Fikhtengol'ts' Foundations of Mathematical Analysis, Volume II
by G. M. Fikhtengol'ts
Translated by Valery Manokhin, PhD
The second volume of the university course in mathematical analysis by the founder of the Leningrad school of the theory of functions, in a faithful new English edition. Ten chapters continue directly from Volume I: numerical series and infinite products; sequences and series of functions, power series and approximate computation; improper integrals and integrals depending on a parameter, with the Eulerian integrals; implicit functions and functional determinants; line, double, surface and triple integrals, the formulas of Green, Ostrogradsky and Stokes, and the elements of field theory; Fourier series and the Fourier integral. A concluding sketch points towards differential equations, the calculus of variations, complex and real analysis and functional analysis. 192 numbered articles (Nos. 234–425), 88 figures, 412 pages with an alphabetical index.
10 chapters· 412 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 II–III, vector calculus and introductory real analysis |
|---|---|---|
| England | Undergraduate 1–2 | second-year real analysis, multivariable and vector calculus, Fourier series |
| Canada (Ontario) | University 1–2 | QC CEGEP 201-NYB / 201-NYC · second-year university calculus and analysis |
How this book fits
See the whole sequence →Work through first
Problems to work alongside it
- Gunter & Kuzmin$99.95
Further reading
A historical text to read beside the course, not a substitute for it.
Table of contents
48 section headings — the printed contents page in full.
Translator's Preface
Numerical Series7 sections
- Introduction
- Convergence of Positive Series
- Convergence of Arbitrary Series
- Properties of Convergent Series
- Infinite Products
- Expansions of Elementary Functions in Power Series
- Approximate Calculations by Means of Series
Functional Sequences and Series4 sections
- Uniform Convergence
- Functional Properties of the Sum of a Series
- Power Series and Series of Polynomials
- A Sketch of the History of Series
Improper Integrals3 sections
- Improper Integrals with Infinite Limits
- Improper Integrals of Unbounded Functions
- Transformation and Evaluation of Improper Integrals
Integrals Depending on a Parameter4 sections
- Elementary Theory
- Uniform Convergence of Integrals
- Use of the Uniform Convergence of Integrals
- Eulerian Integrals
Implicit Functions. Functional Determinants3 sections
- Implicit Functions
- Some Applications of the Theory of Implicit Functions
- Functional Determinants and Their Formal Properties
Line Integrals2 sections
- Line Integrals of the First Type
- Line Integrals of the Second Type
Double Integrals5 sections
- Definition and Simplest Properties of Double Integrals
- Evaluation of a Double Integral
- Green's Formula
- Conditions for the Independence of a Line Integral from the Path of Integration
- Change of Variables in Double Integrals
Area of a Surface. Surface Integrals4 sections
- Two-Sided Surfaces
- Area of a Curved Surface
- Surface Integrals of the First Type
- Surface Integrals of the Second Type
Triple Integrals5 sections
- The Triple Integral and Its Evaluation
- Ostrogradsky's Formula
- Change of Variables in Triple Integrals
- Elements of Field Theory
- Multiple Integrals
Fourier Series5 sections
- Introduction
- Expansion of Functions in Fourier Series
- Fourier Integral
- Closedness and Completeness of the Trigonometric System of Functions
- A Sketch of the History of Trigonometric Series
Conclusion. A Sketch of the Further Development of Mathematical Analysis6 sections
- The Theory of Differential Equations
- The Calculus of Variations
- The Theory of Functions of a Complex Variable
- The Theory of Integral Equations
- The Theory of Functions of a Real Variable
- Functional Analysis
Alphabetical Index
Formats and editions
| Format | Price | ISBN-13 | Where | Buy |
|---|---|---|---|---|
| Paperback | $74.95 | 978-1-80910-056-6 | 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
- 412 pages
- First published
- 2026-10-28
Published by Northern Star Academic Press · First faithful English translation from the original Russian edition
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