On the Shoulders of Giants A Course in Single Variable Calculus - Smith & Mcleland.pdf

TLFeBOOK
CONTENTS
Preface v
1 Terror, tragedy and bad vibrations 1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
The Tower of Terror .................................. 1
....................................... 4
.................................. 7
........................................ 8
................................... 9
2 Functions 11
................................... 11
................................. 15
................................... 17
................................. 20
3 Continuity and smoothness 27
.................................... 27
........................................ 30
4 Differentiation 41
...................................... 41
................................. 48
Velocity, acceleration and rates of change . . . . . . . . . . . . . . . . . . . . . . . 53
5 Falling bodies 57
The Tower of Terror .................................. 57
Solving differential equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
..................................... 65
.......................... 68
..................................... 70
6 Series and the exponential function 75
................................ 75
...................................... 81
.................................. 84
................................. 90
ii CONTENTS
............................. 93
...................................... 96
Properties of the exponential function . . . . . . . . . . . . . . . .