Back substitution, 140, 146

• algorithm, 151

Basic unit vector, 218

Basis, 235

• as maximal linearly independent set, 236, 241

• as minimal spanning set, 242

• as uniquely spanning set, 242

• for $R^3$, 218

• for column space, 246

• for row space, 244

• for solution space, 240

• orthogonal, 253

Batted baseball, 458

Beats, 329

Bernoulli equation, 61

Bessel, Friedrick W. (1784–1846), 642

Bessel equation, 590, 604, 635, 639, 642

Bessel function:

• identities, 647

• order 1, 639

• order $\frac{1}{2}$, 290, 645 12

• order $\frac{3}{2}$, 650 32

• order n, integral order, second kind, 646

• order p, 642

• order p, first kind, 645

• order zero, first kind, 636

• order zero, second kind, 646

• solutions in, 649

Bifurcation diagram, 92

Bifurcation point, 92, 523

Binomial series, 605, 615

Birkhoff, Garrett (1911–1996), 118

Birth rate, 75

Bounded population growth, 76

Brachistochrone problem, 44

Brine tank examples, 366, 389, 393, 395, 496

Broughton Bridge, 330

Buoy problem, 311

Bus orbit, 462