Joseph Kitchen's Calculus (reference)

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.)

• Ralph Palmer Agnew's Calculus. Analytic Geometry and Calculus, with Vectors (1962): amazon link; random PDF

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.

• Tom Apostol (1991) Calculus: amazon link -- $200 is way too steep; random PDF vol 1, random PDF vol 2

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's Introduction to Calculus and Analysis (1999): amazon vol 1, amazon vol II/1, amazon vol II/2; $170 for the three together. unverified PDF.

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's Analysis, Volume I (1964): amazon link; Analysis, Volume II (1966): amazon link

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.

• Robert Clark James' University Mathematics (1963): amazon UK link, online view

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 (2004) Calculus: amazon link, online PDF

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).

I haven't read much of it yet, but here's the table of contents:

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

This book has now been published by Dover.