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. 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
