Calculus / Jerrold Marsden, Alan Weinstein.
Series Undergraduate texts in mathematicsEditor: 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: 26-01Preface 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] 14.4 Quadric Surfaces [719] 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] Gradients, Maxima, and Minima 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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| 26 M271 Séries adhérentes. Régularisation des suites. Applications / | 26 M346 Áreas y logaritmos / | 26 M364c Calculus / | 26 M364c Calculus / | 26 M364c Calculus / | 26 M364cs Student's guide to Calculus by J. Marsden and A. Weinstein. | 26 M364v Vector calculus / |
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] --
14.4 Quadric Surfaces [719] --
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] --
Gradients, Maxima, and Minima --
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] --
MR, REVIEW #
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