Gunter e Kuzmin: Coleção de Problemas de Matemática Superior, Parte I
por N. M. Gunter & R. O. Kuzmin
Traduzido por Valery Manokhin, PhD
A primeira metade do livro russo padrão de problemas de matemática superior, como volume independente: geometria analítica no plano e no espaço, cálculo diferencial e suas aplicações incluindo geometria diferencial, álgebra superior, e integração indefinida e definida. 448 páginas.
🇺🇸 University level (analytic geometry, differential calculus, higher algebra, integration)
🇬🇧 University level
🇨🇦 University level
Adultos e autodidatas são bem-vindos — a grande matemática não tem limite de idade.
Sumário
11 capítulos, 77 seções — o sumário completo do livro impresso.
Translator's Preface
Analytic Geometry in the Plane10 seções
- 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 seções
- 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 seções
- 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 seções
- 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 seções
- 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 seções
- 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 seções
- 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 seções
- 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 seções
- 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
Formatos e edições
| Formato | Preço | ISBN-13 | Onde | Comprar |
|---|---|---|---|---|
| Brochura | $64.95 | 978-1-919012-33-9 | Amazon | Comprar → |
| Capa dura | $99.95 | 978-1-919012-34-6 | Amazon | Comprar → |
Os preços são os de tabela da editora. A Amazon define o preço final em cada loja.
Detalhes do produto
- Editora
- Northern Star Academic Press
- Idioma
- English
- Tradutor
- Valery Manokhin, PhD
- Extensão
- 448 páginas
- Primeira publicação
- 2026-08-25
Publicado por Northern Star Academic Press · Primeira tradução fiel da edição original russa
Mais Desta Série
1001 Problemas de Rachinsky
por S. A. Rachinsky
Mental arithmetic practice · Flexible level
1.001 problemas cuidadosamente selecionados do professor rural cujos alunos foram retratados na famosa pintura de 1895 "Aritmética Mental."
Aritmética Recreativa
por Ya. I. Perelman
Recreational arithmetic · All levels
O clássico da matemática popular russa. Quebra-cabeças, enigmas e curiosidades que tornam a aritmética verdadeiramente divertida.
Markov: Probabilidades
por Andrei A. Markov
University level
A obra fundacional de 1900 sobre a teoria da probabilidade pelo matemático que nos deu as cadeias de Markov.