Math 152: Calculus I

Course Information

  • Institution: Dordt University
  • Course: Math 152-01 (4 cr.)
  • Term: Spring 2022
  • Instructor: Dr. Mike Janssen, Associate Professor of Mathematics
  • Classroom: CL 2241
  • Class time: 8:10-9:25am MWF
  • Office: SB 1612
  • Student Hours: Make an appointment or drop by
  • Catalog Course Description: A study of the basic concepts and techniques of calculus for students in all disciplines. Topics include limits, differentiation, integration, and applications. This course is intended for students without any previous calculus credit. Prerequisite: Mathematics 116 or equivalent or ALEKS PPL score of 70 or higher by third class meeting.

Required Resources

  • Access to the free textbook, Active Calculus
  • Active Calculus Dordt bundle, containing the activities workbook and an Edfinity access code
  • Regular access to our Canvas page

A graphing calculator feature equivalent to a TI-84+ will likely come in handy, but is not required. We will make regular use of Desmos for in-class work.

Learning Objectives

In this course, students will:

  • be learners by demonstrating mastery of the mathematical concepts that have driven the development of our understanding of the inner working of creation and technology over the past 400 years. (RO, CD)
  • be explorers by actively inquiring into/working with and applying the techniques of limits, differentiation, and integration using standard methods of calculus. (CS)
  • be connectors by applying these tools and concepts to mathematical and real-world problems in a variety of settings. (CS, CR)
  • be ambassadors by reflecting on the beauty and truth that can be found through a careful study of God’s mathematical creation. (RO, CD)

Course Liturgies

In this section, we briefly describe the basic rhythms of the course.

Before Class

In order to maximize your learning, it is important that you regularly attend class, and come prepared. For days on which we start a new section, this means that you should:

  • read over the relevant section of the book (especially the Motivating Questions and introduction), and
  • complete the Preview Activity (done on Desmos) and submit it by 8:00am.

Each timely submission of a Desmos Preview Activity on which you have made a good-faith effort to be correct will earn one Engagement Point (EP).

During Class

Unlike many “traditional” courses in mathematics, you will drive the in-class work, not me. A typical class period will begin with a brief reminder of a big idea or two from the pre-class work. We’ll spend the majority of the time working in small groups on activities from our course materials, with occasional interruptions to discuss new insights and confirm that we’re all on the same page.

After Class

In order to build toward proficiency with the fundamental concepts and skills of the course, you will be assigned regular post-section homework, to be accessed on our Canvas site and completed on the Edfinity platform. See the due dates in the tentative schedule.

Assessed Work

Your fluency of the main concepts of calculus (and thus your final grade) will be assessed via the following items of work.

Engagement

Your progress on this aspect of the course will be based on the number of Engagement Points (EPs) earned. You will earn one (1) EP by: submitting a Desmos Preview Activity by 8:00am Central on the assigned due date (see schedule below); and attending one class meeting. Daily Prep assignments and class attendance may not be made up/revised after the fact.

Homework

The online homework (done on Edfinity and accessed via Canvas) consists of regular problems due by 5:00pm Central on the listed due dates, typically the class day after we finish covering the relevant section. Your average on all of the homework sets will affect your final grade. You have an unlimited number of attempts on each problem, so your overall homework average should reflect not only your knowledge of the material but also your perseverance and commitment to finishing the work.

Learning Target Exams

There are 30 learning targets in this course (listed below). Each learning target will be assessed on at least two exams. Each problem will earn a grade of M (meets expectations) or R (revision/reassessment needed). The number of learning targets assessed at M will affect your final grade.

Derivative Calculation Exam

One of the topics that we are going to spend a majority of the semester exploring is the derivative of a function. In order to properly explore and answer questions about applications, it is important that you differentiate a function quickly and correctly. To this end, you will take an exam on which you must correctly differentiate at least 8 of 10 functions given to pass. In order to pass this class and move on to Calculus II, you must pass the Calculation Exam.

Reflections

Dordt University places itself squarely in the Reformed tradition of the Protestant Christian faith. We affirm, as Abraham Kuyper said, that there is not a square inch in all of Creation over which Christ does not claim lordship—not even the abstract aspects of Creation commonly associated with mathematics. You will write two reflection papers this semester: the first will explore the aesthetic qualities of mathematics. In the second, we’ll explore the human story of the development of the Fundamental Theorem of Calculus. These reflection assignments will be due as described below and assessed on a Pass/Not Yet scale. More details are available on each assignment’s Canvas page.

Final Exam

The final exam will be comprehensive and will be used to determine how your base grade is modified (add a plus, leave unchanged, add a minus, drop a letter grade).

