Calculus: Multivariable (update)

2. Auflage 2002
ISBN: 978-0-07-283734-6
Verlag: McGraw-Hill Education

Buch, Englisch, 464 Seiten, Format (B × H): 218 mm x 259 mm, Gewicht: 1111 g

The wide-ranging debate brought about by the calculus reform movement has had a significant impact on calculus textbooks. In response to many of the questions and concerns surrounding this debate, the authors have written a modern calculus textbook, intended for students majoring in mathematics, physics, chemistry, engineering and related fields. The text is written for the average student -- one who does not already know the subject, whose background is somewhat weak in spots, and who requires a significant motivation to study calculus.The authors follow a relatively standard order of presentation, while integrating technology and thought-provoking exercises throughout the text. Some minor changes have been made in the order of topics to reflect shifts in the importance of certain applications in engineering and science. This text also gives an early introduction to logarithms, exponentials and the trigonometric functions. Wherever practical, concepts are developed from graphical, numerical, and algebraic perspectives (the "Rule of Three") to give students a full understanding of calculus. This text places a significant emphasis on problem solving and presents realistic applications, as well as open-ended problems.

Autoren/Hrsg.

Smith, Robert T

Minton, Roland B

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Elementare Analysis und Allgemeine Begriffe

Inhaltsverzeichnis

10 Vectors and the Geometry of Space10.1 Vectors in the Plane10.2 Vectors in Space10.3 The Dot Product10.4 The Cross Product10.5 Lines and Planes in Space10.6 Surfaces in Space11 Vector-Valued Functions11.1 Vector-Valued Functions11.2 The Calculus of Vector-Valued Functions11.3 Motion in Space11.4 Curvature11.5 Tangent and Normal Vectors12 Functions of Several Variables and Differentiation12.1 Functions of Several Variables12.2 Limits and Continuity12.3 Partial Derivatives12.4 Tangent Planes and Linear Approximations12.5 The Chain Rule12.6 The Gradient and Directional Derivatives12.7 Extrema of Functions of Several Variables12.8 Constrained Optimization and Lagrange Multipliers13 Multiple Integrals13.1 Double Integrals13.2 Area, Volume and Center of Mass13.3 Double Integrals in Polar Coordinates13.4 Surface Area13.5 Triple Integrals13.6 Cylindrical Coordinates13.7 Spherical Coordinates13.8 Change of Variables in Multiple Integrals14 Vector Calculus14.1 Vector Fields14.2 Line Integrals14.3 Independence of Path and Conservative Vector Fields14.4 Green's Theorem14.5 Curl and Divergence14.6 Surface Integrals14.7 The Divergence Theorem14.8 Stokes' Theorem