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Results from One-Variable Calculus
2016This chapter gives a quick review of the real number system and of the foundational and basic theorems of one-variable calculus, and then it proceeds to a more extensive discussion of Taylor’s theorem.
J. Shurman
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Fractional non-Archimedean calculus in one variable
P-Adic Numbers, Ultrametric Analysis, and Applications, 2012Let r ≥ 0 be a real number. We will introduce a notion of r-fold differentiability for functions in many variables over a non-Archimedeanly valued complete field K and then examine properties of theirs such as localness, completeness as a locally convex K-algebra, density of (locally) polynomial functions, closure under composition and, for the dual ...
E. Nagel
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Integral Calculus of Functions of One Variable
2016A function \(f:{\mathbb {T}}\rightarrow {\mathbb {R}}\) is called regulated provided its right-sided limits exist (finite) at all right-dense points in \({\mathbb {T}}\) and its left-sided limits exist (finite) at all left-dense points in \({\mathbb {T}}\).
Martin Bohner, Svetlin G. Georgiev
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On formulas of one variable in intuitionistic propositional calculus
Journal of Symbolic Logic, 1960McKinsey and Tarski [3] described Gödel's proof that the number of Brouwerian-algebraic functions is infinite. They gave an example of a sequence of infinitely many distinct Brouwerian-algebraic functions of one argument, which means that there are infinitely many non-equivalent formulas of one variable in the intuitionistic propositional calculus LJ ...
Iwao Nishimura
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Integral Calculus of Functions of One Variable
1994The function F x) is said to be a primitive primitive function indefinite integral) of the function f x) in the interval (a b), if the relation F′(x f x) holds for all x ∈ (a ...
K. Rektorys
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A proof of the completeness of the infinite-valued calculus of Łukasiewicz with one variable
1995In the literature one can find three quite different proofs of the completeness of the infinite-valued sentential calculus of Lukasiewicz [8]: (i). the syntactical proof of Rose and Rosser [7], using McNaughton’s theorem, (ii). the algebraic proof of Chang [1, 2], using quantifier elimination in the first-order theory of divisible ...
MUNDICI, DANIELE, M. PASQUETTO
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Calculus, Volume 1 (One Variable Calculus, with an Introduction to Linear Algebra).
The American Mathematical Monthly, 1970E. D. Bolker, Tom M. Apostol
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Calculus of One Variable. By J. W. KitchenJr. Pp. xiii, 785. 78s. 1968. (Addison-Wesley.)
The Mathematical Gazette, 1969W. Ferrar, J. Jr.
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