Applied Mathematics by Example: Theory
Publisher: Bookboon.com
Published: 2013
ISBN-13: 9788776816247
Table of contents: title: Content; title: 1. Kinematics – motion in a straight line; title: 1.1. Galileo and the acceleration due to gravity; title: 1.2. Constant acceleration formulæ; title: 1.3. Using the constant acceleration formulæ; title: 1.4. Velocity-time graphs; title: 1.5. Using a velocity-time graph; title: 2. Projectiles; title: 2.1. Separating horizontal and vertical motion; title: 2.2. Components of velocity; title: 2.3. Maximum range; title: 2.4. Equation of the trajectory; title: 2.5. The envelope; title: 3. Forces; title: 3.1. Newton’s laws; title: 3.2. Identifying forces; title: 3.3. Equilibrium; title: 3.4. What is a body?; title: 3.5. Connected particles; title: 4. Resistance forces; title: 4.1. Air resistance; title: 4.2. Terminal velocity; title: 4.3. Dynamic friction; title: 4.4. Static friction; title: 4.5. Rolling motion; title: 5. Resolving forces; title: 5.1. Vector addition; title: 5.2. Components of a force; title: 5.3. Resolution of forces; title: 5.4. Resolving forces in two directions; title: 6. Rigid bodies; title: 6.1. Why rigid?; title: 6.2. The lever; title: 6.3. Rigid bodies in equilibrium; title: 7. Centres of gravity; title: 7.1. Using symmetry; title: 7.2. Archimedes’ calculations; title: 7.3. Combining shapes; title: 7.4. Hanging from a fixed point; title: 7.5. Stability; title: 8. Momentum; title: 8.1. Momentum; title: 8.2. Conservation of momentum; title: 8.3. Collisions and explosions; title: 8.4. Impulse; title: 8.5. Duration of impact; title: 8.6. Coecient of restitution; title: 8.7. Oblique impacts; title: 9. Energy; title: 9.1. Potential energy and kinetic energy; title: 9.2. Conservation of mechanical energy; title: 9.3. The work-energy principle; title: 9.4. Power; title: 10. Circular motion; title: 10.1. Centripetal acceleration; title: 10.2. Motion in a horizontal circle; title: 10.3. Motion in a vertical circle; title: 10.4. The pendulum; title: 11. Gravitation and planetary motion; title: 11.1. The Copernican model; title: 11.2. Kepler’s first law; title: 11.3. Kepler’s second law; title: 11.4. Kepler’s third law; title: 11.5. Newton’s law of gravitation; title: 12. The language of vectors; title: 12.1. Vectors; title: 12.2. Displacement vectors and vector addition; title: 12.3. Position vectors; title: 12.4. Vectors for velocity, momentum, acceleration, force; title: 12.5. Unit vectors