Co-16B

Course Information:

  • Class time: MWF 12:10 - 1 pm

  • Location: Class Link

  • Dedicated Office Hours: (TBA)

Overview of 16B

Ch. 4: Exponential and Logarithmic Functions

Ch. 5: Integration

Ch. 6: Techniques of Integration

Ch. 8: Trigonometric Integrals

Ch. 9: Probability and Calculus


**Note: Not all topics in these chapters will be covered and the order may vary with the professor.

Ch. 4: Exponential and Logarithmic Function

Key Concept Questions:

  • What is a logarithm?

      • Hint: If addition is the inverse operation of subtraction, and multiplication is the inverse of division...what is a logarithm the inverse operation of?

      • Complete this sentence: A log is an operation that undoes _________________

  • What is the basic form of an exponential function? Is a parabola an exponential since it has an exponent of 2?

  • What is the basic form of the plot of a log function ?

  • What is the basic form of the plot of an exponential function

  • What 3 general features do they share?

  • How would you compare their domain and range?

  • What is special about the plot of e^x when compared to all other exponential plots (e.g., 2^x, 3^x, 5^x, ... , a^x)

    • Hint...this is why Leonard Euler (pronounced "OY-ler" not "YOU-ler") picked e as the "natural base" for growth.

    • Hint*hint: what is the slope of the e^x function at the y-intercept?

This last bit has IMPORTANT implications for calculus.

  • What is the derivative of e^x?

  • What does this imply about the anti-derivative (the reverse derivative) of e^x?

  • What is the meaning of the anti-derivative?

  • Could you sketch the deriviative and the anti-deriviative of e^x on the same plot?

Day 2: Exponentials and Logarithms

10/2/20

  • 5 Exponent Rules

  • 5 Log Rules

  • General derivative


Class Notes

Day 3: Exponential Growth/Decay

10/5/20

  • Growth: Interest equation

  • Decay and half-life

  • Chain-rule mechanic

Class Notes

Catenary Video Links:

  1. The Catenary and the natural world: Link

  2. Engineering and the hanging chain: Link

These are not essential watching but can help give meaning to otherwise boring/confusing math.

Day 4: More derivatives of exponentials and logs

10/7/20

  • Using MODELS to differentiate

  • Logarithmic Differentiation as alternative to complicated mixed type derivatives (quotient + product + chain rule)



Class Notes

Day 5: Derivatives and Rates of Change

10/9/20

  • Tangent lines

  • Practice with exponential and log differentiation

  • The chain rule and implicit differentiation

Class Notes