MECH102 - Final Exam Review Topics

reading assignments covered: Ch 18, Ch 19, PT 6, Ch 21, Ch 23, PT 7, Ch 25, Ch 27
(see the syllabus for section details)

  1. interpolation
    1. linear
    2. Newton's divided differences
    3. Lagrange interpolating polynomial
    4. polynomial coefficients
    5. MathCAD methods
  2. Fourier approximation
    1. sinusoid terminology (amplitude, frequency, phase)
    2. Fourier series
      1. fundamental frequency
      2. harmonics
      3. spectrum
    3. MathCAD methods
  3. numerical integration
    1. Trapezoid Rule
    2. Simpson's 1/3 Rule
    3. MathCAD methods
      1. symbolic and numeric integration
  4. numerical differentiation
    1. divided difference formulas
    2. error orders of magnitude
    3. MathCAD methods
  5. ordinary differential equations
    1. small angle approximation
    2. Euler's method
    3. Heun's method
    4. midpoint method
    5. Runge-Kutta 4th order method
    6. converting a higher order ODE to a set of 1st order ODEs
    7. solving a set of 1st order ODEs
    8. MathCAD methods
      1. programs and functions
      2. odesolve
      3. rkfixed
  6. boundary value problems
    1. finite difference method
    2. MathCAD methods
  7. miscellaneous
    1. reading assignments
    2. homework assignments
    3. difficulties from Exam I and Exam II
    4. comprehensive questions