Course Info

Title: MAT 136: Calculus I
Semester: Fall 2020
Credits: 4
Section: 14
Time: 1:50-2:40PM MWThF
Location: AMB 225

Instructor Info

  Dana C. Ernst, PhD
  AMB 176
  12:30-1:30PM on MTh, 11:30AM-12:30PM on WF


MAT 125 or MAT 125H with a grade greater than or equal to C or satisfactory mathematics placement.

Catalog Description

Calculus of one variable; basic concepts, interpretations, techniques, and applications of differentiation and integration. Letter grade only. Course fee required.

Additional Information

This course fulfills a requirement in the Science/Applied Science distribution block in the University Liberal Studies program. It supports the mission of the program to prepare students to live responsible, productive, and creative lives as citizens of a dramatically changing world through the study of Calculus and its applications. Essential skills in this course are critical thinking, quantitative reasoning, and scientific reasoning. This course is also a certified First Year Learning Initiative (FYLI) course.


The official textbook for the course is Calculus: Early Transcendentals€ (3rd edition) by Rogawski and Adams. A year ago, the publisher released a new 4th edition of the book, but in an effort to save students money, we opted to stay with the 3rd edition. Unfortunately, it does not appear that the NAU bookstore has sufficient stock of the 3rd edition for all MAT 136 students. In addition, other places (e.g., Amazon) appear to have low stock of the 3rd edition. The upshot is that obtaining a physical copy of the 3rd edition maybe difficult. If you want to purchase a physical copy of the book and are unable to locate the 3rd edition, you may purchase the 4th edition. This might cause some mild inconvenience, but we will deal with it.

You also have the option of purchasing the textbook in electronic format. If you purchased an access code from the NAU bookstore, you can enter it here. You should also be able to purchase an access code at that link. Note: there might be a slight cost difference for the access code at the NAU Bookstore versus purchasing directly from the publisher. Please let me know if you have questions about the textbook.

You are also welcome to utilize other books covering first semester calculus. Check out the Course Materials page for a list of free calculus textbooks and other resources.

I expect you to be reading the textbook. The only way to achieve a sufficient understanding of the material is to be digesting the reading in a meaningful way. You should be seeking clarification about the material in the textbook and notes whenever necessary by asking questions in class or posting questions to the course Google Group.

Don’t just read it; fight it! