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## Calculus / Jerrold Marsden, Alan Weinstein.

Editor: New York : Springer-Verlag, c1985Edición: 2nd edDescripción: 3 v. (xiv, 934, 104, 15 p.) : il. ; 27 cmISBN: 0387909745 (v. 1 : pbk.); 0387909753 (v. 2 : pbk.); 0387909850 (v. 3 : pbk.)Tema(s): CalculusOtra clasificación: 26-01
Contenidos:
```Preface vii
How to Use this Book: A Note to the Student xi
Introduction [1]
Orientation Quizzes [13]
Chapter R
Review of Fundamentals
R.l Basic Algebra: Real Numbers and Inequalities [15]
R.2 Intervals and Absolute Values [21]
R.3 Laws of Exponents [25]
R.4 Straight Lines [29]
R.5 Circles and Parabolas [34]
R.6 Functions and Graphs [39]
Chapter [1]
Derivatives and Limits
1.1 Introduction to the Derivative [49]
1.2 Limits [57]
1.3 The Derivative as a Limit and the Leibniz
Notation [69]
1.4 Differentiating Polynomials [75]
1.5 Products and Quotients [82]
1.6 The Linear Approximation and Tangent Lines [90]
Chapter [2]
Rates of Change and the Chain Rule
2.1 Rates of Change and the Second Derivative [99]
2.2 The Chain Rule [110]
2.3 Fractional Powers and Implicit Differentiation [118]
2.4 Related Rates and Parametric Curves [123]
2.5 Antiderivatives [128]
Chapter [3]
Graphing and Maximum-Minimum Problems
3.1 Continuity and the Intermediate Value Theorem [139]
3.2 Increasing and Decreasing Functions [145]
3.3 The Second Derivative and Concavity I57
3.4 Drawing Graphs [163]
3.5 Maximum-Minimum Problems [177]
3.6 The Mean Value Theorem [191]
Chapter [4]
The Integral
4.1 Summation [201]
4.2 Sums and Areas [207]
4.3 The Definition of the Integral [215]
4.4 The Fundamental Theorem of Calculus [225]
4.5 Definite and Indefinite Integrals [232]
4.6 Applications of the Integral [240]
Chapter [5]
Trigonometric Functions
5.1 Polar Coordinates and Trigonometry [251]
5.2 Differentiation of the Trigonometric Functions [264]
5.3 Inverse Functions [272]
5.4 The Inverse Trigonometric Functions [281]
5.5 Graphing and Word Problems [289]
5.6 Graphing in Polar Coordinates [296]
Chapter [6]
Exponentials and Logarithms
6.1 Exponential Functions [307]
6.2 Logarithms [313]
6.3 Differentiation of the Exponential and Logarithmic Functions [318]
6.4 Graphing and Word Problems [326]```
```Preface vii
How to Use this Book: A Note to the Student xi
Chapter [7]
Basic Methods of Integration
7.1 Calculating Integrals [337]
7.2 Integration by Substitution [347]
7.3 Changing Variables in the Definite Integral [354]
7.4 Integration by Parts [358]
Chapter [8]
Differential Equations
8.1 Oscillations [369]
8.2 Growth and Decay [378]
8.3 The Hyperbolic Functions [384]
8.4 The Inverse Hyperbolic Functions [392]
8.5 Separable Differential Equations [398]
8.6 Linear First-Order Equations [408]
Chapter [9]
Applications of Integration
9.1 Volumes by the Slice Method [419]
9.2 Volumes by the Shell Method [428]
9.3 Average Values and the Mean Value Theorem for Integrals [433]
9.4 Center of Mass [437]
9.5 Energy, Power, and Work [445]
Chapter [10]
Further Techniques and Applications of Integration
10.1 Trigonometric Integrals
10.2 Partial Fractions [457]
10.3 Arc Length and Surface Area [477]
10.4 Parametric Curves [459]
10.5 Length and Area in Polar Coordinates [500]
Chapter [11]
Limits, L’Hdpital’s Rule, and Numerical Methods
11.1 Limits of Functions [509]
11.2 L’Hopital’s Rule [521]
11.3 Improper Integrals [528]
11.4 Limits of Sequences and Newton’s Method [537]
11.5 Numerical Integration [550]
Chapter [12]
Infinite Series
12.1 The Sum of an Infinite Series [561]
12.2 The Comparison Test and Alternating Series [570]
12.3 The Integral and Ratio Tests [579]
12.4 Power Series [586]
12.5 Taylor’s Formula [594]
12.6 Complex Numbers [607]
12.7 Second-Order Linear Differential Equations [617]
