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Gunter and Kuzmin: Collection of Problems in Higher Mathematics cover
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Gunter and Kuzmin: Collection of Problems in Higher Mathematics

by N. M. Gunter & R. O. Kuzmin

Translated by Valery Manokhin, PhD

The standard Russian problem collection for higher mathematics — the book used across Soviet technical universities. 814 pages spanning mathematical analysis, differential and integral calculus, series, differential equations, and probability theory, in the first complete English translation.

· 814 pages

Where this fits in school — US, UK and Canada ↓ Adults and self-learners welcome — great mathematics has no age limit.

$99.95 Buy Now — Paperback Amazon Paperback

Where this fits in school

Full curriculum table — every book by school year →
United StatesUniversity 1–4Parts I and II in one volume
United KingdomUndergraduateundergraduate
CanadaUniversity 1–4

How this book fits

See the whole sequence →

Work through first

Covers much of the same ground

These overlap heavily. Each note says what that book has which this one does not — the differences are what decide between them.

What comes next

Table of contents

148 section headings — the printed contents page in full.

Translator's Preface

Authorial Prefaces

Analytic Geometry in the Plane10 sections
  1. Vectors, Projections, And Coordinates In The Plane. Simplest Applications
  2. The Straight Line And The Circle
  3. Loci
  4. Curves Of The Second Order In Simplest Form
  5. Second-Order Curves Given By An Equation In General Form
  6. Center, Diameters. Simplification Of The Equations Of Second-Order Curves
  7. Conjugate Diameters. Axes Of Symmetry. Asymptotes
  8. Foci And Directrices
  9. Tangents To Second-Order Curves. Poles And Polars
  10. Miscellaneous Problems
Analytic Geometry in Space8 sections
  1. Vectors And Coordinates In Space
  2. Plane
  3. Line In Space
  4. Generation Of Surfaces
  5. Quadratic Surfaces. Center And Diametral Planes
  6. Tangent Planes And Lines To Quadratic Surfaces
  7. Simplification Of The Equations Of Quadric Surfaces
  8. Circular Sections, Rectilinear Generators, And Other Problems
Differential Calculus8 sections
  1. Theory Of Limits
  2. Miscellaneous Problems
  3. Finding Derivatives
  4. Geometric Meaning Of The Derivative
  5. Higher-Order Derivatives
  6. Functions Of Several Variables. Their Derivatives And Differentials
  7. Differentiation Of Implicit Functions
  8. Change Of Variables
Applications of Differential Calculus9 sections
  1. The Theorems Of Rolle, Lagrange, And Cauchy. Increasing And Decreasing Functions. Inequalities
  2. Finding The Greatest And Least Values Of Functions Of One Variable
  3. Plotting The Graphs Of Functions
  4. Miscellaneous Problems On Maximum And Minimum Values
  5. Series, Their Convergence
  6. Expansion Into Series
  7. Series And Operations With Them
  8. Evaluation Of Indeterminate Forms
  9. Extreme Values Of Functions Of Several Variables
Geometric Applications of Differential Calculus (Differential Geometry)11 sections
  1. Equations Of Curves And Their Forms
  2. Tangent And Normal
  3. Convexity, Curvature, And Radius Of Curvature
  4. Evolutes Of Curves
  5. Envelopes Of Curves
  6. Plotting Curves
  7. Curves Of Double Curvature: Tangent Line And Normal Plane
  8. Curves Of Double Curvature: Osculating Plane, Normal, And Binormal
  9. Surfaces. Their Equations
  10. Tangent Planes And Normals. Envelopes
  11. Curves On Surfaces And Curvature Of Surfaces
Higher Algebra9 sections
  1. Complex Numbers
  2. Factorization Of A Polynomial, Relation Between Coefficients And Roots
  3. Polynomial With Real Coefficients. Roll'S Theorem
  4. Rational Fractions. Partial-Fraction Decomposition
  5. Determinants. Systems Of Linear Equations
  6. Matrices. Characteristic Equation. Quadratic Forms
  7. Symmetric Functions
  8. Transformation And Solution Of Equations
  9. Separation And Computation Of Roots
Indefinite Integration5 sections
  1. Basic Formulas And Methods Of Integration
  2. Integration Of Rational Functions
  3. Integration Of Irrational Functions
  4. Integration Of Transcendental Functions
  5. Miscellaneous Problems
Definite Integrals and Plane-Geometric Applications5 sections
  1. The Definite Integral
  2. Calculation Of Areas
  3. Calculation Of Arc Lengths Of Curves
  4. Calculation Of Volumes
  5. Computation Of The Areas Of Surfaces Of Revolution
Multiple, Curvilinear, and Surface Integrals12 sections
  1. Introduction
  2. Computation Of Areas
  3. Computation Of Volumes
  4. Computation Of Surface Areas
  5. Line Integrals
  6. Some Applications Of Double Integrals In Mechanics And Strength Of Materials
