MCS 119, Calculus with Pre-Calculus Review 1b
(10:30-11:20 MTuThF in OHS 318)

Syllabus: Here is the syllabus.

Office hours for the rest of the semester:

• 12:20-2:20 Fri, 5/19
• 12:30-1:30 Sat, 5/20
• 10:30-12:30 Mon, 5/22

Calculus tutoring center: Calculus tutoring is provided by fellow undergraduate students in OHS 321 at 6:00-9:00 Sun-Thu nights. Tutoring runs through the last day of classes, except during college holidays.

Online resources:

• Webwork is where you do your online homework.
• I use Moodle to post your grades periodically throughout the semester
• The grade calculator allows you to input your current running total from Moodle and see what kind of score you need on the final exam for each kind of letter grade. The calculator is a Google Sheets document, so you need to be logged in to a Google account to access it. It is supposed to work with any Google account, not only your Gustavus account. Click Use Template in the upper right corner to start. You can also download an Excel version of the calculator if Google Sheets does not want to cooperate.
• 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
  • 1.6. 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
  • 4.5. The Substitution Rule
• 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
2/6		1.6	No exercises to turn in this week.
2/10	2/17	1.6, 2.1	Webwork: HW1 Offline: 1.5.38, 51 and 1.6.34, 45 Recommended but optional: 1.5.25, 27, 37, 39, 47, 49 and 1.6.1, 5, 7, 10, 13, 21, 23, 27
2/17	2/24	2.2, 3	Webwork: HW2 Offline: 1.6.52, 58 and 2.1.14, and also state the informal and formal definitions of the following limits: limx → a- f(x) = ∞ limx → -∞ f(x) = L limx → ∞ f(x) = -∞ Recommended but optional: 1.6.31, 33, 35, 37, 41, 43, 51, 53, 56 and 2.1.1, 5, 13, 15, 17
2/24	3/3	2.2-4	Webwork: HW3 Offline: 2.1.8, 20, 46 and 2.2.32 Recommended but optional: 2.1.23, 27, 29, 31, 33, 39, 41, 43, 49 and 2.2.1, 3, 5, 9, 13, 31, 33
3/3	3/10	2.3, 4	Webwork: HW4 Offline: 2.2.28, 46 and 2.3.36, 62 Recommended but optional: 2.2.25, 35, 37, 45 and 2.3.1, 11, 13, 19, 21, 25, 39, 53, 65, 67, 69
3/10		2.4	Homework holiday. Review for the upcoming exam.
3/17	3/24	2.5-7	Webwork: HW5 Offline: 2.4.46, 50, 56 and 2.5.62 Recommended but optional: 2.4.1, 5, 13, 21, 31, 35, 43, 47, 51, 55 and 2.5.1, 5, 13, 15, 17, 23, 27, 33, 41
3/24	3/31	2.7 and 3.1, 2	Webwork: HW6 Offline: 2.5.78 and 2.6.34, 42, 46 Recommended but optional: 2.5.63, 73, 77 and 2.6.7, 11, 21, 25, 27, 31, 33, 43
3/31	4/14	3.1-3	Webwork: HW7 Offline: 2.7.18, 24, 42 and 3.1.32 Recommended but optional: 2.7.3, 7, 11, 13, 21, 25, 27, 31 and 3.1.3, 5, 9, 11, 13, 25, 29, 33
4/14		3.2, 3, 5	Homework holiday. Review for the upcoming exam.
4/21	4/28	3.5, 7 and 4.1	Webwork: HW8 Offline: 3.2.22 and 3.3.20, 34 and 3.5.30 Recommended but optional: 3.1.39, 43, 49, 57 3.2.5, 9, 15, 21, 23, 33 3.3.3, 5, 7, 15, 25, 29, 49 3.5.7, 9, 13, 17, 27, 29
4/28	5/5	3.7 and 4.1, 2	Webwork: HW9 Offline: 3.5.32, 54 and 3.7.52, 54 Recommended but optional: 3.5.33, 37, 43, 49, 51 and 3.7.5, 7, 9, 29, 39, 43, 55
5/5	5/12	4.2-4	Webwork: HW10 Offline: 4.1.18, 19 and 4.2.24 and 4.3.50 About exercise 4.1.19: Assume that the partition is uniform. The exercise does not specify this, but appears to assume it in parts (b) and (c). Also, do not forget that b could be smaller than a. First, assume a< b, then think about whether anything changes if b< a. Recommended but optional: 4.1.5, 7, 11, 15, 17 4.2.5, 7, 15, 17, 21, 39, 47 4.3.5, 17, 27, 31, 39, 47, 61
5/12	5/16 (note Tuesday deadline, except Webwork)	4.4, 5	Webwork: HW11 Offline: 4.4.14, 26 Recommended but optional: 4.4.1, 3, 19, 23, 31 and 4.5.3, 5, 7, 21, 37, 41

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
• From MCS 119 in spring 2022:
  • 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