12.8 Series Solutions of Differential Equations [632]```
```Preface vii
How to Use this Book: A Note to the Student xi
Chapter [13]
Vectors
13.1 Vectors in the Plane [645]
13.2 Vectors in Space [652]
13.3 Lines and Distance [660]
13.4 The Dot Product [668]
13.5 The Cross Product [677]
13.5 Matrices and Determinants [683]
Chapter [14]
Curves and Surfaces
14.1 The Conic Sections [695]
14.2 Translation and Rotation of Axes [703]
14.3 Functions, Graphs, and Level Surfaces [710]
14.5 Cylindrical and Spherical Coordinates [728]
14.6 Curves in Space [735]
14.7 The Geometry and Physics of Space Curves [745]
Chapter [15]
Partial Differentiation
15.1 Introduction to Partial Derivatives [765]
15.2 Linear Approximations and Tangent Planes [775]
15.3 The Chain Rule [779]
15.4 Matrix Multiplication and the Chain Rule [784]
Chapter [16]
16.1 Gradients and Directional Derivatives [797]
16.2 Gradients, Level Surfaces, and Implicit Differentiation [805]
16.3 Maxima and Minima [812]
16.4 Constrained Extrema and Lagrange Multipliers [825]
Chapter [17]
Multiple Integration
17.1 The Double Integral and Iterated Integral [839]
17.2 The Double Integral Over General Regions [847]
17.3 Applications of the Double Integral [853]
17.4 Triple Integrals [860]
17.5 Integrals in Polar, Cylindrical, and Spherical Coordinates [869]
17.6 Applications of Triple Integrals [876]
Chapter [18]
Vector Analysis
18.1 Line Integrals [885]
18.2 Path Independence [895]
18.3 Exact Differentials [901]
18.4 Green’s Theorem [908]
18.5 Circulation and Stokes’ Theorem [914]
18.6 Flux and the Divergence Theorem [924]```
Item type Home library Shelving location Call number Materials specified Status Date due Barcode Course reserves
Libros
Libros ordenados por tema 26 M364c (Browse shelf) Vol. 1 Available A-6116
Libros
Libros ordenados por tema 26 M364c (Browse shelf) Vol. 2 Available A-6117
Libros
Libros ordenados por tema 26 M364c (Browse shelf) Vol. 3 Available A-6118

Previous ed. published in 1980 as chapters 1-6 of Calculus.

Includes index.

Preface vii --
How to Use this Book: A Note to the Student xi --
Introduction [1] --
Orientation Quizzes [13] --
Chapter R --
Review of Fundamentals --
R.l Basic Algebra: Real Numbers and Inequalities [15] --
R.2 Intervals and Absolute Values [21] --
R.3 Laws of Exponents [25] --
R.4 Straight Lines [29] --
R.5 Circles and Parabolas [34] --
R.6 Functions and Graphs [39] --
Chapter [1] --
Derivatives and Limits --
1.1 Introduction to the Derivative [49] --
1.2 Limits [57] --
1.3 The Derivative as a Limit and the Leibniz --
Notation [69] --
1.4 Differentiating Polynomials [75] --
1.5 Products and Quotients [82] --
1.6 The Linear Approximation and Tangent Lines [90] --
Chapter [2] --
Rates of Change and the Chain Rule --
2.1 Rates of Change and the Second Derivative [99] --
2.2 The Chain Rule [110] --
2.3 Fractional Powers and Implicit Differentiation [118] --
2.4 Related Rates and Parametric Curves [123] --
2.5 Antiderivatives [128] --
Chapter [3] --
Graphing and Maximum-Minimum Problems --
3.1 Continuity and the Intermediate Value Theorem [139] --
3.2 Increasing and Decreasing Functions [145] --
3.3 The Second Derivative and Concavity I57 --
3.4 Drawing Graphs [163] --
3.5 Maximum-Minimum Problems [177] --
3.6 The Mean Value Theorem [191] --
Chapter [4] --
The Integral --
4.1 Summation [201] --
4.2 Sums and Areas [207] --
4.3 The Definition of the Integral [215] --
4.4 The Fundamental Theorem of Calculus [225] --
4.5 Definite and Indefinite Integrals [232] --
4.6 Applications of the Integral [240] --
Chapter [5] --
Trigonometric Functions --
5.1 Polar Coordinates and Trigonometry [251] --
5.2 Differentiation of the Trigonometric Functions [264] --
5.3 Inverse Functions [272] --
