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1.

図書
図書
1. A student's guide to infinite series and sequences (: hardback ; : pbk)
Bernhard W. Bach Jr.
出版情報: Cambridge, U.K. : Cambridge University Press, 2018  v. ; 23-24 cm
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2.

図書
図書
2. Introduction to real analysis
Liviu I. Nicolaescu
出版情報: Hackensack, N.J. : World Scientific, c2020  xv, 665 p. ; 25 cm
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3.

図書
図書
3. Calculus with analytic geometry. 2nd., International ed
George F. Simmons
出版情報: New York : McGraw-Hill, c1996  xxiii, 887 p. ; 27 cm
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目次情報: 続きを見る
Numbers, Functions, and Graphs / Chapter 1：
Introduction / 1-1：
The Real Line and Coordinate Plane: Pythagoras / 1-2：
Slopes and Equations of Straight Lines / 1-3：
Circles and Parabolas: Descartes and Fermat / 1-4：
The Concept of a Function / 1-5：
Graphs of Functions / 1-6：
Introductory Trigonometry / 1-7：
The Functions Sin O and Cos O / 1-8：
The Derivative of a Function / Chapter 2：
What is Calculus ? / 2-0：
The Problems of Tangents / 2-1：
How to Calculate the Slope of the Tangent / 2-2：
The Definition of the Derivative / 2-3：
Velocity and Rates of Change: Newton and Leibriz / 2-4：
The Concept of a Limit: Two Trigonometric Limits / 2-5：
Continuous Functions: The Mean Value Theorem and Other Theorem / 2-6：
The Computation of Derivatives / Chapter 3：
Derivatives of Polynomials / 3-1：
The Product and Quotient Rules / 3-2：
Composite Functions and the Chain Rule / 3-3：
Some Trigonometric Derivatives / 3-4：
Implicit Functions and Fractional Exponents / 3-5：
Derivatives of Higher Order / 3-6：
Applications of Derivatives / Chapter 4：
Increasing and Decreasing Functions: Maxima and Minima / 4-1：
Concavity and Points of Inflection / 4-2：
Applied Maximum and Minimum Problems / 4-3：
More Maximum-Minimum Problems / 4-4：
Related Rates / 4-5：
Newtons Method for Solving Equations / 4-6：
Applications to Economics: Marginal Analysis / 4-7：
Indefinite Integrals and Differential Equations / Chapter 5：
Differentials and Tangent Line Approximations / 5-1：
Indefinite Integrals: Integration by Substitution / 5-3：
Differential Equations: Separation of Variables / 5-4：
Motion Under Gravity: Escape Velocity and Black Holes / 5-5：
Definite Integrals / Chapter 6：
The Problem of Areas / 6-1：
The Sigma Notation and Certain Special Sums / 6-3：
The Area Under a Curve: Definite Integrals / 6-4：
The Computation of Areas as Limits / 6-5：
The Fundamental Theorem of Calculus / 6-6：
Properties of Definite Integrals / 6-7：
Applications of Integration / Chapter 7：
Introduction: The Intuitive Meaning of Integration / 7-1：
The Area between Two Curves / 7-2：
Volumes: The Disk Method / 7-3：
Volumes: The Method of Cylindrical Shells / 7-4：
Arc Length / 7-5：
The Area of a Surface of Revolution / 7-6：
Work and Energy / 7-7：
Hydrostatic Force PART II / 7-8：
Exponential and Logarithm Functions / Chapter 8：
Review of Exponents and Logarithms / 8-1：
The Number e and the Function y = e x / 8-3：
The Natural Logarithm Function y = ln x / 8-4：
Applications Population Growth and Radioactive Decay / 8-5：
More Applications / 8-6：
Trigonometric Functions / Chapter 9：
Review of Trigonometry / 9-1：
The Derivatives of the Sine and Cosine / 9-2：
The Integrals of the Sine and Cosine / 9-3：
The Derivatives of the Other Four Functions / 9-4：
The Inverse Trigonometric Functions / 9-5：
Simple Harmonic Motion / 9-6：
Hyperbolic Functions / 9-7：
Methods of Integration / Chapter 10：
The Method of Substitution / 10-1：
Certain Trigonometric Integrals / 10-3：
Trigonometric Substitutions / 10-4：
Completing the Square / 10-5：
The Method of Partial Fractions / 10-6：
Integration by Parts / 10-7：
A Mixed Bag / 10-8：
Numerical Integration / 10-9：
Further Applications of Integration / Chapter 11：
The Center of Mass of a Discrete System / 11-1：
Centroids / 11-2：
The Theorems of Pappus / 11-3：
Moment of Inertia / 11-4：
Indeterminate Forms and Improper Integrals / Chapter 12：
Introduction. The Mean Value Theorem Revisited / 12-1：
The Interminate Form 0/0. L'Hospital's Rule / 12-2：
Other Interminate Forms / 12-3：
Improper Integrals / 12-4：
The Normal Distribution / 12-5：
Infinite Series of Constants / Chapter 13：
What is an Infinite Series ? / 13-1：
Convergent Sequences / 13-2：
Convergent and Divergent Series / 13-3：
General Properties of Convergent Series / 13-4：
Series on Non-negative Terms: Comparison Test / 13-5：
Numbers, Functions, and Graphs / Chapter 1：
Introduction / 1-1：
The Real Line and Coordinate Plane: Pythagoras / 1-2：
4.

図書
図書
4. Advanced calculus : an introduction to modern analysis
William L. Voxman, Roy H. Goetschel, Jr.
出版情報: New York : M. Dekker, c1981  xii, 678 p. ; 24 cm
シリーズ名: Monographs and textbooks in pure and applied mathematics ; 63
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5.

