preface xi
1 f = ma1
1.1 prelude to newton's principia 1
1.2 equal area in equal time 5
1.3 the law of gravity 9
1.4 exercises16
1.5 reprise with calculus 18
1.6 exercises26
2 vector algebra 29
2.1 basic notions29
2.2 the dot product 34
2.3 the cross product39
2.4 using vector algebra 46
2.5 exercises 50
3 celestial mechanics 53
3.1 the calculus of curves 53
3.2 exercises05
3.3 orbital mechanics 06
3.4 exercises75
4 differential forms 77
4.1 some history77
4.2 differential 1-forms 79
4.3 exercises 86
4.4 constant differential 2-forms 89
4.5 exercises 96
4.6 constant differential k-forms 99
4.7 prospects 105
4.8 exercises 107
5 line integrals, multiple integrals 111
5.1 the riemann integral 111
5.2 linelntegrals.113
5.3 exercises llo
5.4 multiple- -integrals 120
5.5 using multiple integrals 131
5.6 exercises
6 linear transformations 139
6.1 basicnotions.139
0.2 determinants 146
6.3 history and comments 157
6.4 exercises 158
6.5 invertibility 165
6.6 exercises
7 differential calculus 171
7.1 limits 171
7.2 exercises 178
7.3 directional derivatives 181
7.4 the derivative 187
7.5 exercises 197
7.6 the chain rule._a201
7.7 usingthegradient.205
7.8 exercises 207
8 integration by pullback 211
8.1 change of variables 211
8.2 interlude with'lagrange 213
8.4 thesurfacelntegral 221
8.5 heatflow228
8.6 exercises 230
9 techniques of differential calculus 233
9.1 implicitdifferentiation 233
9.2 invertibility 238
9 3 exercises 244
9.4 locating extrema 248
9.5 taylor's formula in several variables 254
9.6 exercises 262
9.7 lagrangemultipliers266
9 8 exercises277
10 the fundamental theorem of calculus 279
10.1 overview 279
10.2 independence of path 286
10.3 exercises 294
10.4 the divergence theorems 297
10.5 exercises 310
10.6 stokes' theorem 314
10.7 summary for r3 321
10.8 exercises 323
10.9 potential theory 326
11 e = mc2 333
11.2 flow in space-time 338
11.3 electromagnetic potential 345
11.4 exercises 349
11.5 specialrelativity 352
11.6 exercises 360
appendices
a an opportunity missed 361
b bibliography365
c clues and solutions367
index 382
鄂公网安备 42010302001612号 