5.4 The Inverse Trigonometric Functions [281] --
5.5 Graphing and Word Problems [289] --
5.6 Graphing in Polar Coordinates [296] --
Chapter [6] --
Exponentials and Logarithms --
6.1 Exponential Functions [307] --
6.2 Logarithms [313] --
6.3 Differentiation of the Exponential and Logarithmic Functions [318] --
6.4 Graphing and Word Problems [326] --

Preface vii --
How to Use this Book: A Note to the Student xi --
Chapter [7] --
Basic Methods of Integration --
7.1 Calculating Integrals [337] --
7.2 Integration by Substitution [347] --
7.3 Changing Variables in the Definite Integral [354] --
7.4 Integration by Parts [358] --
Chapter [8] --
Differential Equations --
8.1 Oscillations [369] --
8.2 Growth and Decay [378] --
8.3 The Hyperbolic Functions [384] --
8.4 The Inverse Hyperbolic Functions [392] --
8.5 Separable Differential Equations [398] --
8.6 Linear First-Order Equations [408] --
Chapter [9] --
Applications of Integration --
9.1 Volumes by the Slice Method [419] --
9.2 Volumes by the Shell Method [428] --
9.3 Average Values and the Mean Value Theorem for Integrals [433] --
9.4 Center of Mass [437] --
9.5 Energy, Power, and Work [445] --
Chapter [10] --
Further Techniques and Applications of Integration --
10.1 Trigonometric Integrals --
10.2 Partial Fractions [457] --
10.3 Arc Length and Surface Area [477] --
10.4 Parametric Curves [459] --
10.5 Length and Area in Polar Coordinates [500] --
Chapter [11] --
Limits, L’Hdpital’s Rule, and Numerical Methods --
11.1 Limits of Functions [509] --
11.2 L’Hopital’s Rule [521] --
11.3 Improper Integrals [528] --
11.4 Limits of Sequences and Newton’s Method [537] --
11.5 Numerical Integration [550] --
Chapter [12] --
Infinite Series --
12.1 The Sum of an Infinite Series [561] --
12.2 The Comparison Test and Alternating Series [570] --
12.3 The Integral and Ratio Tests [579] --
12.4 Power Series [586] --
12.5 Taylor’s Formula [594] --
12.6 Complex Numbers [607] --
12.7 Second-Order Linear Differential Equations [617] --
12.8 Series Solutions of Differential Equations [632] --

Preface vii --
How to Use this Book: A Note to the Student xi --
Chapter [13] --
Vectors --
13.1 Vectors in the Plane [645] --
13.2 Vectors in Space [652] --
13.3 Lines and Distance [660] --
13.4 The Dot Product [668] --
13.5 The Cross Product [677] --
13.5 Matrices and Determinants [683] --
Chapter [14] --
Curves and Surfaces --
14.1 The Conic Sections [695] --
14.2 Translation and Rotation of Axes [703] --
14.3 Functions, Graphs, and Level Surfaces [710] --
14.5 Cylindrical and Spherical Coordinates [728] --
14.6 Curves in Space [735] --
14.7 The Geometry and Physics of Space Curves [745] --
Chapter [15] --
Partial Differentiation --
15.1 Introduction to Partial Derivatives [765] --
15.2 Linear Approximations and Tangent Planes [775] --
15.3 The Chain Rule [779] --
15.4 Matrix Multiplication and the Chain Rule [784] --
Chapter [16] --
16.1 Gradients and Directional Derivatives [797] --
16.2 Gradients, Level Surfaces, and Implicit Differentiation [805] --
16.3 Maxima and Minima [812] --
16.4 Constrained Extrema and Lagrange Multipliers [825] --
Chapter [17] --
Multiple Integration --
17.1 The Double Integral and Iterated Integral [839] --
17.2 The Double Integral Over General Regions [847] --
17.3 Applications of the Double Integral [853] --
17.4 Triple Integrals [860] --
17.5 Integrals in Polar, Cylindrical, and Spherical Coordinates [869] --
17.6 Applications of Triple Integrals [876] --
Chapter [18] --
Vector Analysis --
18.1 Line Integrals [885] --
18.2 Path Independence [895] --
18.3 Exact Differentials [901] --
18.4 Green’s Theorem [908] --
18.5 Circulation and Stokes’ Theorem [914] --
18.6 Flux and the Divergence Theorem [924] --

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