This comprehensive textbook explores the topics of vector functions and functions of several variables. With over 500 exercises and problems, carefully chosen for their challenging, interesting, and educational value, this book is an ideal resource for undergraduate students of mathematics, statistics, computer science, engineering and the basic sciences. The material is organized into 10 chapters, each of which begins with necessary definitions, concepts and theorems to provide a solid foundation for understanding the topic. In addition, the book includes detailed solutions to all exercises and problems to help students test their understanding and reinforce their learning. Overall, this book is an excellent choice for anyone seeking a thorough introduction to calculus.
Author(s): Bijan Davvaz
Edition: 1
Publisher: Springer Nature
Year: 2023
Language: English
Pages: 428
Preface
Contents
1 Vectors and Analytic Geometry
1.1 Vectors and Their Properties
1.2 Lines and Planes in Space
1.3 Cylinder and Surface of Revolution
1.4 Quadric Surfaces
1.5 Polar, Cylindrical and Spherical Coordinates
1.6 Solved Problems
1.7 Exercises
2 Vector Functions and Parametric Equations
2.1 Definition and Calculus of Vector Functions
2.2 Velocity and Acceleration in Space
2.3 Unit Tangent Vector, Unit Normal Vector and Curvature
2.4 Radius of Curvature
2.5 Solved Problems
2.6 Exercises
3 Functions of Several Variables, Limits and Continuity
3.1 Functions of Several Variables
3.2 Limits
3.3 Continuity
3.4 Solved Problems
3.5 Exercises
4 Partial Derivatives, Directional Derivatives and Gradient Vectors
4.1 Partial Derivatives
4.2 Directional Derivatives and Gradient Vectors
4.3 Tangent Plane and Normal Line to a Surface
4.4 Solved Problems
4.5 Exercises
5 Differentiability and Differential
5.1 Differentiability
5.2 The Chain Rule
5.3 Taylor Series
5.4 Solved Problems
5.5 Exercises
6 Extreme of Functions
6.1 Derivative Tests for Local Extreme Values
6.2 Lagrange Multipliers
6.3 Solved Problems
6.4 Exercises
7 Vector Fields
7.1 Vector Fields, Limits and Continuity
7.2 Linear Transformations
7.3 Total Derivatives
7.4 Conservative Vector Fields
7.5 Divergence and Curl
7.6 Solved Problems
7.7 Exercises
8 Line Integrals
8.1 Work as a Line Integral
8.2 Line Integrals Independent of the Path
8.3 Solved Problems
8.4 Exercises
9 Multiple Integrals
9.1 Double Integral over Rectangle Region
9.2 Double Integral over Bounded Non-rectangular Region
9.3 Triple Integrals
9.4 Masses and Moments in Three Dimensions
9.5 Solved Problems
9.6 Exercises
10 Surface Integrals
10.1 Green's, Divergence and Stokes' Theorems
10.2 Surface Area
10.3 Solved Problems
10.4 Exercises
Appendix References
Index
