This book is a deep rethinking of the pedagogy of a subject of much beauty and great depth, that is central to the education of scientists of the future. For the ambitious student it provides a stairway to climb higher.

Divakar Viswanath, University of Michigan

What makes this book timely is the judicious selection of topics and the thoughtful and balanced treatment thereof, whereby the contents are limited to what is appropriate for a one-semester course. The treatment is careful and intuitive rather than rigorous and terse. The diagrams are well-designed and beautifully drawn. The exercises are neither routine nor redundant and build nicely to increasingly challenging levels.

Ashwani Kapila, Rensselaer Polytechnic Institute

Vector and complex calculus are essential for applications to electromagnetism, fluid and solid mechanics, and the differential geometry of surfaces. Moving beyond the limits of standard multivariable calculus courses, this comprehensive textbook takes students from the geometry and algebra of vectors, through to the key concepts and tools of vector calculus. Topics explored include the differential geometry of curves and surfaces, curvilinear coordinates, ending with a study of the essential elements of the calculus of functions of one complex variable. Vector and Complex Calculus is richly illustrated to help students develop a solid visual understanding of the material, and the tools and concepts explored are foundational for upper-level engineering and physics courses. Each chapter includes a section of exercises which lead the student to practice key concepts and explore further interesting results.
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This comprehensive and richly illustrated textbook takes students from the geometry and algebra of vectors, through to the key concepts and tools of vector calculus. The tools and concepts explored are foundational for upper-level engineering and physics courses.
Les mer
Part I: Vector Geometry and Algebra 1: Find your bearings 2: Vector spaces 3: Dot product 4: Cross Product 5: Cartesian index notation 6: Determinant 7: Points, lines, planes, etc. 8: Orthogonal transformations 9: Matrices and tensors Part II: Vector Calculus 10: Kinematics 11: Dynamics 12: Curves 13: Surfaces 14: Curves on surfaces 15: Curvilinear coordinates 16: Fields 17: Electromagnetism Part III: Complex calculus 18: Complex algebra and geometry 19: Elementary complex functions 20: Functions of a complex variable 21: Complex integration Index
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Professor Fabian Waleffe is a Professor in the Department of Mathematics, Dept. of Mechanical Engineering, and the Dept. of Engineering Physics at the University of Wisconsin-Madison. He has previously held positions as a Postdoctoral Fellow at Stanford University/NASA Ames, Center for Turbulence Research, Assistant Professor of Applied Mathematics at MIT, and has taught numerous courses at all levels.
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Explores vector calculus comprehensively from precalculus to advanced concepts Richly illustrated with clear figures Provides numerous exercises at the end of each section for students to practice key concepts
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Produktdetaljer

ISBN
9780198927839
Publisert
2024
Utgiver
Vendor
Oxford University Press
Vekt
1036 gr
Høyde
205 mm
Bredde
192 mm
Dybde
25 mm
Aldersnivå
U, 05
Språk
Product language
Engelsk
Format
Product format
Innbundet
Antall sider
416

Forfatter

Biographical note

Professor Fabian Waleffe is a Professor in the Department of Mathematics, Dept. of Mechanical Engineering, and the Dept. of Engineering Physics at the University of Wisconsin-Madison. He has previously held positions as a Postdoctoral Fellow at Stanford University/NASA Ames, Center for Turbulence Research, Assistant Professor of Applied Mathematics at MIT, and has taught numerous courses at all levels.