MCS 119, Calculus with Pre-Calculus Review 1b
(12:30-1:20 MTuThF in OHS 320)

Syllabus: Here is the syllabus.

Office hours for the rest of the semester:

• 11-12 and 3-4:30 Fri, 5/13
• 10:30-12:30 and 1:30-4:30 Mon, 5/16
• 10:30-11:30 and 1:00-3:00 Tue, 5/17

Online resources:

• Webwork is where you do your online homework.
• I use Moodle to post your grades periodically throughout the semester
• Definitions of infinite limits
• Here is a list of the topics we have covered. It is updated before each exam.
• Here are my notes to supplement your textbook
  • 1.5. Continuity
  • 1.6. Limits Involving Infinity
  • 2.1. Derivatives and Rates of Change
  • 2.2. The Derivative as a Function
  • 2.3. Basic Differentiation Formulas
  • 2.4. The Product and Quotient Rules
  • 2.5. The Chain Rule
  • 2.6. Implicit Differentiation
  • 2.7. Related Rates
  • 3.1. Maximum and Minimum Values
  • 3.2. The Mean Value Theorem
  • 3.3. Derivatives and the Shapes of Graphs
  • 3.5. Optimization Problems
  • 3.7. Antiderivatives
  • 4.1. Areas and Distances
  • 4.2. The Definite Integral
  • 4.3. Evaluating Definite Integrals
  • 4.4. The Fundamental Theorem of Calculus
• Desmos is everyone's favorite graphing website.
• The following app on secant lines and tangent lines is a good tool to visualize those lines.
• Here is another app on tangent lines.
• Here is yet another app which allows you to see both the tangent line and the corresponding point on the graph of the derivative at the same time.
• Here is an app to visualize the secant line and the tangent line in the Mean Value Theorem.
• The Riemann sums app on Desmos is a good way to visualize how various kinds of Riemann sums approximate the area under a graph.
• Wolfram MathWorld is an interactive math encyclopedia.
• Wolfram Alpha gives you access to many features of Mathematica, an extremely powerful computer algebra program, without paying $$$ and learning Mathematica syntax. It does not only do algebra.

Homework:

Assigned	Due	Read	Exercises
2/3		1.5	No exercises to turn in this week.
2/4	2/11	1.5	Webwork: HW1 Offline: 1.4.52, 54, 62 and 1.5.12 Hint for 1.4.62: Suppose limx → a [f(x)/g(x)] did exist and were equal to L. Could you then use LL4 to figure out limx → a f(x)? Recommended but optional: 1.4.53, 55, 65 and 1.5.5, 7, 13, 15, 17
2/11	2/18	1.6	Webwork: HW2 Offline: 1.5.22, 38, 51 and 1.6.34ab Recommended but optional: 1.5.21, 23, 25, 27, 29, 33, 37, 39, 47, 49 and 1.6.1, 5, 7
2/18	2/25	2.1	Webwork: HW3 Offline: 1.6.34c, 45, 52, 58, and state the informal and formal definitions of the following limits: limx → a- f(x) = ∞ limx → -∞ f(x) = L limx → ∞ f(x) = -∞ Recommended but optional: 1.6.10, 13, 15, 17, 21, 23, 25, 26, 27, 31, 33, 35, 37, 41, 43, 51, 53, 56
2/25	3/4	2.1, 2	Webwork: HW4 Offline: 2.1.8, 14, 20, 46 Recommended but optional: 2.1.1, 5, 13, 15, 17, 23, 27, 29, 31, 33, 39, 41, 43, 49
3/4		2.3	Homework holiday. Review for the upcoming exam.
3/11	3/18	2.3-5	Webwork: HW5 (Hint for problem 13: use the definition of the derivative.) Offline: 2.2.28, 32, 46, 50 Recommended but optional: 2.2.1, 3, 5, 9, 13, 25, 31, 33, 35, 37, 43, 45, 49
3/18	4/1	2.5-7	Webwork: HW6 Offline: 2.3.36, 62 and 2.4.46 and 2.5.62 Recommended but optional: 2.3.1, 19, 21, 25, 33, 39, 51, 53, 65, 67, 69 2.4.1, 5, 13, 21, 29, 31, 35, 43, 47, 51, 55 2.5.1, 5, 11, 15, 17, 23, 27, 33, 41
4/1	4/8	3.1, 2	Webwork: HW7 Offline: 2.5.78 and 2.6.34, 46 and 2.7.24 Recommended but optional: 2.5.63, 73, 77 2.6.7, 11, 21, 27, 43 2.7.3, 7, 11, 13, 21, 25, 27, 31
4/8		3.2	Homework holiday. Review for the upcoming exam.
4/14	4/22	3.2, 3, 5	Webwork: HW8 Offline: 2.7.42 and 3.1.59, 60 and 3.2.22 Hint for 2.7.42: You will probably need to use the Law of Cosines Recommended but optional: 3.1.3, 5, 9, 11, 13, 25, 29, 33, 39, 43, 49, 57 and 3.2.5, 9, 15, 21, 23, 33
4/22	4/29	3.5, 7 and 4.1	Webwork: HW9 Offline: 3.3.20, 34 and 3.5.30, 32 Recommended but optional: 3.3.3, 5, 7, 15, 25, 29, 49 and 3.5.7, 9, 13, 17, 27, 29
4/29	5/6	4.1-3	Webwork: HW10 Offline: 3.7.54 and 4.1.18, 19 and 4.2.24 Recommended but optional: 3.7.5, 7, 9, 29, 39, 43, 55 4.1.5, 7, 11, 15, 17 4.2.5, 7, 15, 17, 21, 39, 47
5/6	5/12	4.3, 4	Webwork: HW11 Offline: 4.3.32, 50 and 4.4.26 Recommended but optional: 4.3.5, 17, 27, 31, 39, 47, 61 and 4.4.1, 3, 19, 23, 31

Exam solutions:

• First midterm exam pdf
• Second midterm exam pdf
• Final exam pdf

Past exams and solutions: You can use these as practice exams as you review and prepare for current exams.

• From MCS 119 in spring 2019:
  • First midterm exam and its solutions
  • Second midterm exam and its solutions
  • Final exam and its solutions
• From MCS 119 in spring 2020:
  • First midterm exam and its solutions
  • Second midterm exam and its solutions
  • Final exam and its solutions
• From MCS 119 in spring 2021:
  • First midterm exam and its solutions
  • Second midterm exam and its solutions
  • Final exam and its solutions

Educational links:

• A serious paper on teaching/learning at the university level by Prof. Steven Zucker

Some scholarship opportunities for prospective teachers:

• Knowles Science Teaching Foundation