A Course in Mathematics for Students of Physics: Volume 2This 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. |
Contents
396 | |
II | 399 |
III | 407 |
IV | 411 |
V | 419 |
VI | 429 |
VII | 431 |
VIII | 433 |
LIX | 641 |
LX | 646 |
LXI | 651 |
LXII | 653 |
LXIII | 660 |
LXIV | 662 |
LXV | 664 |
LXVI | 674 |
IX | 436 |
X | 444 |
XI | 446 |
XII | 451 |
XIV | 458 |
XV | 461 |
XVI | 466 |
XVII | 469 |
XVIII | 474 |
XIX | 477 |
XX | 482 |
XXI | 485 |
XXII | 487 |
XXIII | 492 |
XXV | 502 |
XXVI | 520 |
XXVII | 526 |
XXIX | 532 |
XXX | 535 |
XXXI | 539 |
XXXII | 541 |
XXXIII | 553 |
XXXIV | 564 |
XXXV | 574 |
XXXVII | 583 |
XXXVIII | 585 |
XXXIX | 586 |
XL | 588 |
XLI | 596 |
XLII | 597 |
XLIII | 600 |
XLIV | 602 |
XLV | 604 |
XLVI | 606 |
XLVII | 608 |
XLVIII | 612 |
L | 615 |
LI | 616 |
LII | 621 |
LIII | 626 |
LIV | 628 |
LV | 633 |
LVI | 636 |
LVIII | 638 |
LXVIII | 686 |
LXIX | 689 |
LXX | 692 |
LXXI | 695 |
LXXII | 697 |
LXXIII | 700 |
LXXIV | 704 |
LXXVI | 706 |
LXXVII | 707 |
LXXVIII | 709 |
LXXIX | 711 |
LXXX | 715 |
LXXXI | 724 |
LXXXII | 729 |
LXXXIII | 735 |
LXXXIV | 740 |
LXXXV | 744 |
LXXXVII | 750 |
LXXXVIII | 755 |
LXXXIX | 758 |
XC | 761 |
XCI | 762 |
XCII | 764 |
XCIII | 766 |
XCV | 768 |
XCVI | 775 |
XCVII | 780 |
XCVIII | 785 |
XCIX | 796 |
C | 800 |
CI | 805 |
CII | 808 |
CIII | 814 |
CIV | 816 |
CV | 823 |
CVI | 826 |
CVII | 831 |
CVIII | 835 |
CIX | 836 |
CX | 838 |
CXI | 845 |
848 | |
Other editions - View all
A Course in Mathematics for Students of Physics:, Volume 2 Paul Bamberg,Shlomo Sternberg No preview available - 1990 |
A Course in Mathematics for Students of Physics:, Volume 2 Paul Bamberg,Shlomo Sternberg No preview available - 1990 |
Common terms and phrases
algebra B₁ basis element boundary nodes C₁ C₂ Calculate Chapter charge Clifford algebra complex compute conductors consider constant coordinates corresponding defined definition denote determine differential form dim H₁ dimension Dirichlet problem dual dual space dx dy dx Ʌ dy dy Ʌ dz electrical networks entropy equation equilibrium equivalence class evaluate example expression exterior finite formula given Green's hence holomorphic function integral interior nodes k-form Kirchhoff's Kirchhoff's current law Kirchhoff's voltage law linear differential form linear function matrix maximal tree null curve one-cochain one-form orientation orthogonal Poisson's equation potential prove quotient space region resistors scalar product solution sphere star operator subspace Suppose surface temperature theorem theory two-form V₁ V₂ vanishes variables vector field vector space Ʌ dx w₁ w₂ write Z₁ zero ди