Review of Mathematics and Mechanics

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Plane Geometry
Plane Trigonometry
Vector
Basic Statistics
Basic Dynamics

Plane Geometry

• angles, sides, and area of a triangle

  where

• angles, sides, and area of a polygon
• radius, diameter, circumference, and area of a circle
• arc length and area of a sector of a circle

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Plane Trigonometry

• define an angle between 2 lines
• units used to measure angles
  • degree (deg)
  • radius (rad) = 57.9º
• orthogonal projections of a line segment onto two perpendicular axes
• defintion  of sine (sin)
• definition of cosine (cos)
• definition of tangent (tan)
• inverse trigonometric relationship：
  • if sinq = a     then   q = sin^-1 a
  • if cosq = a     then   q = cos^-1 a
  • if tanq = a     then   q = tan^-1 a
• law of sine:
                       
• law of cosine:
                       
• solution of an arbitrary triangle
• knowing 3 sides to determine the angles
• knowing 2 sides and 1 angle to find the rest of the angles and sides
• knowing 2 angles and 1 side to find the rest of the angles and sides
• area of an arbitrary triangle
  • 
  •      ^where       

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Vector

　　
• scalar vs. vector
  scalar quantities： quantities with magnitude only, e.g. speed of 5 m/s
  vector quantities： quantities with magnitude and direction, e.g. velocity of 5 m/s to right
• vector addition or subtraction
• vector decomposition
• expressed by unit vectors

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