- Other editions of text may have different section and problem numbers
- Problem sets have summaries of problems to help you find the right ones
- But not complete problem statements!
- I’ll try to give you topics as well as section numbers for readings to help you find them
- Problem sets have summaries of problems to help you find the right ones
- Google Calendar for appointments
- Invite me to the appointment! (Otherwise Google won’t tell me about it)
- Question 2 on problem set?
- Slope of inverse is reciprocal of slope of f theorem
- Final answer = 1/2
- But why?
- Section 7.2
- Natural logarithm = ln x
- Derivative = 1/x
- Proof?
- Proof?
- Properties
- ln 1 = 0
- ln xk = k lnx
- ln xy = lnx + lny
- ln x/y = lnx - lny
- e defined by ln e = 1
- Anti-derivatives follow from d/dx (lnx) = 1/x
- Logarithmic differentiation?
- (Inverse of ln x is ex)
- What is a logarithm in general?
- Exponent, in kind of an inverse way
- logbx = c means bc = x
- Examples
- Simplify
- ln (x sinx)
- = lnx + ln (sinx) by product property
- ln (x+1)3
- = 3 ln(x+1) by exponentiation property
- ln( (x2 + 2x) / (x-1) )
- ln (x sinx)
- More examples of derivatives non-trivially involving the chain rule
- Logarithmic differentiation
- Simplify
- Problem Set
- Natural logarithms and integration
- Hopefully start talking about the exponential function
- Section 7.3