## A Course in Mathematics for Students of Physics:This text breaks new ground in presenting and applying sophisticated mathematics in an elementary setting. Aimed at physics students, it covers the theory and physical applications of linear algebra and of the calculus of several variables, particularly the exterior calculus. The exterior differential calculus is now being recognized by mathematicians and physicists as the best method of formulating the geometrical laws of physics, and the frontiers of physics have already begun to reopen fundamental questions about the geometry of space and time. Covering the basics of differential and integral calculus, the authors then apply the theory to interesting problems in optics, electronics (networks), electrostatics, wave dynamics, and finally to classical thermodynamics. The authors adopt the "spiral method" of teaching (rather than rectilinear), covering the same topic several times at increasing levels of sophistication and range of application. |

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### Contents

II | 1 |

III | 7 |

IV | 13 |

V | 16 |

VI | 18 |

VII | 21 |

VIII | 22 |

IX | 24 |

LIII | 219 |

LV | 222 |

LVI | 230 |

LVII | 240 |

LVIII | 242 |

LIX | 247 |

LX | 250 |

LXI | 264 |

X | 26 |

XI | 32 |

XII | 36 |

XIII | 39 |

XIV | 43 |

XV | 45 |

XVI | 46 |

XVII | 55 |

XIX | 58 |

XX | 66 |

XXI | 72 |

XXII | 73 |

XXIII | 81 |

XXV | 83 |

XXVI | 89 |

XXVII | 95 |

XXVIII | 103 |

XXIX | 113 |

XXXI | 120 |

XXXIII | 124 |

XXXIV | 131 |

XXXV | 137 |

XXXVI | 141 |

XXXVII | 148 |

XXXVIII | 157 |

XXXIX | 160 |

XL | 166 |

XLI | 167 |

XLII | 168 |

XLIII | 175 |

XLV | 178 |

XLVI | 183 |

XLVII | 189 |

XLVIII | 197 |

XLIX | 205 |

L | 209 |

LI | 214 |

LII | 215 |

LXII | 266 |

LXIII | 267 |

LXIV | 272 |

LXV | 277 |

LXVI | 278 |

LXVII | 285 |

LXVIII | 289 |

LXIX | 295 |

LXX | 297 |

LXXI | 305 |

LXXII | 306 |

LXXIII | 311 |

LXXV | 315 |

LXXVI | 324 |

LXXVII | 326 |

LXXVIII | 328 |

LXXIX | 335 |

LXXXI | 340 |

LXXXII | 341 |

LXXXIII | 342 |

LXXXIV | 343 |

LXXXV | 345 |

LXXXVI | 350 |

LXXXVII | 352 |

LXXXVIII | 358 |

LXXXIX | 360 |

XC | 368 |

XCI | 374 |

XCII | 377 |

XCIII | 378 |

XCIV | 388 |

XCV | 389 |

XCVI | 396 |

XCVII | 397 |

XCVIII | 399 |

XCIX | 401 |

404 | |

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### Common terms and phrases

affine plane affine transformation algebra apply approximation ball calculate called chain rule Chapter column compute conformal matrix consider constant construct coordinates cosh critical point defined definition denote described determinant differential equation differential form dimension double integral dual space eigenvalues eigenvectors equivalence class Euclidean evaluate example expression Figure formula Gaussian optics geometry given Green's theorem hence initial conditions inverse isomorphism iterated integral kernel leading entry length lens line integral linear function linear transformation linearly independent Lorentz transformation matrix motion multiplication non-zero notation one-dimensional one-form orientation origin orthogonal parallelogram partial derivatives particle path physical polynomials positive power series properties prove pullback quotient space real number refraction region represents rotation row reduction satisfies scalar product segment Show Similarly solution curves solve spanned straight line subspace Suppose symplectic tangent theory two-dimensional two-form unique variables vector space write zero