Grading

Base Grade

Your Base Grade will be determined by your work on the assignments described above. In general, the highest fully completed row the following table will determine your Base Grade.

Base Grade Learning Targets Homework Average Engagement Points Reflections Derivative Calculation Exam
A 28 92% 60 2 8/10
B 25 80% 50 2 7/10
C 22 67% 40 2 6/10
D 16 55% 30 1 4/10

Final Exam Modifier

The final exam will consist of 10 problems (each graded out of 10 points) corresponding to the bolded learning targets. The final exam will modify your base grade in the following way:

  • If you earn 85 points or more, your base grade will have a plus attached to it (unless it is an A; Dordt does not award A+ grades).
  • If you earn 65 – 84 points, your base grade will be unmodified.
  • If you earn 50 – 64 points, your base grade will have a minus attached to it.
  • If you earn 49 points or less, your base grade will drop by a full letter grade.

Note that if your base grade is an F, your course grade will be an F regardless of your performance on the final exam.

Reassessments and Revisions

There are two goals of the assessments in this course. The first goal is to hold you accountable for being an active and engaged member of our classroom learning community. This is where the Preview Activities come into play. Since these are intended to keep you on pace with the course material, late submissions will not be accepted.

The second goal of the assessments is to measure how well you are meeting the learning outcomes of the course. However, I am primarily concerned with your ability to eventually demonstrate mastery of the learning outcomes, so the opportunity to reattempt or to revise and resubmit is available for the other assessment categories.

Reattempts

If you do not pass the Calculation Exam or a learning target during the scheduled exam times in class, you will be able to reattempt them during weekly quiz reassessments. During non-exam weeks, you will be allowed to sign up by Tuesday at 11:59pm to reassess the Calculation Exam or up to 2 learning targets on Fridays at 9:00am. Learning Targets may only be reassessed after they first appear on an exam. The schedule of available learning targets is available below.

Other Polices and Advice

  • I am generally fairly accepting of late work, with a built-in 24-hour grace period for any non-classroom activities. Additional time beyond the 24-hour grace period must be approved ahead of time.
  • Student hours are your time to ask questions about all aspects of the class and college life. If you can’t find an appointment, send me an email! I will do my very best to accommodate your schedule.
  • Email Policy: I check my email twice per school day: once in the morning, where I’ll deal with any emergencies, and once in the afternoon, when I’ll respond to other emails (including any that have come in since the morning). If you require a more immediate response, you’re welcome to come find me in my office.

Additional Information

Dordt University Student’s Right to Accommodations Policy

Dordt University is committed to providing reasonable accommodations for students with documented qualifying disabilities in accordance with federal laws and university policy. Any student who needs access to accommodations based on the impact of a documented disability should contact the Academic Enrichment Director: Sharon Rosenboom, Academic Enrichment Center, Office: L166, (712) 722-6488, Email: Sharon.Rosenboom@dordt.edu.

Dordt University Academic Dishonesty Policy

Dordt University is committed to developing a community of Christian scholars where all members accept the responsibility of practicing personal and academic integrity in obedience to biblical teaching. For students, this means not lying, cheating, or stealing others’ work to gain academic advantage; it also means opposing academic dishonesty. Students found to be academically dishonest will receive academic sanctions from their professor (from a failing grade on the particular academic task to a failing grade in the course) and will be reported to the Student Life Committee for possible institutional sanctions (from a warning to dismissal from the university). Appeals in such matters will be handled by the student disciplinary process. For more information, see the Student Handbook.

Classroom Attendance Protocol

As we begin the Spring 2022 semester, class attendance policies and procedures as outlined in the Student Handbook are in place. To paraphrase the Student Handbook, Dordt University as an institution remains committed to in person instruction for face-to-face courses. As a result, you are expected to be present for every class period and laboratory period. Should you need to miss class for any reason, contact your instructor as soon as possible (either prior to the absence or immediately following). Absences for Dordt-sponsored curricular or co-curricular activities will be communicated by the activity sponsor and are considered excused.

Methods of making arrangements for missed work are back to normal (pre-COVID). You are responsible to contact your instructor. Your instructor is not required to provide real time (synchronous) learning for you should you be absent for class for any reason (ex. Zooming into your real time class). Your instructor is also not required to provide asynchronous virtual learning materials for you (ex. recordings of missed classes, slide decks, other materials on Canvas). While some instructors might utilize some of the synchronous/asynchronous methods of making up work on occasion, you should not expect all instructors to provide these experiences automatically. Methods of making up missed work might include: contacting a fellow student to get notes from class, extensions on assignments or labs, or other methods as determined by your instructor. Making arrangements for missed class work is your responsibility!

