## Applied Calculus I

NOTE: The "Main lecture topics" entries are not exhaustive, and entries referring to future class meetings are speculative.
Date Main lecture topics Relevant book sections Homework due
5/15 Hello. What calculus is about. Syllabus. Questionnaire. Exponents, factoring, quadratic formula, absolute values, inequalities, distances, equations of circles, properties and equations of lines. Classwork. 1.1-4
5/16 A little about the previous classwork, and a little more about lines. Functions: domain, range, graph, piecewise-defined, composition. Classwork.
2.1-2 HW 1
5/17 Diagnostic quiz and its solution. Some discussion of previous classwork. Arithmetic with rational functions. Rationalizing. An example of math modeling. Classwork. Limits. 2.3-4 HW 2
5/18 All about limits: meaning, computational evidence, graphical significance, limit laws, indeterminate forms, one-sided limits, limits at infinity (especially for rational functions), continuity. Word problems. Classwork. 2.3-5
5/19 Comments on the last classwork. The Intermediate Value Theorem. Derivative: meaning as the slope of the tangent line, and definition as a limit. Classwork. 2.5-6 HW 3
5/22 Average velocity versus instantaneous velocity, which is a rate of change, which is a derivative. Tangent lines. Differentiability versus continuity. Some differentiation rules. Classwork. 2.6,3.1 HW 4
5/23 Product rule, quotient rule, chain rule. Classwork. 3.2-3 HW 5
5/24 Average velocity converges to instantaneous velocity, which is a derivative. Higher derivatives: definition, examples, and meaning (including acceleration). Implicit differentiation. Classwork. 3.5-6 --
5/25 Midterm 1, covering all material through 5/22 lecture and HW 5. Here are some old midterms and their solutions, but students must realize that our course may not have covered or emphasized exactly the same material: S16 Exam solution; F15 Exam solution; S15 Exam solution.
Our midterm and its solution. The median was 34 out of 50, and the grade breaks are as follows: A/B 39, B/C 32, C/D 26, D/F 20.
Applying differentiation rules in various ways. Graphical significance of the sign of the first and second derivative. Classwork.
(last day to drop)
4.1 HW 6a
5/26 Review of implicit differentiation. Increasing/decreasing, concavity, points of inflection. The invention of modern calculus (see the homework handout). Related rates. Classwork. 3.6,4.1-2 HW 6b
5/29 Memorial Day holiday
5/30 Finishing classwork and discussing related rates problems. Position functions. Review of increasing/decreasing and concavity. Graphing f' from the graph of f. The First Derivative Test. The Second Derivative Test. Classwork. 4.1-2 --History handout (due at the beginning of class)
--HW 7 (at 11:59 pm)
5/31 Review of last class, including FDT and SDT. Asymptotes. How boats speed up as you pull them in. A graphing checklist (not for memorization). A little about exponential functions and logarithms. Classwork. 4.1-3, 5.1 HW 8
6/1 Donut day. An implicit differentiation example. Recap of exponentials and logarithms. The derivatives of ex and ln(x), and doing other derivatives based on this. Classwork with curve sketching.
5.1-2, 5.4-5 --
6/2 Midterm 2, covering all material through 4.3 and HW 8. Here are some old midterms and their solutions, but students must realize that our course may not have covered or emphasized exactly the same material: S16 Exam solution; F15 Exam solution; S14 Exam solution. There are also extra ungraded practice problems available on WebAssign.
Our midterm and its solution. The median was 41.5 out of 50, and the grade breaks are as follows: A/B 43, B/C 36, C/D 29, D/F 23.
Review of ex and ln x: graphs, asymptotes, derivatives, equation-solving. Interest compounded at regular intervals or continuously.
(last day to withdraw)
5.1-5 HW 9
6/5 Review of Ch. 5. Absolute extrema and the Extreme Value Theorem. Antidifferentiation = integration = finding indefinite integrals. Rules and examples for antiderivatives. An initial-value problem. Classwork. 4.4,6.1 HW 10ab
6/6 Discussion of previous classwork. An optimization word problem. Integration by substitution. Classwork. 4.5,6.2 --
6/7 Definite integrals defined as signed area under a curve. Discussing the open tray problem from the last classwork (and p.314). The indefinite integrals we can do: sums of multiples of ex and powers of x (without thinking), and u-substitution (with thinking). Reviewing why and how we integrate by substitution. Classwork, with answers put up on the board. About the mathematical definition of a definite integral. The Fundamental Theorem of Calculus. Practice. 6.3-4 HW 11
6/8 Optimal path for a dog swimming and running to food. Review of definite integrals. The FTC and net change. An example: integrating production rate to get total production. Minimizing the surface area of a cylinder with fixed volume. Classwork: a capstone optimization problem, minimizing cost of cable. 4.5,6.5 HW 12ab
6/9 Optional review/practice session/glorified office hours, 12-1:30 in Monroe 116 (our usual classroom). -- --
6/10 FINAL EXAM at the usual time (10:30-12:45) and location (Monroe 116), covering all material. Here are some old finals and their solutions, but students must realize that our course may not have covered or emphasized exactly the same material: S16 Exam solution; F15 Exam solution; S14 Exam solution. There are also extra ungraded practice problems available on WebAssign.

Final exam scores

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