図書
図書
5. Calculus of several variables and differentiable manifolds
[by] Carl B. Allendoerfer
出版情報: New York : Macmillan, [1974]  xi, 227 p. ; 26 cm
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6.

図書
図書
6. Mathematics of Kalman-Bucy filtering. 2nd ed (: U.S. ; : Germany)
P.A. Ruymgaart, T.T. Soong
出版情報: Berlin ; Tokyo : Springer-Verlag, c1988  xii, 170 p. ; 24 cm
シリーズ名: Springer series in information sciences ; 14
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7.

図書
図書
7. Multivariable analysis
G. Baley Price
出版情報: New York : Springer-Verlag, c1984  xiv, 655 p. ; 24 cm
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8.

図書
図書
8. Vector calculus. 2nd ed
Jerrold E. Marsden, Anthony J. Tromba ; with the assistance of Michael Hoffman and Joanne Seitz
出版情報: San Francisco : W.H. Freeman and Co., c1981  xviii, 591 p. ; 24 cm
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目次情報: 続きを見る
The Geometry of Euclidean Space / 1：
Vectors in Two- and Three-Dimensional Space / 1.1：
The Inner Product, Length, and Distance / 1.2：
Matrices, Determinants, and the Cross Product / 1.3：
Cylindrical and Spherical Coordinates / 1.4：
n-Dimensional Euclidean Space / 1.5：
Differentiation Space / 2：
The Geometry of Real-Valued Functions / 2.1：
Limits and Continuity / 2.2：
Differentiation / 2.3：
Introduction to Paths / 2.4：
Properties of the Derivative / 2.5：
Gradients and Directional Derivatives / 2.6：
Higher-Order Derivatives: Maxima and Minima / 3：
Iterated Partial Derivatives / 3.1：
Taylor's Theorem / 3.2：
Extrema of Real-Valued Functions / 3.3：
Constrained Extrema and Lagrange Multipliers / 3.4：
The Implicit Function Theorem / 3.5：
Vector-Valued Functions / 4：
Acceleration and Newton's Second Law / 4.1：
Arc Length / 4.2：
Vector Fields / 4.3：
Divergence and Curl / 4.4：
Double and Triple Integrals / 5：
Introduction / 5.1：
The Double Integral Over a Rectangle / 5.2：
The Double Integral Over More General Regions / 5.3：
Changing the Order of Integration / 5.4：
The Triple Integral / 5.5：
The Change of Variables Formula and Applications of Integration / 6：
The Geometry of Maps from R2 to R2 / 6.1：
The Change of Variables Theorem / 6.2：
Applications of Double and Triple / 6.3：
Improper Integrals / 6.4：
Integrals / 7：
The Path Integral / 7.1：
Line Integrals / 7.2：
Parametrized Surfaces / 7.3：
Area of a Surface / 7.4：
Integrals of Scalar Functions Over Surfaces / 7.5：
Surface Integrals of Vector Functions / 7.6：
Applications to Differential Geometry, Physics and Forms of Life / 7.7：
The Integral Theorems of Vector Analysis / 8：
Green's Theorem / 8.1：
Stokes' Theorem / 8.2：
Conservative Fields / 8.3：
Gauss' Theorem / 8.4：
Applications to Physics, Engineering, and Differential Equations / 8.5：
Differential Forms / 8.6：
The Geometry of Euclidean Space / 1：
Vectors in Two- and Three-Dimensional Space / 1.1：
The Inner Product, Length, and Distance / 1.2：
9.

図書
図書
9. Much ado about calculus : a modern treatment with applications prepared for use with the computer (: us ; : gw)
Robert L. Wilson
出版情報: New York : Springer-Verlag, c1979  xvii, 788 p. ; 25 cm
シリーズ名: Undergraduate texts in mathematics
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10.

図書
図書
10. Introduction to calculus and analysis (v. 1 - v. 2. : pbk)
Richard Courant and Fritz John, with the assistance of Albert A. Blank, Alan Solomon
出版情報: New York : Interscience Publishers, 1965-1974  2 v. ; 24 cm
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目次情報: 続きを見る
Relations Between Surface and Volume Integrals: Connection Between Line Integrals and Double Integrals in the Plane
Vector Form of the Divergence Theorem / Stokes's Theorem
Formula for Integration by Parts in Two Dimensions: / Green's Theorem
The Divergence Theorem Applied to the Transformation of Double Integrals
Area Differentiation
Interpretation of the Formulae of Gauss and Stokes by Two-Dimensional Flows
Orientation of Surfaces
Integrals of Differential Forms and of Scalars over Surfaces
Gauss's and Green's Theorems in Space
Appendix: General Theory of Surfaces and of Surface Integrals.- Differential Equations: The Differential Equations for the Motion of a Particle in Three Dimensions
The General Linear Differential Equation of the First Order
Linear Differential Equations of Higher Order
General Differential Equations of the First Order
Systems of Differential Equations and Differential Equations of Higher Order
Integration by the Method of Undermined Coefficients
The Potential of Attracting Charges and Laplace's Equation
Further Examples of Partial Differential Equations from Mathematical Physics
Calculus of Variations: Functions and Their Extreme Values of a Functional
Generalizations
Problems Involving Subsidiary Conditions. Lagrange Multipliers
Functions of a Complex Variable: Complex Functions Represented by Power Series
Foundations of the General Theory of Functions of a Complex Variable
The Integration of Analytic Functions
Cauchy's Formula and Its Applications
Applications to Complex Integration (Contour Integration)
Many-Valued Functions and Analytic Extension.
List of Biographical Dates
Index
Relations Between Surface and Volume Integrals: Connection Between Line Integrals and Double Integrals in the Plane
Vector Form of the Divergence Theorem / Stokes's Theorem
Formula for Integration by Parts in Two Dimensions: / Green's Theorem
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