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1.

図書
図書
1. 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：
2.

図書
図書
2. From calculus to chaos : an introduction to dynamics (: hbk ; : pbk)
David Acheson
出版情報: Oxford : Oxford University Press, 1997  ix, 269 p. ; 24 cm
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目次情報: 続きを見る
Introduction / 1：
A Brief Review of Calculus / 2：
Ordinary Differential Equations / 3：
Computer Solution Methods / 4：
Elementary Oscillations / 5：
Planetary Motion / 6：
Waves and diffusion / 7：
The Best of all Possible Worlds? / 8：
Fluid Flow / 9：
Instability and Catastrophe / 10：
Nonlinear Oscillations and Chaos / 11：
The Not-so-simple Pendulum / 12：
Further reading
Elementary programming in QBASIC / Appendix A：
Ten programs for exploring dynamics / Appendix B：
Solutions to the exercises
Index
Introduction / 1：
A Brief Review of Calculus / 2：
Ordinary Differential Equations / 3：
3.

図書
図書
3. Calculus : a liberal art. 2nd ed
William McGowen Priestley
出版情報: New York : Springer, c1998  xvi, 401 p. ; 25 cm
シリーズ名: Undergraduate texts in mathematics
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4.

図書
図書
4. Introduction to calculus and analysis. Reprint of the 1989 ed (v. 1 ; v. II/1 ; v. II/2)
Richard Courant, Fritz John
出版情報: Berlin ; New York ; Tokyo : Springer-Verlag, c1999-c2000  3 v. ; 24-25 cm
シリーズ名: Classics in mathematics
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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
Functions of Several Variables and Their Derivatives: Points and Points Sets in the Plane and in Space
Functions of Several Independent Variables
Continuity
The Partial Derivatives of a Function
The Differential of a Function and Its Geometrical Meaning
Functions of Functions (Compound Functions) and the Introduction of New Independent Variables
The mean Value Theorem and Taylor's Theorem for Functions of Several Variables
Integrals of a Function Depending on a Parameter
Differentials and Line Integrals
The Fundamental Theorem on Integrability of Linear Differential Forms
Appendix.- Vectors, Matrices, Linear Transformations: Operatios with Vectors
Matrices and Linear Transformations
Determinants
Geometrical Interpretation of Determinants
Vector Notions in Analysis.- Developments and Applications of the Differential Calculus: Implicit Functions
Curves and Surfaces in Implicit Form
Systems of Functions, Transformations, and Mappings
Applications
Families of Curves, Families of Surfaces, and Their Envelopes
Alternating Differential Forms
Maxima and Minima
Appendix.- Multiple Integrals: Areas in the Plane
Double Integrals
Integrals over Regions in three and more Dimensions
Space Differentiation. Mass and Density
Reduction of the Multiple Integral to Repeated Single Integrals
Transformation of Multiple Integrals
Improper Multiple Integrals
Geometrical Applications
Physical Applications
Multiple Integrals in Curvilinear Coordinates
Volumes and Surface Areas in Any Number of Dimensions
Improper Single Integrals as Functions of a Parameter
The Fourier Integral
The Eulerian Integrals (Gamma Function)
Appendix
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
5.

図書
図書
5. Second year calculus : from celestial mechanics to special relativity (: us ; : gw)
David M. Bressoud
出版情報: New York ; Tokyo : Springer-Verlag, c1991  xi, 386 p. ; 24 cm
シリーズ名: Undergraduate texts in mathematics
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F=ma
Vector Algebra
Celestial Mathematics
Differential Forms
Line Integrals, Multiple Integrals
Linear Transformations
Differential Calculus
Integration by Pullback
Techniques of Differential Calculus
The Fundamental Theorem
E=mc^2
F=ma
Vector Algebra
Celestial Mathematics
6.

図書
図書
6. Calculus two : linear and nonlinear functions. 2nd ed. / revised by David L. Frank, Bert E. Fristedt, and Lawrence F. Gray (: us ; : gw)
Francis J. Flanigan, Jerry L. Kazdan
出版情報: New York : Springer-Verlag, c1990  xvii, 619 p. ; 25 cm
シリーズ名: Undergraduate texts in mathematics
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7.

図書
図書
7. Extensions of calculus
C. Goldsmith, D. Nelson
出版情報: Cambridge : Cambridge University Press, c1990  viii, 344 p. ; 23 cm
シリーズ名: SMP further mathematics series
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8.

図書
図書
8. Advanced mathematical methods (: pbk)
Adam Ostaszewski
出版情報: Cambridge ; New York : Cambridge University Press, 1990  xiii, 545 p. ; 23 cm
シリーズ名: LSE mathematical series
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Preface
Linear Algebra / Part I：
Vector spaces (revision) / 1：
Geometry in R / 2：
Matrices / 3：
Projections / 4：
Spectral theory / 5：
The upper triangular form / 6：
The tri-diagonal form / 7：
Inverses / 8：
Convexity / 9：
The separating hyperplane theorem / 10：
Linear inequalities / 11：
Linear programming and game theory / 12：
The simplex method / 13：
Partial derivatives (revision) / 14：
Convex functions / 15：
Non-linear programming / 16：
Advanced Calculus / Part II：
The integration process
Manipulation of integrals
Multiple integrals
Differential and difference equations (revision)
Laplace transforms
Series solutions of differential equations
Calculus of variations
Solutions to Selected Exercises / Part III：
Index
Preface
Linear Algebra / Part I：
Vector spaces (revision) / 1：
9.

図書
図書
9. On the refinement calculus (: us ; : gw)
edited by Carroll Morgan and Trevor Vickers
出版情報: London : Springer-Verlag, 1994  159 p. ; 25 cm
シリーズ名: Formal approaches to computing and information technology (FACIT)
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10.

図書
図書
10. Generalized fractional calculus and applications
Virginia Kiryakova
出版情報: Harlow, Essex, England : Longman Scientific & Technical , New York : Wiley, 1994  388 p. ; 25 cm
シリーズ名: Pitman research notes in mathematics series ; 301
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