5. 
CONTENTS 
Continuation. Proof by Line Integrals ..<••• 
Xlll 
PAGE 
266 
6. 
The Iterated Integral • 
268 
PAGE 
7. 
Extension to Triple Integrals 
270 
. 208 
8. 
Continuation. Proof by Surface Integrals 
271 
. 211 
9. 
Application to Hydrodynamics and Elasticity • 
275 
10. 
Flux across a Surface 
276 
. 213 
11. 
Continuation. Proof of the Formula 
279 
. 213 
12. 
The Equation of Continuity 
286 
iAT 
. 215 
. 216 
1. 
CHAPTER XIII 
VECTOR ANALYSIS 
Vectors and their Addition 
288 
. 220 
2. 
The Scalar Product 
292 
. 222 
3. 
The Vector Product ........ 
294 
4. 
Rotation of the Axes; Direction Cosines .... 
297 
. 225 
5. 
Invariants .......... 
299 
6. 
Symbolic Vectors. Curl 
301 
. 226 
7. 
Green’s Theorem and Stokes’s Theorem in Vector Form 
303 
8. 
Curvature and Torsion of Twisted Curves. Frenet’s Formulas 
304 
. 228 
9. 
Notation .......... 
. 307 
. 232 
. 233 
. 237 
1. 
CHAPTER XIV 
DIFFERENTIAL EQUATIONS 
Ordinary Differential Equations 
. 309 
. 241 
. 243 
. 245 
. 246 
. 247 
. 248 
. 249 
2. 
I. Equations op the First Order 
Separation of Variables ........ 
. 311 
3. 
Linear Equations ......... 
. 312 
4. 
Homogeneous Equations ....... 
. 313 
5. 
Equations of the Second Order with One Letter Absent 
. 316 
. 250 
. 251 
6. 
Applications 
The Catenary 
. 317 
7. 
Continuation. Discussion of the Catenary .... 
. 322 
8. 
Rope round a Post... 1 .... . 
. 324 
OF 
9. 
Heavy Strings on Surfaces, Rough or Smooth 
. 326 
10. 
Problems in Kinematics ....... 
. 330 
. 253 
. 257 
. 259 
11. 
II. Linear Equations op the Second Order, and Higher 
Elementary Theorems 
. 333 
. 263 
12. 
Constant Coefficients ........ 
. 336