Advanced Calculus and Vector Field Theory

✍ Scribed by Kathleen M. Urwin

• Publisher: Pergamon Press
• Year: 1966
• Tongue: English
• Leaves: 279
• Category: Library

✦ Table of Contents

Content: Front Cover
Advanced Calculus and Vector Field Theory
Copyright Page
Table of Contents
FOREWORD
PREFACE
CHAPTER 1. INTRODUCTION
1:1 Introduction
1:2 Partial differentiation
1:3 Taylor's Theorem
1:4 Vector algebra
CHAPTER 2. FUNCTIONS OF SEVERAL INDEPENDENT VARIABLES
2:1 The Chain Rule
2:2 Change of Variable
2:3 The use of equivalent operators
2:4 Two important transformations
2:5 Total differentials and their use
2:6 Jacobians
CHAPTER 3. LINE INTEGRALS
3:1 Line integrals in two dimensions
3:2 Condition for independence of the path of integration. 3:3 Another type of line integral3:4 Line integrals in three dimensions
CHAPTER 4. MULTIPLE INTEGRALS
4:1 An integral expression for the volume of a cylinder
4:2 Evaluation of +"AzdA
4:3 Change of order of integration
4:4 Change of variables in double integrals
4:5 The plane polar transformation
4:6 Green's Theorem
4:7 Triple integrals
4:8 Types of problem
CHAPTER 5. SURFACE INTEGRALS
5:1 Introduction
5:2 Calculation of surface areas
5:3 Definition of +"F(x, y, z) dx dy over z = f(x, y)
5:4 Definition of +"F(x, y, z)dS
5:5 Two theorems
CHAPTER 6. VECTOR FIELD THEORY (1). 6:1 Introductory definitions6:2 Gradient of a scalar field
6:3 The vector operator ơ% 6:4 Line integrals
6:5 Irrotational vector fields
6:6 Surface integrals
6:7 The divergence of a vector field
6:8 Expression of the divergence by means of ơ% 6:9 Solenoidal vector fields
6:10 The Divergence Theorem
CHAPTER 7. VECTOR FIELD THEORY (2)
7:1 The curl of a vector
7:2 Expression of curl V by means of ơ% 7:3 Alternative condition for an irrotational vector field
7:4 Stokes's Theorem
7:5 Summary of the main results for gradient, divergence and curl
7:6 Orthogonal curvilinear coordinates. 7:7 Gradient, divergence and curl in curvilinear systems7:8 Two important curvilinear systems
CHAPTER 8. APPLICATIONS OF VECTOR FIELD THEORY
8:1 Introduction
8:2 Hydrodynamics
8:3 Newtonian gravitational attraction
8:4 Electrostatics
8:5 Magnetostatics
8:6 Electromagnetism
ANSWERS TO EXERCISES
INDEX.

✦ Subjects

MATHEMATICS Mathematical Analysis Calculus Vector analysis