverse functions
• The inverse trigonometric functions
• Definitions and basic properties of the exponential and logarithmic functions
• Further study of the exponential function
• The hyperbolic functions
• Some important limits
• Some inequalities
• An analytic treatment of the trigonometric functions
• Euler's formula
10. Techniques of Integration

• Reduction to standard formulas
• Integration by parts
• Rational functions
• Some standard substitutions
• Wallis' product and Stirling's formula
11. Higher-Order Mean-Value Theorem

• L'Hopital's rule
• Taylor's theorem
• Polynomial interpolation
• Numerical integration
• Newton's method
12. Plane Curves

• The conics in central position
• $\mathbb R^2$ as a vector space
• Affine mappings of the plane
• The general second-degree equation
• A little more about vectors
• Curvature of plane curves
13. Infinite Series

• A humble beginning
• Series with nonnegative terms
• Absolute versus conditional convergence
• Double series
• Pointwise versus uniform convergence
• Power series
• Real analytic functions
• Fourier series
• Infinite products