Lecture Materials

Below you will find copies of the overheads that I use in lecture. Most of lecture I write out during class, so if you missed class, then you will want to get a copy of the notes from a classmate. These overheads just contain the entry task or summary information that I used for that topic in lecture:

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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