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Multivariable Calculus with Applications.

Bibliographic Details
Main Author: Lax, Peter D.
Other Authors: Terrell, Maria Shea.
Format: eBook
Language:English
Published: Cham : Springer International Publishing AG, 2018.
Series:Undergraduate Texts in Mathematics Ser.
Subjects:
Multivariate analysis..
Mathematical analysis.
Electronic books.
Online Access:View fulltext via EzAccess
Table of Contents:
  • Intro
  • Preface
  • Contents
  • 1 Vectors and matrices
  • 1.1 Two-dimensional vectors
  • 1.2 The norm and dot product of vectors
  • 1.3 Bilinear functions
  • 1.4 n-dimensional vectors
  • 1.5 Norm and dot product in n dimensions
  • 1.6 The determinant
  • 1.7 Signed volume
  • 1.8 Linear functions and their representation by matrices
  • 1.9 Geometric applications
  • 2 Functions
  • 2.1 Functions of several variables
  • 2.2 Continuity
  • 2.3 Other coordinate systems
  • 3 Differentiation
  • 3.1 Differentiable functions
  • 3.2 The tangent plane and partial derivatives
  • 3.3 The Chain Rule
  • 3.4 Inverse functions
  • 3.5 Divergence and curl
  • 4 More about differentiation
  • 4.1 Higher derivatives of functions of several variables
  • 4.2 Extrema of functions of two variables
  • 4.3 Extrema of functions of several variables
  • 4.4 Extrema on level sets
  • 5 Applications to motion
  • 5.1 Motion in space
  • 5.2 Planetary motion
  • 6 Integration
  • 6.1 Introduction to area, volume, and integral
  • 6.2 The integral of a continuous function of two variables
  • 6.3 Double integrals as iterated single integrals
  • 6.4 Change of variables in a double integral
  • 6.5 Integration over unbounded sets
  • 6.6 Triple and higher integrals
  • 7 Line and surface integrals
  • 7.1 Line integrals
  • 7.2 Conservative vector fields
  • 7.3 Surfaces and surface integrals
  • 8 Divergence and Stokes' Theorems and conservation laws
  • 8.1 Green's Theorem and the Divergence Theorem in mathbbR2
  • 8.2 The Divergence Theorem in mathbbR3
  • 8.3 Stokes' Theorem
  • 8.4 Conservation laws
  • 8.5 Conservation laws and one-dimensional flows
  • 9 Partial differential equations
  • 9.1 Vibration of a string
  • 9.2 Vibration of a membrane
  • 9.3 The conduction of heat
  • 9.4 Equilibrium
  • 9.5 The Schrödinger equation
  • Answers to selected problems
  • Index.

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