Gunter and Kuzmin: Collection of Problems in Higher Mathematics, Part I
by N. M. Gunter & R. O. Kuzmin
Translated by Valery Manokhin, PhD
The first half of the standard Russian problem book for higher mathematics, as a volume on its own: analytic geometry in the plane and in space, differential calculus and its applications including differential geometry, higher algebra, and indefinite and definite integration. 448 pages.
🇺🇸 University level (analytic geometry, differential calculus, higher algebra, integration)
🇬🇧 University level
🇨🇦 University level
Adults and self-learners welcome — great mathematics has no age limit.
Table of contents
11 chapters, 77 sections — the full contents of the printed book.
Translator's Preface
Analytic Geometry in the Plane10 sections
- Vectors, Projections, And Coordinates In The Plane. Simplest Applications
- The Straight Line And The Circle
- Loci
- Curves Of The Second Order In Simplest Form
- Second-Order Curves Given By An Equation In General Form
- Center, Diameters. Simplification Of The Equations Of Second-Order Curves
- Conjugate Diameters. Axes Of Symmetry. Asymptotes
- Foci And Directrices
- Tangents To Second-Order Curves. Poles And Polars
- Miscellaneous Problems
Analytic Geometry in Space8 sections
- Vectors And Coordinates In Space
- Plane
- Line In Space
- Generation Of Surfaces
- Quadratic Surfaces. Center And Diametral Planes
- Tangent Planes And Lines To Quadratic Surfaces
- Simplification Of The Equations Of Quadric Surfaces
- Circular Sections, Rectilinear Generators, And Other Problems
Differential Calculus8 sections
- Theory Of Limits
- Miscellaneous Problems
- Finding Derivatives
- Geometric Meaning Of The Derivative
- Higher-Order Derivatives
- Functions Of Several Variables. Their Derivatives And Differentials
- Differentiation Of Implicit Functions
- Change Of Variables
Applications of Differential Calculus9 sections
- The Theorems Of Rolle, Lagrange, And Cauchy. Increasing And Decreasing Functions. Inequalities
- Finding The Greatest And Least Values Of Functions Of One Variable
- Plotting The Graphs Of Functions
- Miscellaneous Problems On Maximum And Minimum Values
- Series, Their Convergence
- Expansion Into Series
- Series And Operations With Them
- Evaluation Of Indeterminate Forms
- Extreme Values Of Functions Of Several Variables
Geometric Applications of Differential Calculus (Differential Geometry)11 sections
- Equations Of Curves And Their Forms
- Tangent And Normal
- Convexity, Curvature, And Radius Of Curvature
- Evolutes Of Curves
- Envelopes Of Curves
- Plotting Curves
- Curves Of Double Curvature: Tangent Line And Normal Plane
- Curves Of Double Curvature: Osculating Plane, Normal, And Binormal
- Surfaces. Their Equations
- Tangent Planes And Normals. Envelopes
- Curves On Surfaces And Curvature Of Surfaces
Higher Algebra9 sections
- Complex Numbers
- Factorization Of A Polynomial, Relation Between Coefficients And Roots
- Polynomial With Real Coefficients. Roll'S Theorem
- Rational Fractions. Partial-Fraction Decomposition
- Determinants. Systems Of Linear Equations
- Matrices. Characteristic Equation. Quadratic Forms
- Symmetric Functions
- Transformation And Solution Of Equations
- Separation And Computation Of Roots
Indefinite Integration5 sections
- Basic Formulas And Methods Of Integration
- Integration Of Rational Functions
- Integration Of Irrational Functions
- Integration Of Transcendental Functions
- Miscellaneous Problems
Definite Integrals and Plane-Geometric Applications5 sections
- The Definite Integral
- Calculation Of Areas
- Calculation Of Arc Lengths Of Curves
- Calculation Of Volumes
- Computation Of The Areas Of Surfaces Of Revolution
Multiple, Curvilinear, and Surface Integrals12 sections
- Introduction
- Computation Of Areas
- Computation Of Volumes
- Computation Of Surface Areas
- Line Integrals
- Some Applications Of Double Integrals In Mechanics And Strength Of Materials
- Surface Integrals, Coordinates Of Centers Of Gravity And Moments Of Inertia Of Surfaces
- Triple Integral
- Computation Of Volumes
- Coordinates Of Centers Of Gravity And Moments Of Inertia Of Bodies
- Integrals Of Field Theory And Potential Theory
- Multiple Integrals
Answers
Formats and editions
| Format | Price | ISBN-13 | Where | Buy |
|---|---|---|---|---|
| Paperback | $64.95 | 978-1-919012-33-9 | Amazon | Buy → |
| Hardcover | $99.95 | 978-1-919012-34-6 | 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
- 448 pages
- First published
- 2026-08-25
Published by Northern Star Academic Press · First faithful English translation from the original Russian edition
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