Vector calculus

• Verfasst von: Krantz, Steven G. [VerfasserIn]
• Verfasst von: Parks, Harold R. [VerfasserIn]
• Titel: Vector calculus
• Verf.angabe: Steven G. Krantz, Harold Parks
• Ausgabe: First edition
• Verlagsort: Boca Raton ; London ; New York
• Verlag: CRC Press
• Jahr: 2024
• Umfang: 1 Online-Ressource (xxi, 659 Seiten)
• Illustrationen: Illustrationen, Diagramme
• Gesamttitel/Reihe: Textbooks in mathematics
• Gesamttitel/Reihe: A Chapman & Hall book
• Fussnoten: Literaturverzeichnis und Index
• ISBN: 978-1-003-30424-1
• DOI: doi:10.1201/9781003304241
• Schlagwörter: (s)Vektoranalysis / (s)Vektorrechnung / (s)Vektorwertige Funktion / (s)Mehrfaches Integral / (s)Mehrere reelle Variable / (s)Kinematik / (s)Vektorfeld
• Datenträger: Online-Ressource
• Dokumenttyp: Lehrbuch
• Sprache: eng
• Bibliogr. Hinweis: Erscheint auch als : Druck-Ausgabe: Krantz, Steven G., 1951 - : Vector calculus. - Boca Raton : CRC Press, 2024. - xxi, 659 Seiten
• RVK-Notation: SK 220
• Sach-SW: MATHEMATICS / Calculus
• Sach-SW: MATHEMATICS / Mathematical Analysis
• K10plus-PPN: 1915209080
• K10plus-PPN:
  Universitätsbibliothek
• Lokale URL UB: Zum Volltext

Abstract

"Using meaningful examples, credible applications, and incisive technology, this book strives to empower students, enhance their critical thinking skills, and equip them with the knowledge and skills to succeed in the major or discipline they ultimately choose to study. An engaging style and clear writing make the language of mathematics accessible, understandable, and enjoyable, with a high standard for mathematical rigor. A calculus book must tell the truth. This book is carefully written in the accepted language of mathematics in a readable exposition. It includes useful and fascinating applications, acquaints students with the history of the subject and offers a sense of what mathematics is all about. Technique is presented, yet so are ideas. The author helps students to master basic methods and how to discover and build their own concepts in a scientific subject. There is an emphasis on using modeling and numerical calculation"--

Abstract

A calculus book must tell the truth.This book is carefully written in the accepted language of mathematics in a readable exposition.It includes useful and fascinating applications, acquaints students with the history of the subject and offers a sense of what mathematics is all about.

Abstract

Cover -- Half Title -- Series Page -- Title Page -- Copyright Page -- Dedication -- Contents -- Preface -- 1. Vectors -- 1.1. Vectors in the Plane -- 1.1.1. The Idea of Vector -- 1.1.2. Vector Algebra -- 1.1.3. The Length of a Vector -- 1.1.4. Unit Vectors and Directions -- 1.1.5. An Application to Physics -- 1.1.6. The Special Unit Vectors i and j -- 1.1.7. The Triangle Inequality -- 1.1.8. Problems for Practice -- 1.1.9. Further Theory and Practice -- 1.1.10. Calculator/Computer Exercises -- 1.2. Vectors in Three-Dimensional Space -- 1.2.1. Distance -- 1.2.2. Vectors in Space -- 1.2.3. Vector Operations -- 1.2.4. Vector Length -- 1.2.5. Unit Vectors and Directions -- 1.2.6. The Special Unit Vectors i, j, and k -- 1.2.7. Relations among Addition, Length, and Scalar Product -- 1.2.8. Problems for Practice -- 1.2.9. Further Theory and Practice -- 1.2.10. Calculator and Computer Exercises -- 1.3. The Dot Product and Applications -- 1.3.1. Algebraic Rules for the Dot Product -- 1.3.2. A Geometric Formula for the Dot Product -- 1.3.3. Projection -- 1.3.4. The Standard Basis Vectors -- 1.3.5. Direction Cosines and Direction Angles -- 1.3.6. Applications -- 1.3.7. A Final Remark -- 1.3.8. Problems for Practice -- 1.3.9. Further Theory and Practice -- 1.3.10. Calculator and Computer Exercises -- 1.4. The Cross Product and Triple Product -- 1.4.1. The Relationship between Cross Products and Determinants -- 1.4.2. A Geometric Understanding of the Cross Product -- 1.4.3. Cross Products and the Calculation of Area -- 1.4.4. A Physical Application of the Cross Product -- 1.4.5. The Triple Scalar Product -- 1.4.6. Problems for Practice -- 1.4.7. Further Theory and Practice -- 1.4.8. Calculator and Computer Exercises -- 1.5. Lines and Planes in Space -- 1.5.1. Cartesian Equations of Planes in Space -- 1.5.2. Parametric Equations of Planes in Space.