This textbook, available in two volumes, has been developed from a course taught at Harvard over the last decade. The course covers principally the theory and physical applications of linear algebra and of the calculus of several variables, particularly the exterior calculus. The authors adopt the 'spiral method' of teaching, covering the same topic several times at increasing levels of sophistication and range of application. Thus the reader develops a deep, intuitive understanding of the subject as a whole, and an appreciation of the natural progression of ideas. Topics covered include many items previously dealt with at a much more advanced level, such as algebraic topology (introduced via the analysis of electrical networks), exterior calculus, Lie derivatives, and star operators (which are applied to Maxwell's equations and optics). This then is a text which breaks new ground in presenting and applying sophisticated mathematics in an elementary setting. Any student, interpreted in the widest sense, with an interest in physics and mathematics, will gain from its study.
"synopsis" may belong to another edition of this title.
This textbook covers the theory and physical applications of linear algebra and of the calculus of several variables, particularly the exterior calculus. It uses the 'spiral' method of teaching ñ covering the same topic several times with increasing depth and range of application in order to give the reader an intuitive understanding of the subject.
This textbook has been developed from a course taught at Harvard over the last decade. The course covers principally the theory and physical applications of linear algebra, and of the calculus of several variables, particularly the exterior calculus.
The authors adopt the 'spiral method' of teaching covering the same topic several times at increasing levels of sophistication and range of application. Thus the student develops a deep intuitive understanding of the subject as a whole and an appreciation of the natural progression of ideas.
This the second volume, opens with an introduction to algebraic topology, introduced by the analysis of electrical networks or mathematically speaking, the topology of one-dimensional complexes.
Chapters 15-18 develop the exterior differential calculus as a continuous version of the discrete theory of complexes. Facts of the exterior calculus are presented: exterior algebra, k-forms, pullback, exterior derivative and Stokes' theorem.
Chapter 16 presents another physical theory, electrostatics. The authors argue that the dielectric properties of the vacuum determine Euclidean geometry in three-dimensional space. The basic facts of potential theory are presented.
Chapters 17 and 18 continue and conclude the study of the exterior differential calculus, developing the notions of vector fields and flows, interior products and Lie derivatives, and applying them to magnetostatics. The star operator is discussed in a general context.
Chapter 19 can be thought of as the culmination of the course. It applies the results of the preceding chapters to the study of Maxwell's equations and the associated wave equations.
The last two chapters covercomplex analysis and elementary asymptotics, and the book ends with a sophisticated treatment of thermodynamics.
"About this title" may belong to another edition of this title.
Shipping:
FREE
Within U.S.A.
Seller: ThriftBooks-Atlanta, AUSTELL, GA, U.S.A.
Paperback. Condition: Good. No Jacket. Pages can have notes/highlighting. Spine may show signs of wear. ~ ThriftBooks: Read More, Spend Less 1.85. Seller Inventory # G0521406501I3N00
Quantity: 1 available
Seller: Books From California, Simi Valley, CA, U.S.A.
Paperback. Condition: Very Good. The copy shows minor external wear, but is in otherwise good condition. Seller Inventory # mon0003731034
Quantity: 1 available
Seller: The Maryland Book Bank, Baltimore, MD, U.S.A.
paperback. Condition: Good. Corners are slightly bent. Used - Good. Seller Inventory # 4-Z-7-0465
Quantity: 1 available
Seller: HPB-Red, Dallas, TX, U.S.A.
Paperback. Condition: Good. Connecting readers with great books since 1972! Used textbooks may not include companion materials such as access codes, etc. May have some wear or writing/highlighting. We ship orders daily and Customer Service is our top priority! Seller Inventory # S_400306650
Quantity: 1 available
Seller: Zubal-Books, Since 1961, Cleveland, OH, U.S.A.
Condition: Fine. *Price HAS BEEN REDUCED by 10% until Monday, April 14 (sale item)* 464 pp., Paperback, a minor crease to back cover else fine. - If you are reading this, this item is actually (physically) in our stock and ready for shipment once ordered. We are not bookjackers. Buyer is responsible for any additional duties, taxes, or fees required by recipient's country. Seller Inventory # ZB1320576
Quantity: 1 available
Seller: TextbookRush, Grandview Heights, OH, U.S.A.
Condition: Very Good. Ships SAME or NEXT business day. We Ship to APO/FPO addr. Choose EXPEDITED shipping and receive in 2-5 business days within the United States. See our member profile for customer support contact info. We have an easy return policy. Seller Inventory # 52733385
Quantity: 1 available
Seller: Bingo Used Books, Vancouver, WA, U.S.A.
Soft cover. Condition: Fine. Trade paperback in fine condition. Volume 2 only. Seller Inventory # 159738
Quantity: 1 available
Seller: BennettBooksLtd, North Las Vegas, NV, U.S.A.
paperback. Condition: New. In shrink wrap. Looks like an interesting title! Seller Inventory # Q-0521406501
Quantity: 1 available
Seller: Toscana Books, AUSTIN, TX, U.S.A.
Paperback. Condition: new. Excellent Condition.Excels in customer satisfaction, prompt replies, and quality checks. Seller Inventory # Scanned0521406501
Quantity: 1 available
Seller: PBShop.store UK, Fairford, GLOS, United Kingdom
PAP. Condition: New. New Book. Delivered from our UK warehouse in 4 to 14 business days. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Seller Inventory # L0-9780521406505
Quantity: Over 20 available