Advanced Calculus and Its Applications to Engineering and Physical Sciences

✍ Scribed by John C. Amazigo, Lester A. Rubenfeld

• Publisher: John Wiley and Sons Ltd
• Year: 1980
• Tongue: English
• Leaves: 417
• Edition: International Ed
• Category: Library

✦ Synopsis

Written in problem-solving format, this book emphasizes the purpose of an advanced calculus course by offering a more thorough presentation of some topics to which engineering and physical science students have already been exposed. By supplementing and extending these subjects, the book demonstrates how the tools and ideas developed are vital to an understanding of advanced physical theories.

✦ Table of Contents

Cover
Preface
Contents
1. Functions Of Several Variables
1.1 Coordinate Systems
1.2 Functions Of Several Variables; Limits, Continuity, Partial Derivatives
1.3 Mapping Of Curves And Regions
1.4 Curves And Surfaces And Their Parametric Representations
2. Vectors And Vector Fields
2.1 Coordinate Free Vector Concepts
2.2 Coordinate Representation Of Vectors; Base Vectors; Lines And Planes
2.3 Vector Functions And Fields
2.4 Limits, Continuity, And Derivatives Of Vector Functions; Tangents, Arc Length, Normals
2.5 Vector Differential Operations; Gradient, Divergence, Curl
3. Differential Calculus Of Functions Of Several Variables
3.1 Tangent Plane Approximation And Differentials; Directional Derivative
3.2 Composite Functions And The Chain Rule; Law Of The Mean; Taylor’s Formula
3.3 Implicit Functions; Jacobians; Inverse Functions
3.4 Orthogonal Curvilinear Coordinates
4. Extrema For Functions Of Several Variables
4.1 The One Dimensional Case
4.2 Maxima And Minima For Functions Of Several Variables
4.3 Extremum Problems With Constraints; Lagrange Multipliers
5. Integrals Of Functions Of Several Variables
5.1 Single Integrals: Leibnitz’s Rule; Numerical Integration
5.2 Multiple Integrals; Change Of Variables; Surface Integrals
5.3 Line Integrals; Path Independence; Green’s Theorem
5.4 Three Dimensional Vector Integral Theorems; Divergence And Stokes’ Theorem
5.5 Improper Integrals
6. Calculus Of Variations
6.1 Formulation Of Some Basic Problems
6.2 Functionals Of One Function Of One Variable
6.3 Functionals Of Functions Of Several Variables
6.4 Problems With Constraints; Lagrange Multipliers
7. Infinite Series Of Functions
7.1 Sequences And Series Of Functions; Convergence
7.2 Convergence Tests; Uniform Convergence; Operations On Series; Power And Taylor Series
7.3 Application Of Infinite Series; Series Solutions Of Differential Equations
8. Partial Differential Equations
8.1 Introduction
8.2 Separation Of Variables
8.3 Sturm-Liouville Theory
8.4 Solution Of Some Nonhomogeneous Equations
References
Answers To Problems
Appendices
A. Some Orthogonal Coordinate Systems
B. Vector Relations
C. Some Differential Equations Of Mathematical Physics
D. Review Of Ordinary Differential Equations (ODE)
Index