PHY5200 F06

Reading

final review (today) and Taylor 14.6 (Wednesday).

Review for the Final Exam

The final will be cumulative. Topics may appear from any of chapters 1 to 5 and 8. I will emphasize the maeial in chapters 5 and 8, however since that material relies and builds on the material in the earlier chapters, the earlier chapters can't be ignored.

Review of Chapters 5 and 8 for the Final Exam

Mathematical Techniques

  1. Operators in Differential Equations
  2. Using complex exponentials to solve real differential equations
  3. Four ways to write SHO solution
  4. Knowing when an extra solution to a DE must be sought
  5. Pparticular (steady-state) and homogeneous solution
  6. Fourier series
  7. Polar coordinates
  8. Transforming radial equation with change of variables and chain rule

Physics Topics

  1. Stable and unstable equilibria
  2. Expansion of the potential energy about a stable equilibrium
  3. Energy in the SHO
  4. Two-dimensional oscillator
  5. Damped oscillator
  6. Overdamped, underdamped, and critically damped solutions
  7. Q of the underdamped oscillator
  8. Driven oscillator
  9. Amplitude and phase of the driven oscillator
  10. Resonance, Q, and phase
  11. Two-body central force problem generalities
  12. Separation of the problem into CM and relative motion
  13. Central force and conservation of angular momentum
  14. Effective potential and conservation of energy
  15. The transformed radial equation
  16. Ellipses, parabolas, and hyperbolas in polar coordinates
  17. Relation of eccentricity and energy
  18. Definition of aphelion, perihelion, focus, semi-major and semi-minor axes
  19. Stability of orbits
  20. Kepler's laws
  21. Changing orbits
  22. Dark matter; gravity due to a spherical shell of material; virial theorem
  23. Rutherford scattering

Problem Sets 1 to 12, with particular emphasis on problem sets 9 to 12.

Review any questions on these problems.

Review of Chapters 3 and 4 for the Final Exam

Mathematical Techniques

  1. Volume Integrals for Mass and Center of Mass
  2. Line Integrals (for work)
  3. Partial Derivatives
  4. The Gradient
  5. The Curl
  6. Spherical Coordinates
  7. The Gradient in Spherical Coordinates (formula will be provided)
  8. The Curl in Spherical Coordinates (formula will be provided)

Physics Topics

  1. Conservation of Momentum
  2. Inellastic Collisions
  3. Rockets and Variable Mass Motion
  4. The Center of Mass
  5. Angular Momentum
  6. Torque
  7. Conservation of Angular Momentum
  8. Kepler's Second Law
  9. Moment of Inertia
  10. Kinetic Energy
  11. Work
  12. Work-Energy Theorem
  13. Rotational versus Translational Kinetic Energy
  14. Potential Energy
  15. Conservative Forces
  16. Mechanical Energy
  17. Conservation of Energy
  18. Time Dependent Potential Energy
  19. Energy in One-Dimensional Systems
  20. Potential Energy Graphs
  21. Stable and Unstable Equilibria and Turning Points
  22. Solution for Velocity and Position in 1-D System
  23. Central Forces
  24. Conservative Central Forces
  25. Elastic Collisions
  26. Rigid Bodies
  27. Solving Problems with Roations using Energy

Review of Chapters 1 and 2 for the First Exam

Mathematical Techniques

  1. Vectors
    1. vector operations: addition/subtraction, muliplication by a scalar, scalar product, and cross product
    2. differentiation of vectors: including differentiation of scalar or vector product
  2. Coordinate Systems
    1. Cartesian or rectangular (2 and 3 dimensions)
    2. polar (2 dimensions) / cylindrical (3 dimensions)
    3. spherical (3 dimensions)
  3. Derivatives in Polar Coordinates: I will give you the expressions for r[dot] and r[ddot]
  4. Differential Equations
    1. simple integration
    2. guess solution
    3. separation of variables
    4. change of variables
    5. resolving vector equations into components
    6. don't forget constants of integration
  5. Taylor Series Expansion
  6. Hyberbolic Functions
  7. Complex Numbers
  8. Exponential Functions, both real and complex

Physics Topics

  1. Units
  2. Reference Frames
  3. Forces: uniform gravity, friction, normal, linear and quadratic drag, Lorentz (magnetic)
  4. Newton's Laws
    1. First: defines inertial reference frames
    2. Second: basic equation of motion
    3. Third: reaction force, yields conservation of momentum
  5. Inclined Plane Problems
  6. Simple Problems in Polar Coordinates
  7. Projectile Problems
    1. without air drag
    2. with linear air drag
    3. with quadratic air drag
    4. range and limits to motion
    5. terminal velocity
    6. making approximations such as effect of small air drag
  8. Motion of a Charge in Electric and Magnetic Fields
© Robert Harr 2006