MECH102 - Exam I Review Topics

reading assignments covered: PT1, Ch 1, Ch 3, Ch 4, PT2, Ch 5, Ch 6
(see the syllabus for section details)

  1. numerical methods overview
    1. roots
    2. optimization
    3. curve fit
  2. sources of error
    1. true value
    2. true % relative error
    3. approximate % relative error
    4. computer representation of numbers
      1. base 2 (binary) numbers
      2. largest integer given number of bits
      3. overflow
      4. chopping (truncation) and round off
  3. Taylor Series
    1. nth order approximation
    2. remainder
    3. derivative approximations
      1. backward, centered, and forward differences
  4. Excel
    1. formulas
    2. cell referencing options
    3. operator precedence
    4. "IF" function
  5. MathCAD
    1. equal signs
    2. subscripts
      1. literal
      2. iterative (array)
    3. range variables
    4. entering/modifying expressions
    5. Greek letters
    6. if() function
    7. imaginary numbers
    8. vector and matrix subscripts
  6. finding roots
    1. bracketing methods
      1. graphical
      2. bisection method
      3. false-position method
      4. stopping criteria
      5. error calculations
    2. open methods
      1. fixed-point iteration
      2. Newton-Raphson method
      3. secant method
    3. MathCAD techniques
      1. plotting
      2. iteration
      3. root, polyroots
  7. miscellaneous
    1. reading assignments
    2. homework assignments
    3. car transmission analysis
      1. relationships between engine and rear axle speeds
      2. gear ratios
    4. Billiards cue ball physics and principles
      1. 90-degree rule
      2. 30-degree rule