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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.
List of contents
- 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
About the author
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.
Summary
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.
Additional text
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.
