Fikhtengol'ts' Foundations of Mathematical Analysis, Volume I
by G. M. Fikhtengol'ts
Translated by Valery Manokhin, PhD
The university course in mathematical analysis by the founder of the Leningrad school of the theory of functions, in first faithful English translation from the original Russian edition. Fourteen chapters run from the real numbers through functions, limits and the number e, continuity, the derivative and the differential, the mean-value theorems and Taylor's formula, the study of functions by their derivatives, functions of several variables and their differentiation and extrema, the indefinite and the definite integral, geometric and mechanical applications, curvature, and a historical survey of the origins of analysis from its prehistory to Newton and Leibniz. 390 pages with an alphabetical index.
14 chapters· 390 pages
Where this fits in school — US, UK and Canada ↓Adults and self-learners welcome — great mathematics has no age limit.
Where this fits in school
Full curriculum table — every book by school year →| United States | University 1–2 | Calculus I–III and introductory real analysis |
|---|---|---|
| England | Undergraduate 1–2 | first- and second-year real analysis and multivariable calculus |
| Canada (Ontario) | University 1–2 | QC CEGEP 201-NYA / NYB · first- and second-year university calculus and analysis |
How this book fits
See the whole sequence →Work through first
- Kiselev's Calculus$54.95
Problems to work alongside it
- Gunter & Kuzmin$99.95
What comes next
Further reading
A historical text to read beside the course, not a substitute for it.
Table of contents
43 section headings — the printed contents page in full.
Translator's Preface
Real Numbers3 sections
- The Set of Real Numbers and Its Ordering
- Arithmetic Operations on Real Numbers
- Further Properties and Applications of Real Numbers
Functions of One Variable2 sections
- The Concept of Function
- The Most Important Classes of Functions
Theory of Limits6 sections
- Limit of a Function
- Theorems on Limits
- Monotone Function
- The Number e
- Convergence Principle
- Classification of Infinitesimal and Infinitely Large Quantities
Continuous Functions of One Variable2 sections
- Continuity (and Discontinuities) of a Function
- Properties of Continuous Functions
Differentiation of Functions of One Variable3 sections
- Derivative and Its Computation
- Differential
- Derivatives and Differentials of Higher Orders
Fundamental Theorems of Differential Calculus2 sections
- Mean Value Theorems
- Taylor's Formula
Investigation of Functions by Means of Derivatives3 sections
- Study of the Course of Variation of a Function
- Greatest and Least Values of a Function
- Removal of Indeterminate Forms
Functions of Several Variables2 sections
- Fundamental Concepts
- Continuous Functions
Differentiation of Functions of Several Variables3 sections
- Derivatives and Differentials of Functions of Several Variables
- Derivatives and Differentials of Higher Orders
- Extrema, Greatest and Least Values
Primitive Function (Indefinite Integral)5 sections
- Indefinite Integral and the Simplest Methods of Its Evaluation
- Integration of Rational Expressions
- Integration of Certain Expressions Containing Radicals
- Integration of Expressions Containing Trigonometric and Exponential Functions
- Elliptic Integrals
Definite Integral4 sections
- Definition and Conditions for the Existence of the Definite Integral
- Properties of Definite Integrals
- Evaluation and Transformation of Definite Integrals
- Approximate Evaluation of Integrals
Geometric and Mechanical Applications of Integral Calculus3 sections
- Areas and Volumes
- Arc Length
- Evaluation of Mechanical and Physical Quantities
Some Geometric Applications of Differential Calculus2 sections
- Tangent and Tangent Plane
- Curvature of a Plane Curve
Historical Survey of the Origin of the Fundamental Ideas of Mathematical Analysis3 sections
- Prehistory of Differential and Integral Calculus
- Isaac Newton (1642–1727)
- Gottfried Wilhelm Leibniz (1646–1716)
Formats and editions
| Format | Price | ISBN-13 | Where | Buy |
|---|---|---|---|---|
| Kindle | $69.95 | — | Amazon | Buy → |
| Paperback | $79.95 | 978-1-80910-054-2 | Amazon | Buy → |
| Hardcover | $99.95 | 978-1-80910-055-9 | Amazon | Buy → |
Prices are the publisher list prices. Amazon sets the final price in each store.
Product details
- Publisher
- Northern Star Academic Press
- Language
- English
- Translator
- Valery Manokhin, PhD
- Print length
- 390 pages
- First published
- 2026-10-15
Published by Northern Star Academic Press · First faithful English translation from the original Russian edition
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