PHY5200 F07

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
    1. product rule and chain rule
    2. in Polar Coordinates: I will give you the expressions for dtr and d²tr
  4. Differential Equations
    1. simple integration
    2. guess solution
    3. separation of variables
    4. change of variables
    5. ½ d²v/dx² rule
    6. partial fractions
    7. resolving vector equations into components
    8. 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
    1. Dimensional analsis
    2. A useful technique for checking an answer, or quickly deriving an approximate expression for a result
  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: the equation of motion
    3. Third: reaction force, yields conservation of momentum with second law
  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
    1. Helix or helical path
    2. Transverse velocity
    3. cyclotron frequency

Problem Sets 1 to 4

Review any questions on these problems.

© Robert Harr 2006