Applied Mathematics by Example: Theory

Mathematics is an exceptionally useful subject, having numerous applications in business, computing, engineering and medicine to name but a few. `Applied mathematics’ refers to the study of the physical world using mathematics. You can download the book for free via the link below. 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 ......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 Content 1. Kinematics – motion in a straight line 1.1. Galileo and the acceleration due to gravity 1.2. Constant acceleration formulæ 1.3. Using the constant acceleration formulæ 1.4. Velocity-time graphs 1.5. Using a velocity-time graph 2. Projectiles 2.1. Separating horizontal and vertical motion 2.2. Components of velocity 2.3. Maximum range 2.4. Equation of the trajectory 2.5. The envelope 3. Forces 3.1. Newton’s laws 3.2. Identifying forces 3.3. Equilibrium 3.4. What is a body? 3.5. Connected particles 4. Resistance forces 4.1. Air resistance 4.2. Terminal velocity 4.3. Dynamic friction 4.4. Static friction 4.5. Rolling motion 5. Resolving forces 5.1. Vector addition 5.2. Components of a force 5.3. Resolution of forces 5.4. Resolving forces in two directions 6. Rigid bodies 6.1. Why rigid? 6.2. The lever 6.3. Rigid bodies in equilibrium 7. Centres of gravity 7.1. Using symmetry 7.2. Archimedes’ calculations 7.3. Combining shapes 7.4. Hanging from a fixed point 7.5. Stability 8. Momentum 8.1. Momentum 8.2. Conservation of momentum 8.3. Collisions and explosions 8.4. Impulse 8.5. Duration of impact 8.6. Coecient of restitution 8.7. Oblique impacts 9. Energy 9.1. Potential energy and kinetic energy 9.2. Conservation of mechanical energy 9.3. The work-energy principle 9.4. Power 10. Circular motion 10.1. Centripetal acceleration 10.2. Motion in a horizontal circle 10.3. Motion in a vertical circle 10.4. The pendulum 11. Gravitation and planetary motion 11.1. The Copernican model 11.2. Kepler’s first law 11.3. Kepler’s second law 11.4. Kepler’s third law 11.5. Newton’s law of gravitation 12. The language of vectors 12.1. Vectors 12.2. Displacement vectors and vector addition 12.3. Position vectors 12.4. Vectors for velocity, momentum, acceleration, force 12.5. Unit vectors Innhold Kinematics – motion in a straight line Galileo and the acceleration due to gravity Constant acceleration formulæ Using the constant acceleration formulæ Velocity-time graphs Using a velocity-time graph Projectiles Separating horizontal and vertical motion Components of velocity Maximum range Equation of the trajectory The envelope Forces Newton’s laws Identifying forces Equilibrium What is a body? Connected particles Resistance forces Air resistance Terminal velocity Dynamic friction Static friction Rolling motion Resolving forces Vector addition Components of a force Resolution of forces Resolving forces in two directions Rigid bodies Why rigid? The lever Rigid bodies in equilibrium Centres of gravity Using symmetry Archimedes’ calculations Combining shapes Hanging from a fixed point Stability Momentum Momentum Conservation of momentum Collisions and explosions Impulse Duration of impact Coecient of restitution Oblique impacts Energy Potential energy and kinetic energy Conservation of mechanical energy The work-energy principle Power Circular motion Centripetal acceleration Motion in a horizontal circle Motion in a vertical circle The pendulum Gravitation and planetary motion The Copernican model Kepler’s first law Kepler’s second law Kepler’s third law Newton’s law of gravitation The language of vectors Vectors Displacement vectors and vector addition Position vectors Vectors for velocity, momentum, acceleration, force Unit vectors