Please see your instructor’s specific attendance policy.

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Learning Targets

Bolded Learning Targets will be covered on the Final Exam. Representative problems appear in parentheses, though note that you should not expect exam problems to look exactly like one of these.

  1. Given information about a function (either a table of data or a graph), answer questions about its average and/or instantaneous rates of change. (Exercises, 1.1.1.1.1.2, 1.1.4, 1.1.5, 1.6.3)
  2. Sketch a graph that has specific behaviors at indicated points and intervals. (Exercise 1.2.7, 1.6.9)
  3. Given the graph of a function, answer questions about the function, its derivative, and its second derivative. (Exercises 1.3.1, 1.3.2, 1.3.3, 1.4.3, 1.4.4, 1.6.1, 1.6.2)
  4. Use the limit definition to find the derivative function. (Exercises 1.4.2, 1.4.5)
  5. Use the central difference and other estimation techniques to answer questions about applications of the derivative. (Exercises 1.5.1, 1.5.2, 1.5.3, 1.5.4, 1.6.8)
  6. Given the graph of the derivative, answer questions about the function, the first derivative, and the second derivative. (Exercise 1.6.5, 1.6.7)
  7. Given the graph of a function, determine the values of indicated limits. (Exercises 1.2.1, 1.2.2, 1.2.3, 1.7.1, 1.7.2)
  8. Given the graph of a function, determine the x-values where the function is not continuous and the points where it is not differentiable. (Exercises 1.7.3, 1.7.5)
  9. Find a local linearization, use it to estimate the function at a nearby point, and answer questions about the accuracy of that estimate. (Exercises 1.8.1, 1.8.2, 1.8.3, 1.8.4)

  1. Find the equation of a tangent line. (Exercises 2.1.8, 2.2.2, 2.3.12b, 2.4.5)
  2. Given information about two or more functions (either graphs or values, but not the equations), answer questions about new functions involving those functions and their derivatives. (Exercises 2.1.10, 2.1.11. 2.3.8, 2.3.9, 2.3.12a,d, 2.5.5, 2.5.6, 2.6.5, 2.8.1)
  3. Find $dy/dx$ for a function given implicitly. (Exercises 2.1.1, 2.1.2, 2.1.3, 2.1.4, 2.1.5)
  4. Use L’Hopital’s Rule to evaluate limits involving indeterminate forms. (Exercises 2.8.3, 2.8.4, 2.8.5)

  1. Find the intervals where a function is increasing/decreasing and identify the relative maximums and minimums of the function. (Exercises 3.1.1, 3.1.4)
  2. Find the intervals where a function is concave up/down and identify the inflection points of the function. (Exercises 3.1.1, 3.1.2)
  3. Use the second derivative test to identify the local maximums and minimums of a function.
  4. Given information about a function (but not its equation), answer questions about the function, its first derivative, and its second derivative. (Exercise 1.6.6, 3.1.5)
  5. Given a family of functions, answer questions about the function and its derivative.(Exercises 3.2.3, 3.2.4)
  6. Given a function and a closed interval, identify the absolute maximum and minimum on that interval. (Exercises 3.4.2, 3.4.4)
  7. Solve an applied optimization problem. (Exercises 3.4.1, 3.4.2, 3.4.3, 3.4.4, 3.4.5)
  8. Solve a related rates problem. (Exercises 3.5.1, 3.5.2, 3.5.3, 3.5.4, 3.5.5)

  1. Use antiderivatives to answer questions involving total distance traveled, change in position, velocity, and acceleration. (Exercises 4.1.1, 4.1.2, 4.1.3, 4.1.4, 4.1.5)
  2. Use Riemann sums to estimate the area between a positive function and the horizontal axis. (Exercises 4.2.1, 4.2.2, 4.2.3, 4.2.4)
  3. Given a Riemann sum, identify the function and interval it is approximating to the area under the curve for. (Exercise 4.2.5)
  4. Use graphs of functions and properties of definite integrals to evaluate definite integrals. (Exercises4.3.1, 4.3.2, 4.3.3, 4.3.4, 4.3.6, 4.3.7)
  5. Use the fundamental theorem of calculus to evaluate definite integrals. (Exercises 4.4.2, 4.4.3, 4.4.4, 4.4.5)

  1. Given the graph of a function, answer questions about its antiderivatives. (Exercises 5.1.1, 5.1.4, 5.1.5
  2. Given the graph of a function, sketch a specified accumulation function of that function. (Exercises5.1.3, 5.2.4)
  3. Use the second fundamental theorem of calculus to determine the derivative of an accumulation function. (Exercise 5.2.2)
  4. Use substitution to evaluate definite and indefinite integrals. (Exercises 5.3.1, 5.3.2, 5.3.3, 5.3.4, 5.3.5, 5.3.6)

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Tentative Schedule

I aim to build a dynamic classroom; as such, the schedule below may be changed as the semester progresses. Any changes will be reflected here.

