Calculus & Vector Algebra

Calculus

• Functions
• Polynomials
• Slope
  • Average - Secant Line
  • Instantaneous - Tangent Line
• Derivatives
  • Definition
  • Compute Derivatives of Simple Polynomials
• Integrals
  • Definition
  • Compute Integral of Simple Polynomials
• Understand the relationship between the Derivative and the Integral
• Why are the concepts of derivation and integration important in biomechanics?

Concepts for Review

• Metric System
• Angular Measurements
  • Degrees
  • Radians
• Trigonometric Functions
  • sine
  • cosine
  • tangent
• Law of cosines
• Pythagorean Theorem

Vector Algebra

• Scalars
• Vectors
• Vector Notation
• Vector Representation
• Coordinate Systems
  • 2D
  • 3D
• Vector Projections
  • onto axes of a reference frame
  • onto another vector
• Vector Addition
  • Parallelogram Law
  • Triangle Rule
  • Component Addition
• Vector Subtraction
  • Graphical
  • By Components (Numerical)
• Vector & Scalar Operations
  • Addition (Subtraction)
  • Multiplication
• Unit Vectors
  • Meaning
  • Computation
• Revisit Vector Projections
• Revisit Vector Notation
• Using vectors to represent Body Segments
• Vector Operations
  • Dot or Scalar Product
    • Physical Meaning
    • Interpretation
  • Vector or Cross Product
    • Physical Meaning
    • Interpretation

LINKS