Applied Mathematics by Example: Theory

Applied Mathematics by Example: Theory (2010)......Page 1
ISBN: 9788776816247......Page 4
--> Contents......Page 5
Preface......Page 9
Introduction by the Author......Page 11
About the Author......Page 13
Editor’s Note......Page 15
A note on symbols......Page 16
1.1 Galileo and the acceleration due to gravity......Page 17
1.2 Constant acceleration formulæ......Page 18
1.3 Using the constant acceleration formulæ......Page 20
1.4 Velocity-time graphs......Page 23
1.5 Using a velocity-time graph......Page 24
2.1 Separating horizontal and vertical motion......Page 27
2.2 Components of velocity......Page 30
2.3 Maximum range......Page 31
2.4 Equation of the trajectory......Page 33
2.5 The envelope......Page 35
3.1 Newton’s laws......Page 37
3.2 Identifying forces......Page 38
3.4 What is a body?......Page 40
3.5 Connected particles......Page 43
4.1 Air resistance......Page 46
4.2 Terminal velocity......Page 47
4.3 Dynamic friction......Page 49
4.4 Static friction......Page 50
4.5 Rolling motion......Page 54
5.1 Vector addition......Page 56
5.2 Components of a force......Page 57
5.3 Resolution of forces......Page 58
5.4 Resolving forces in two directions......Page 62
6.2 The lever......Page 64
6.3 Rigid bodies in equilibrium......Page 66
7.2 Archimedes’ calculations......Page 74
7.3 Combining shapes......Page 76
7.4 Hanging from a fixed point......Page 77
7.5 Stability......Page 80
8.2 Conservation of momentum......Page 81
8.3 Collisions and explosions......Page 82
8.4 Impulse......Page 84
8.5 Duration of impact......Page 86
8.6 Coefficient of restitution......Page 87
8.7 Oblique impacts......Page 90
9.1 Potential energy and kinetic energy......Page 93
9.2 Conservation of mechanical energy......Page 94
9.3 The work-energy principle......Page 96
9.4 Power......Page 98
10.1 Centripetal acceleration......Page 101
10.2 Motion in a horizontal circle\r......Page 102
10.3 Motion in a vertical circle......Page 106
10.4 The pendulum......Page 108
11.2 Kepler’s first law......Page 113
11.3 Kepler’s second law......Page 115
11.4 Kepler’s third law......Page 117
11.5 Newton’s law of gravitation......Page 118
A.2 Displacement vectors and vector addition......Page 123
A.3 Position vectors......Page 125
A.4 Vectors for velocity, momentum, acceleration, force......Page 126
A.5 Unit vectors......Page 130