Calculus

著者

• Marsden, Jerrold E.
• Weinstein, Alan

書誌事項

Calculus

Jerrold Marsden, Alan Weinstein

（Undergraduate texts in mathematics）

Springer-Verlag, c1985

2nd ed

• 1 : us
• 1 : gw
• 2 : us
• 2 : gw
• 3 : us
• 3 : gw

注記

Previous ed., published in 1980

"AMS subject classification: 26-01"--T.p. verso

Includes index

内容説明・目次

巻冊次

1 : us ISBN 9780387909745

内容説明

The goal of this text is to help students learn to use calculus intelligently for solving a wide variety of mathematical and physical problems. This book is an outgrowth of our teaching of calculus at Berkeley, and the present edition incorporates many improvements based on our use of the first edition. We list below some of the key features of the book. Examples and Exercises The exercise sets have been carefully constructed to be of maximum use to the students. With few exceptions we adhere to the following policies. * The section exercises are graded into three consecutive groups: (a) The first exercises are routine, modelled almost exactly on the exam ples; these are intended to give students confidence. (b) Next come exercises that are still based directly on the examples and text but which may have variations of wording or which combine different ideas; these are intended to train students to think for themselves. (c) The last exercises in each set are difficult. These are marked with a star (*) and some will challenge even the best students. Difficult does not necessarily mean theoretical; often a starred problem is an interesting application that requires insight into what calculus is really about. * The exercises come in groups of two and often four similar ones.

目次

Orientation Quizzes.- R Review of Fundamentals.- R.1 Basic Algebra: Real Numbers and Inequalities.- R.2 Intervals and Absolute Values.- R.3 Laws of Exponents.- R.4 Straight Lines.- R.5 Circles and Parabolas.- R.6 Functions and Graphs.- 1 Derivatives and Limits.- 1.1 Introduction to the Derivative.- 1.2 Limits.- 1.3 The Derivative as a Limit and the Leibniz Notation.- 1.4 Differentiating Polynomials.- 1.5 Products and Quotients.- 1.6 The Linear Approximation and Tangent Lines.- 2 Rates of Change and the Chain Rule.- 2.1 Rates of Change and the Second Derivative.- 2.2 The Chain Rule.- 2.3 Fractional Powers and Implicit Differentiation.- 2.4 Related Rates and Parametric Curves.- 2.5 Antiderivatives.- 3 Graphing and Maximum-Minimum Problems.- 3.1 Continuity and the Intermediate Value Theorem.- 3.2 Increasing and Decreasing Functions.- 3.3 The Second Derivative and Concavity.- 3.4 Drawing Graphs.- 3.5 Maximum-Minimum Problems.- 3.6 The Mean Value Theorem.- 4 The Integral.- 4.1 Summation.- 4.2 Sums and Areas.- 4.3 The Definition of the Integral.- 4.4 The Fundamental Theorem of Calculus.- 4.5 Definite and Indefinite Integrals.- 4.6 Applications of the Integral.- 5 Trigonometric Functions.- 5.1 Polar Coordinates and Trigonometry.- 5.2 Differentiation of the Trigonometric Functions.- 5.3 Inverse Functions.- 5.4 The Inverse Trigonometric Functions.- 5.5 Graphing and Word Problems.- 5.6 Graphing in Polar Coordinates.- 6 Exponentials and Logarithms.- 6.1 Exponential Functions.- 6.2 Logarithms.- 6.3 Differentiation of the Exponential and Logarithmic Functions.- 6.4 Graphing and Word Problems.- Answers A.1.- Index I.1.

巻冊次

2 : us ISBN 9780387909752

内容説明

The second of a three-volume work, this is the result of the authors'experience teaching calculus at Berkeley. The book covers techniques and applications of integration, infinite series, and differential equations, the whole time motivating the study of calculus using its applications. The authors include numerous solved problems, as well as extensive exercises at the end of each section. In addition, a separate student guide has been prepared.

目次

7 Basic Methods of Integration.- 7.1 Calculating Integrals.- 7.2 Integration by Substitution.- 7.3 Changing Variables in the Definite Integral.- 7.4 Integration by Parts.- 8 Differential Equations.- 8.1 Oscillations.- 8.2 Growth and Decay.- 8.3 The Hyperbolic Functions.- 8.4 The Inverse Hyperbolic Functions.- 8.5 Separable Differential Equations.- 8.6 Linear First-Order Equations.- 9 Applications of Integration.- 9.1 Volumes by the Slice Method.- 9.2 Volumes by the Shell Method.- 9.3 Average Values and the Mean Value Theorem for Integrals.- 9.4 Center of Mass.- 9.5 Energy, Power, and Work.- 10 Further Techniques and Applications of Integration.- 10.1 Trigonometric Integrals.- 10.2 Partial Fractions.- 10.3 Arc Length and Surface Area.- 10.4 Parametric Curves.- 10.5 Length and Area in Polar Coordinates.- 11 Limits, L'Hopital's Rule, and Numerical Methods.- 11.1 Limits of Functions.- 11.2 L'Hopital's Rule.- 11.3 Improper Integrals.- 11.4 Limits of Sequences and Newton's Method.- 11.5 Numerical Integration.- 12 Infinite Series.- 12.1 The Sum of an Infinite Series.- 12.2 The Comparison Test and Alternating Series.- 12.3 The Integral and Ratio Tests.- 12.4 Power Series.- 12.5 Taylor's Formula.- 12.6 Complex Numbers.- 12.7 Second-Order Linear Differential Equations.- 12.8 Series Solutions of Differential Equations.- Answers.

