Mathematics Recap

While all of you have had lots of math – from basic arithmetic through algebra, trig, calculus, and probability, the way math is typically done in a math course is very different from the way the math is actually used in science courses.  In math, they rarely tell you why they do something or what it’s good for.  This can make it hard to understand what math to reach for in thinking about a situation in science or to know what to do with it when you’ve finished a mathematical analysis. 

In this section we briefly review the math you need to know for this class. In many cases, our approach may be different from what you have seen in math.  We focus on the conceptual underpinnings of the math and explain how to use it to map to physical meaning.

• • Significant (and insignificant) figures
  • Scientific notation
  • The idea of algebra: Unknowns and relationships
    • Symbols in science
    • Variables, constants, and parameters
      • More complex constants and parameters
  • Functions
    
    • Units, Scaling, and functional dependence
    • Powers and exponentials
      • Log-log plots
    • The concept of field
  • Values, change, and rates of change
    • Derivatives 
      • What is a derivative, anyway? (WO, EX)
      • The chain and product rules
        • Proving the chain and product rules (technical)
      • Differential Equations (EX)
    • Integrals: The mathematical meaning
      
      • How can I actually use integrals?
  • Trigonometry
    • The small angle approximation
    • Trig functions for any value of the argument
    • The derivatives of trig functions
  • Probability
    
    • Why probability matters
    • Expected values
    • Permutations and combinations