PRACTICAL MATHEMATICS 

 CHAPTER XIX 



PAGE 



Bending Moment and Shearing Force 286 



Deflection of Beams 294 



Distribution of Shear Stress over a Section .... 303 



Twisting Moment 312 



CHAPTER XX 



Differential Equations of the First Order . . . .319 



When the Variables can be separated . . . . . 321 



The Use of the Integrating Factor 322 



The Motion of a Projectile ... . .3.25 



Electrical Example 330 



Compound Interest Law 338 



Work done by an Expanding Gas . ... 343 



CHAPTER XXI 



Differential Equations of the Second Order .... 349 



Simple Harmonic Motion 352 



Theory of Struts, Euler's Formulae, Rankine-Gordon For- 

 mula 357 



Damped and Forced Vibrations . ... 363 



Electrical Example .... ... 370 



CHAPTER XXII 



Integration of Periodic Functions ... . 376 



Sine and Cosine Series . 379 



Fourier's Series ....... . 385 



Harmonic Analysis . 389 



CHAPTER XXIII 



Interpolation by the Method of Finite Differences . . 403 

 The Method of finding the best Values of -j- and 3? .413 

 The Case when b?u x =0 .419 



