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.
Arvustused
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 *
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 geometry
19: Elementary complex functions
20: Functions of a complex variable
21: Complex integration
Index
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 help positions as a Postdoctoral Fellow at Stanford University/NASA Ames, Center for Turbulence Research, MIT Applied Math, and has taught numerous courses at all levels.
