Lectures

Here I will post the notes I write during class using the document camera. I might revise part of them after class (to spot possible mistakes), but they will be left untouched for the most part. This is to encourage you to take and edit your own notes; in this way, you will naturally organize the material in ways that are most helpful to your learning and visualizing schemes. These lecture notes do not substitute the textbook, so it is important that you compare and integrate them with what is written on the book itself. You can expect to see the lecture notes uploaded by the day after class.

Week 1 (Sep 10-Sep 16).

1. Lecture 1 (Sep 10). Here you can find a set-theory handout if you feel rusty on sets.
2. Lecture 2 (Sep 13).

Key words for this week (make sure you know the definition of all of these): even and odd functions, increasing and decreasing functions, one-to-one function, inverse function, exponential, logarithm.

Week 2 (Sep 17-Sep 23).

1. Lecture 3 (Sep 17). Here you can find a handout with the domain and range of common functions. You need to know about all of these.
2. Lecture 4 (Sep 19).

Key words for this week (make sure you know the definition or the content of all of these): sine, cosine, tangent, addition formula, duplication formula, inverse trigonometric functions, limits at a point, right limit, left limit.

Week 3 (Sep 24-Sep 30)

1. Lecture 5 (Sep 24). In the notes you will find a couple of pages with "infinite limit" laws that could be helpful.
2. Lecture 6 (Sep 26).

Key words for this week (make sure you know the definition or the content of all of these): limit laws, squeeze theorem, continuous function, Intermediate Value Theorem (IVT).

Week 4 (Oct 1-Oct 7)

1. Lecture 7 (Oct 1). Here and here you can find two cheat sheets on continuity and asymptotes for some important functions and on important limits. You should know about all of those.
2. Lecture 8 (Oct 3).

Key words for this week (make sure you know the definition or the content of all of these): vertical and horizontal asymptotes, tangent line, slope, derivative, product rule, quotient rule.

Week 5 (Oct 15-Oct 21).

1. Lecture 9 (Oct 15).

2. Lecture 10 (Oct 17).

3. I have put together a study-guide for the midterm. You can find it here.

Key words for this week (make sure you know the definition or the content of all of these): derivatives of sin, cos and tan, chain rule, implicit differentiation

Week 6 (Oct 22-Oct 28).

1. Lecture 11 (Oct 22).
2. Midterm review (Oct 24).

Week 7 (Oct 29-Nov 4)

1. Lecture 12 (Oct 29).
2. Lecture 13 (Oct 31).

Key words for this week (make sure you know the definition or the content of all of these): logarithmic differentiation, related rates, absolute minimum and maximum value, relative minimum and maximum value, Extreme Value Theorem, critical point, Fermat Theorem, Closed Interval Method.

Week 8 (Nov 5-Nov11).

1. Lecture 14 (Nov 5). Here you can find a handout that explains how sometimes you can mix the Increasing/Decreasing test with the Closed Interval Method to find absolute minimum and maximum values.
2. Lecture 15 (Nov 7).

Key words for this week (make sure you know the definition or the content of all of these): Increasing/Decreasing Test (IDT), First Derivative Test (FDT), concave up, concave down, inflection point, Concavity Test (CT), Second Derivative Test (SDT), optimization problems.

Week 9 (Nov 12-Nov 18).

1. Lecture 16 (Nov 12).
2. Lecture 17 (Nov 14).

Key words for this week (make sure you know the definition or the content of all of these): L'Hospital rule (and when to use it or not use it), Antiderivatives, Most general antiderivative of a function, Sigma Notation.

Week 10 (Nov 19-25).

1. Lecture 18 (Nov 19).
2. Lecture 19 (Nov 21).

Key words for this week (make sure you know the definition or the content of all of these): (Left and right) Riemann sums, Area, Definite Integral, Integrable function, Fundamental Theorem of Calculus (Parts 1 and 2).

Week 11 (Nov 26-Dec 2)

1. Lecture 20 (Nov 26).
2. Lecture 21 (Nov 28). Here is a checklist on integrals you might find useful.

Key words for this week (make sure you know the definition or the content of all of these): Indefinite Integral, Net Change, Substitution rule(s).

Week 12 (Dec 3-Dec 9)

1. Lecture 22 (Dec 3).
2. Lecture 23 (Dec 5).

Key words for this week (make sure you know the definition or the content of all of these): Area between curves, Volumes.