What did we do?
- We studied logarithmic functions by seeing examples of how they are used to make multiplication fast, and how they appear un examples of exponential functions.
- We introduced trigonometric functions by discussing how the sine and the cosine are defined. We compared these new definitions with the classical ones where triangles are used. We made the example of computing sine and cosine of 120.
- We talked about wave functions and how they look according to whether there is one or several components.
- We spoke about polynomial functions, the concept of degree and the difficulty we might have to find solutions to them.
What we did not do?
- We didn’t define radians formaly although we used it when we spoke about wave functions.
- We didn’t talk about an example similar as Example 3 and 4 of section 1.4. Make sure to read this examples.
- We didn’t talk about the graphs of the inverse trigonometric functions.
- We didn’t talk about which function dominates among polynomials and exponentials.
Comments on section 1.4
- It is important to feel comfortable with the properties of the logarithms that appear in page 33, but in there they show it for two bases: base 10 and base e, but they are true of any base.
Comments on section 1.5
- It is important to do not forget that the formula for arc length that appears in page 40 requires the measurement to be in radians. The reason for this is that, if we change the unit of measurement (for example to degrees), a constant that takes into account this change must appear at the front and then the formula looks slightly more complicated.
Comments on section 1.6
- The book gives a special name to power functions, but they are just a particular case of polynomials and should be treated in the same way. They are important particular cases, but giving them a particular name maybe is a bit too much.
- The comment about “local” views and “global” views at the end of page 50 is unfortunate. You cannot have a global view of the graph of a function unless you really see it entirely, even if we see it from very far away, which for functions defined in all the real numbers we cannot do (we cannot really draw an infinite graph). All the drawings we usually make are just local drawings.
- Example 1 and Example 4 are particularly useful.