Date Daily Plan Prep Due Other Work Due
F Jan 14, 2022 Course Intro/1.1: How do we measure velocity?
M Jan 17, 2022 1.1 How do we measure velocity/1.2 The notion of a limit 1.2
W Jan 19, 2022 1.2 The notion of a limit 1.1 Homework
F Jan 21, 2022 1.3 The derivative of a function at a point 1.3 1.2 Homework
M Jan 24, 2022 1.4 The derivative function 1.4 1.3 Homework
W Jan 26, 2022 1.5 Interpreting, estimating, and using the derivative 1.5 1.4 Homework
F Jan 28, 2022 1.6 The second derivative 1.6 1.5 Homework
M Jan 31, 2022 1.7 Limits, Continuity, and Differentiability 1.7 1.6 Homework
W Feb 2, 2022 1.8 Tangent line approximation 1.8 1.7 Homework
F Feb 4, 2022 Review/catch-up 1.8 Homework
M Feb 7, 2022 Exam 1: LTs 1-9
W Feb 9, 2022 2.1 Elementary Derivative rules 2.1
F Feb 11, 2022 2.2 Sine and cosine 2.2 Quiz LTs 1-9; 2.1 Homework
M Feb 14, 2022 2.3 Product and Quotient rules 2.3 2.2 Homework
W Feb 16, 2022 2.4 Derivatives of other trig functions 2.4 2.3 Homework
F Feb 18, 2022 2.5 Chain rule I 2.5 Quiz LTs 1-9; 2.4 Homework
M Feb 21, 2022 2.5 Chain rule II
W Feb 23, 2022 2.6 Derivatives of inverse functions 2.6 2.5 Homework
F Feb 25, 2022 2.7 Implicit differentiation 2.7 Quiz LTs 1-9; 2.6 Homework
M Feb 28, 2022 2.8 Using derivatives to evaluate limits 2.8 2.7 Homework
W Mar 2, 2022 Derivative Practice/Review 2.8 Homework
F Mar 4, 2022 Exam 2: LTs 1-13, Calculation Exam
M Mar 7, 2022 No Class: Spring Break
W Mar 9, 2022 No Class: Spring Break
F Mar 11, 2022 No Class: Spring Break
M Mar 14, 2022 No Class: Spring Break
W Mar 16, 2022 3.1 Using derivatives to identify extreme values 3.1
F Mar 18, 2022 3.1 Using derivatives to identify extreme values/3.2: Using derivatives to describe families of functions Quiz LTs 1-13
M Mar 21, 2022 3.2: Using derivatives to describe families of functions 3.2 3.1 Homework
W Mar 23, 2022 3.3: Global optimization 3.3 3.2 Homework
F Mar 25, 2022 3.4: Applied optimization 3.4 Quiz LTs 1-13; 3.3 Homework
M Mar 28, 2022 3.4: Applied optimization Reflection 1
W Mar 30, 2022 3.5: Related Rates 3.5 3.4 Homework
F Apr 1, 2022 3.5 Related Rates Quiz LTs 1-13
M Apr 4, 2022 Exam 3: Learning Targets 10-21
W Apr 6, 2022 4.1: Distance from velocity 4.1 3.5 Homework
F Apr 8, 2022 4.2: Riemann sums 4.2 Quiz LTs 10-21; 4.1 Homework
M Apr 11, 2022 4.3: The definite integral 4.3 4.2 Homework
W Apr 13, 2022 4.4: FTC I 4.4 4.3 Homework
F Apr 15, 2022 No Class: Easter Break
M Apr 18, 2022 No Class: Easter Break
W Apr 20, 2022 Exam 4: LTs 14-26
F Apr 22, 2022 5.1: Constructing graphs of antiderivatives Quiz LTs 14-26; 4.4 Homework
M Apr 25, 2022 5.2: FTC II 5.2 5.1 Homework
W Apr 27, 2022 5.3: Substitution 5.3 5.2 Homework
F Apr 29, 2022 5.3: Substitution Quiz LTs 14-26
M May 2, 2022 Review 5.3 Homework
W May 4, 2022 Exam 5: LTs 22-30
F May 6, 2022 Review for final Quiz LTs 22-30; Reflection 2
T May 10, 2022 Final Exam 8-10am