巻冊次

3 : us ISBN 9780387909851

内容説明

The third of a three-volume work, this book is the outgrowth of the authors' experience teaching calculus at Berkeley. It covers multivariable calculus and begins with the necessary material from analytical geometry. It goes on to cover partial differention, the gradient and its applications, multiple integration, and the theorems of Green, Gauss and Stokes. The authors motivate the study of calculus using its applications. Features many solved problems and extensive exercises.

目次

13 Vectors.- 13.1 Vectors in the Plane.- 13.2 Vectors in Space.- 13.3 Lines and Distance.- 13.4 The Dot Product.- 13.5 The Cross Product.- 13.6 Matrices and Determinants.- 14 Curves and Surfaces.- 14.1 The Conic Sections.- 14.2 Translation and Rotation of Axes.- 14.3 Functions, Graphs, and Level Surfaces.- 14.4 Quadric Surfaces.- 14.5 Cylindrical and Spherical Coordinates.- 14.6 Curves in Space.- 14.7 The Geometry and Physics of Space Curves.- 15 Partial Differentiation.- 15.1 Introduction to Partial Derivatives.- 15.2 Linear Approximations and Tangent Planes.- 15.3 The Chain Rule.- 15.4 Matrix Multiplication and the Chain Rule.- 16 Gradients, Maxima, and Minima.- 16.1 Gradients and Directional Derivatives.- 16.2 Gradients, Level Surfaces, and Implicit Differentiation.- 16.3 Maxima and Minima.- 16.4 Constrained Extrema and Lagrange Multipliers.- 17 Multiple Integration.- 17.1 The Double Integral and Iterated Integral.- 17.2 The Double Integral Over General Regions.- 17.3 Applications of the Double Integral.- 17.4 Triple Integrals.- 17.5 Integrals in Polar, Cylindrical, and Spherical Coordinates.- 17.6 Applications of Triple Integrals.- 18 Vector Analysis.- 18.1 Line Integrals.- 18.2 Path Independence.- 18.3 Exact Differentials.- 18.4 Green's Theorem.- 18.5 Circulation and Stokes' Theorem.- 18.6 Flux and the Divergence Theorem.- Answers.

巻冊次

2 : gw ISBN 9783540909750

内容説明

This is the second book of a three-volume work called "Calculus" by Jerrold Marsden and Alan Weinstein. This book is the outgrowth of the authors' experience teaching calculus at Berkeley. It covers techniques and applications of integration, infinite series, and differential equations. Throughout the book, the authors motivate the study of calculus using its applications. Many solved problems are included, and extensive exercises are given at the end of each section. In addition, a separate student guide has been prepared.

目次

7: Basic Methods of Integration. 8: Differential Equations. 9: Applications of Integration. 10: Further Techniques and Applications of Integration. 11: Limits, L'Hopital's Rule, and Numerical Methods. 12: Infinite Series.

巻冊次

3 : gw ISBN 9783540909859

内容説明

This book, the third of a three-volume work, is the outgrowth of the authors' experience teaching calculus at Berkeley. It is concerned with multivariable calculus, and begins with the necessary material from analytic geometry. It goes on to cover partial differentiation, the gradient and its applications, multiple integration, and the theorems of Green, Gauss and Stokes. Throughout the book the authors motivate the study of calculus using its applications. Many solved problems are included, and extensive exercises are given at the end of each section. In addition, a separate student guide has been prepared.

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詳細情報

• NII書誌ID(NCID): BA01310095
• ISBN:
  • 0387909745
  • 3540909745
  • 0387909753
  • 3540909753
  • 0387909850
  • 3540909850
• LCCN: 84005478
• 出版国コード: us
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: New York ; Tokyo
• ページ数/冊数: 3 v.
• 大きさ: 27 cm
• 分類:
  • NDC9 : 413
  • LCC : QA303
  • DC19 : 515
  • NDLC : MA111
• 件名:
  • LCSH : Calculus
• 親書誌ID:
  • BA00018418