List price: $106.25
Basic Multivariable Calculus helps students make the difficult transition to advanced calculus by focusing exclusively on topics traditionally covered in the third-semester course in the calculus of functions of several variables. The concepts of vector calculus are clearly and accurately explained, with an emphasis on developing students' intuitive understanding and computational technique.
Only first year calculus required--all necessary linear algebra is explained
Incorporates wide range of physical applications, dozens of graphics, and a large number of exercises
Boxes highlight important definitions and formulas
Notes to the student on exceptionally difficult topics
1. Algebra and Geometry of Euclidean Space
Vectors in the Plane and Space
The Inner Product and Distance
2 x 2 and 3 x 3 Matrices and Determinants
The Cross Product and Planes
n-dimensional Euclidean Space
Curves in the Plane and in Space
2. Differentiation
Graphs and Level Surfaces
Partial Derivatives and Continuity
Differentiability, the Derivative
Matrix and Tangent Planes
The Chain Rule
Gradients and Directional Derivatives
Implicit Differentiation
3. Higher Derivatives and Extrema
Higher Order Partial Derivatives
Taylor's Theorem
Maxima and Minima
Second Derivative Test
Constrained Extrema and Lagrange Multipliers
4. Vector Valued Functions
Acceleration
Arc Length
Vector Fields
Divergence and Curl
5. Multiple Integrals
Volume and Cavalieri's Principle
The Double Integral over a Rectangle
The Double Integral over Regions
The Triple Integral
Change of a Variable, Cylindrical and Spherical Coordinates
Applications of Multiple Integrals
6. Integrals over Curves and Surfaces
Line Integrals
Parametrized Surfaces
Area of a Surface
Surface Integrals
7. The Integral Theorems of Vector Analysis
Green's Theorem
Stokes' Theorem
Gauss' Theorem
Path Independence and the Fundamental Theorems of Calculus
Epilogue
Practice Exams
Answers to Odd-Numbered Exercises
Index
Basic Multivariable Calculus helps students make the difficult transition to advanced calculus by focusing exclusively on topics traditionally covered in the third-semester course in the calculus of functions of several variables. The concepts of vector calculus are clearly and accurately explained, with an emphasis on developing students' intuitive understanding and computational technique.
Only first year calculus required--all necessary linear algebra is explained
Incorporates wide range of physical applications, dozens of graphics, and a large number of exercises
Boxes highlight important definitions and formulas
Notes to the student on exceptionally difficult topics
Table of Contents
1. Algebra and Geometry of Euclidean Space
Vectors in the Plane and Space
The Inner Product and Distance
2 x 2 and 3 x 3 Matrices and Determinants
The Cross Product and Planes
n-dimensional Euclidean Space
Curves in the Plane and in Space
2. Differentiation
Graphs and Level Surfaces
Partial Derivatives and Continuity
Differentiability, the Derivative
Matrix and Tangent Planes
The Chain Rule
Gradients and Directional Derivatives
Implicit Differentiation
3. Higher Derivatives and Extrema
Higher Order Partial Derivatives
Taylor's Theorem
Maxima and Minima
Second Derivative Test
Constrained Extrema and Lagrange Multipliers
4. Vector Valued Functions
Acceleration
Arc Length
Vector Fields
Divergence and Curl
5. Multiple Integrals
Volume and Cavalieri's Principle
The Double Integral over a Rectangle
The Double Integral over Regions
The Triple Integral
Change of a Variable, Cylindrical and Spherical Coordinates
Applications of Multiple Integrals
6. Integrals over Curves and Surfaces
Line Integrals
Parametrized Surfaces
Area of a Surface
Surface Integrals
7. The Integral Theorems of Vector Analysis
Green's Theorem
Stokes' Theorem
Gauss' Theorem
Path Independence and the Fundamental Theorems of Calculus
Epilogue
Practice Exams
Answers to Odd-Numbered Exercises
Index