Lecture Materials

Below you will find copies of my lecture materials. I am posting all my lectures using old copies to start the quarter (so you can read ahead of you want), but I do update my notes each quarter so there will often be a few examples done in class that don't exactly match these notes, but these notes are sufficient to give you the main ideas of what we are doing in class.

4.9 Notes: Antiderivatives, "+C", solving for constants
5.1 Notes: Reimann Sums intro, notation, and interpretting.
5.2 Notes: The definite integral notation and introduction.
5.3 Notes: FTOC - Part 1 with examples, Part 2 with examples, and proof outlines
5.4 Notes: Net Change/Total Change (working with absolute values), Indefinite Integrals, and intro to substitution.
5.5 Notes: Substitution Rules, changing bounds, many examples, then intro to area between curves.
More on Substitution (solutions on my main website):
- More on theory of substitution
- Easy practice sheet - Solns: Practie until these are easy.
- Examples similar in difficulty to exams - Solns
6.1 Notes: Area between curves, choosing dx/dy
- Choosing dx/dy Quiz - Solns
6.2 Notes: Volume by cross-sectional slicing
- Two Classic Examples (Volume of Sphere and Volume of Cone)
6.3 Notes: Volumes of revolution using cylindrical shells
Exam 1 Review
Exam 1 Rules and Topics

6.4 Notes: Work! Introduction (leaky bucket & stack of books)
- One-Page Summary of Work Facts
- Easy-ish Work Practice Problem - Solns: 3 leaky bucket, 3 chain, 3 pumping
6.4/5 Notes: More examples of work, and average value
7.1 Notes: Lots of integration by-parts
7.2 Notes: Trig Integrals, combinations of sin(x)cos(x) and combos of sec(x)tan(x)
7.2/3 Notes: More trig Integrals, and Trig Substitution (integrals involving square roots of quadratics)
7.3 Notes: More Trig Substitution (completing the square)
7.4 Notes: Partial Fractions, integrating rational functions (polynomials over polynomials)
7.5 Notes: More partial fractions and summary of all methods (then intro to approximation 7.7)
7.7 Notes: More integration practice, then ways to approximate integrals (when our methods fail).
7.8 Notes: Improper integrals: what to do when integrating functions with asymptotes within the interval of integration.
Exam 2 Review Notes: Overview of all topics on exam 2, basic sample problems of each type (4 work problems)
Exam 2 Rules and One-Page Overview - Listing of rules, skills and topics.

8.1 Notes: Arc Length, in terms of y=f(x) and parametric x=x(t), y=y(t).
8.3 Notes Center of Mass/Centroid, moment about x-axis, moment about y-axis and derivations.
9.1 Lecture Outline - 9.1 Notes: Introduction to Differential Equations.
9.3 Lecture Outline - 9.3 Notes - Mechanics of solving separable differential equations.
9.4 Lecture 1 Outline - 9.4 Notes 1 - Differential equation applications.
9.4 Lecture 2 Outline - 9.4 Notes 2 - Differential equation applications.
Final Topics

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