Vector Calculus 6th Edition by Jerrold Marsden, Anthony Tromba – Ebook PDF Instant Download/Delivery: 1429215089 , 978-1429215084
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Product details:
ISBN 10: 1429215089
ISBN 13: 978-1429215084
Author: Jerrold Marsden, Anthony Tromba
With a contemporary balance between theory, application, and historical development, Vector Calculus gives you insight into how mathematics progresses while being influenced by the natural world.
Vector Calculus 6th Table of contents:
1 The Geometry of Euclidean Space
1.1 Vectors in Two- and Three-Dimensional Space
1.2 The Inner Product, Length, and Distance
1.3 Matrices, Determinants, and the Cross Product
1.4 Cylindrical and Spherical Coordinates
1.5 n-Dimensional Euclidean Space
Review Exercises for Chapter 1
2 Differentiation
2.1 The Geometry of Real-Valued Functions
2.2 Limits and Continuity
2.3 Differentiation
2.4 Introduction to Paths and Curves
2.5 Properties of the Derivative
2.6 Gradients and Directional Derivatives
Review Exercises for Chapter 2
3 Higher-Order Derivatives: Maxima and Minima
3.1 Iterated Partial Derivatives
3.2 Taylor’s Theorem
3.3 Extrema of Real-Valued Functions
3.4 Constrained Extrema and Lagrange Multipliers
3.5 The Implicit Function Theorem [Optional]
Review Exercises for Chapter 3
4 Vector-Valued Functions
4.1 Acceleration and Newton’s Second Law
4.2 Arc Length
4.3 Vector Fields
4.4 Divergence and Curl
Review Exercises for Chapter 4
5 Double and Triple Integrals
5.1 Introduction
5.2 The Double Integral Over a Rectangle
5.3 The Double Integral Over More General Regions
5.4 Changing the Order of Integration
5.5 The Triple Integral
Review Exercises for Chapter 5
6 The Change of Variables Formula and Applications of Integration
6.1 The Geometry of Maps from R2 to R2
6.2 The Change of Variables Theorem
6.3 Applications
6.4 Improper Integrals [Optional]
Review Exercises for Chapter 6
7 Integrals Over Paths and Surfaces
7.1 The Path Integral
7.2 Line Integrals
7.3 Parametrized Surfaces
7.4 Area of a Surface
7.5 Integrals of Scalar Functions Over Surfaces
7.6 Surface Integrals of Vector Fields
7.7 Applications to Differential Geometry, Physics, and Forms of Life
Review Exercises for Chapter 7
8 The Integral Theorems of Vector Analysis
8.1 Green’s Theorem
8.2 Stokes’ Theorem
8.3 Conservative Fields
8.4 Gauss’ Theorem
8.5 Differential Forms
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