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Miroslav Lovric, Ph.D, is Associate Professor in the Department of Mathematics and Statistics at McMaster University in Ontario, Canada.
Vectors, Matrices, and Applications | p. 1 |
Vectors | p. 1 |
Applications in Geometry and Physics | p. 10 |
The Dot Product | p. 20 |
Matrices and Determinants | p. 30 |
The Cross Product | p. 39 |
Chapter Review | p. 48 |
Calculus of Functions of Several Variables | p. 52 |
Real-Valued and Vector-Valued Functions of Several Variables | p. 52 |
Graph of a Function of Several Variables | p. 62 |
Limits and Continuity | p. 76 |
Derivatives | p. 93 |
Paths and Curves in R[superscript 2]-and R[superscript 3] | p. 112 |
Properties of Derivatives | p. 123 |
Gradient and Directional Derivative | p. 135 |
Cylindrical and Spherical Coordinate Systems | p. 151 |
Chapter Review | p. 159 |
Vector-Valued Functions of One Variable | p. 164 |
World of Curves | p. 164 |
Tangents, Velocity, and Acceleration | p. 181 |
Length of a Curve | p. 191 |
Acceleration and Curvature | p. 200 |
Introduction to Differential Geometry of Curves | p. 209 |
Chapter Review | p. 215 |
Scalar and Vector Fields | p. 219 |
Higher-Order Partial Derivatives | p. 219 |
Taylor's Formula | p. 230 |
Extreme Values of Real-Valued Functions | p. 242 |
Optimization with Constraints and Lagrange Multipliers | p. 261 |
Flow Lines | p. 272 |
Divergence and Curl of a Vector Field | p. 278 |
Implicit Function Theorem | p. 292 |
Appendix: Some Identities of Vector Calculus | p. 298 |
Chapter Review | p. 302 |
Integration Along Paths | p. 306 |
Paths and Parametrizations | p. 306 |
Path Integrals of Real-Valued Functions | p. 316 |
Path Integrals of Vector Fields | p. 325 |
Path Integrals Independent of Path | p. 341 |
Chapter Review | p. 360 |
Double and Triple Integrals | p. 363 |
Double Integrals: Definition and Properties | p. 363 |
Double Integrals Over General Regions | p. 375 |
Examples and Techniques of Evaluation of Double Integrals | p. 394 |
Change of Variables in a Double Integral | p. 401 |
Triple Integrals | p. 417 |
Chapter Review | p. 427 |
Integration Over Surfaces, Properties, and Applications of Integrals | p. 431 |
Parametrized Surfaces | p. 431 |
World of Surfaces | p. 448 |
Surface Integrals of Real-Valued Functions | p. 462 |
Surface Integrals of Vector Fields | p. 474 |
Integrals: Properties and Applications | p. 484 |
Chapter Review | p. 495 |
Classical Integration Theorems of Vector Calculus | p. 499 |
Green's Theorem | p. 499 |
The Divergence Theorem | p. 511 |
Stokes' Theorem | p. 524 |
Differential Forms and Classical Integration Theorems | p. 536 |
Vector Calculus in Electromagnetism | p. 553 |
Vector Calculus in Fluid How | p. 566 |
Chapter Review | p. 576 |
Various Results Used in This Book and Proofs of Differentiation Theorems | p. 581 |
Answers to Odd-Numbered Exercises | p. 590 |
Index | p. 615 |
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The Used, Rental and eBook copies of this book are not guaranteed to include any supplemental materials. Typically, only the book itself is included. This is true even if the title states it includes any access cards, study guides, lab manuals, CDs, etc.