  7. Surface Integrals, Coordinates Of Centers Of Gravity And Moments Of Inertia Of Surfaces
  8. Triple Integral
  9. Computation Of Volumes
  10. Coordinates Of Centers Of Gravity And Moments Of Inertia Of Bodies
  11. Integrals Of Field Theory And Potential Theory
  12. Multiple Integrals
Ordinary and Partial Differential Equations19 sections
  1. Forming Differential Equations From Their Given Integrals
  2. Finding Functions From Their Total Differential
  3. Integration Of Complete Differentials
  4. Equations With Separable Variables
  5. Homogeneous Equations And Those Reducible To Them
  6. Linear Equations And Those Reducible To Them
  7. The Riccati Equation
  8. The Jacobi Equation
  9. Integrating Factor
  10. Euler Equations
  11. Equations
  12. Singular Solutions Of Equations
  13. Problems On Trajectories
  14. Miscellaneous Problems
  15. Higher-Order Equations Admitting Reduction Of Order
  16. Linear Equations With Constant Coefficients And Equations Reducible To Them
  17. Linear Equations. Miscellaneous Problems
  18. Systems Of Differential Equations
  19. Linear Equations In Partial Derivatives Of The First Order
Improper Integrals, Beta/Gamma, Special Functions, Fourier Integrals9 sections
  1. The Definite Integral As The Limit Of A Sum
  2. Mean-Value Theorems. Improper Integrals
  3. Evaluation Of Definite Integrals By Integration And Substitutions
  4. Evaluation Of Integrals By Means Of Reduction Formulas
  5. Integration By Means Of Series
  6. Differentiation And Integration Under The Integral Sign
  7. Eulerian Integrals
  8. Miscellaneous Problems
  9. Fourier Series And Related Questions
Series and Fourier Series4 sections
  1. Investigation Of The Convergence Of Series
  2. Direct Summation Of Finite Sums And Infinite Series
  3. Finding Sums Of Series By Differentiation; Some Series Expansions
  4. Miscellaneous Problems
Approximate Computation7 sections
  1. Interpolation. Theory Of Errors
  2. Approximate Evaluation Of Integrals
  3. The Euler—Maclaurin Formula And Similar Methods
  4. Acceleration Of The Convergence Of Series
  5. Evaluation Of Integrals By Means Of Series
  6. Solution Of Numerical Equations
  7. Approximate Integration Of Differential Equations
Functions of a Complex Variable11 sections
  1. The Cauchy—Riemann Equations
  2. Singular Points Of A Function. The Taylor And Maclaurin Series
  3. Residues And Their Applications
  4. Distribution Of The Zeros Of The Function
  5. Expansion Of Functions Into Partial Fractions
  6. Other Expansions In Series
  7. Generating Functions And Special Polynomials
  8. Conformal Mappings
  9. The Maximum Modulus Principle
  10. Differential Equations For A Complex Variable
  11. Applications To Problems Of Mathematical Physics
Mathematical Physics — Partial Differential Equations8 sections
  1. Is Introductory In Character To The Principal Methods: The Method Of Characteristics And The Fourier Method, To Which § 15.3 And § 15.5 Are Devoted.
  2. —Integral Equations—Relates Chiefly To The Theory Of Linear Equations Of Fredholm Type.
  3. Formation Of Second-Order Partial Differential Equations
  4. Reduction Of Linear Equations Of The Second Order To Canonical Form
  5. The Method Of Characteristics
  6. Riemann’S Method
  7. Fourier Method
  8. Integral Equations
Calculus of Variations8 sections
  1. Euler—Lagrange Equations
  2. Necessary And Sufficient Conditions For The Simplest Problem Of The Calculus Of Variations
  3. Parametric Form Of Integrals, Transversality
  4. The Hamilton—Jacobi Equation
  5. Integrals Depending On Higher-Order Derivatives Or On Several Functions
  6. Discontinuous Solutions. One-Sided Variation
  7. Multiple Integrals
  8. Isoperimetric Problems
Probability Theory5 sections
  1. Is Devoted To Problems On The Calculation Of Geometric Probabilities. In This Paragraph Attention Is Paid To The Construction Of Distribution Curves, And Examples Are Given Of The Calculation Of The Characteristic Function.
  2. Application Of The Basic Theorems. Bayes'S Formula
  3. Mathematical Expectations. The Method Of Finite Differences And Generating Functions
  4. Bernoulli'S Theorem. Chebyshev'S Inequalities
  5. Laplace'S And Lyapunov—Markov'S Theorems

Answers

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Formats and editions

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Product details

Publisher
Northern Star Academic Press
Language
English
Translator
Valery Manokhin, PhD
Print length
814 pages
First published
2026-08-18

Published by Northern Star Academic Press · First faithful English translation from the original Russian edition

Browse the full Russian Math Classics series on Amazon →

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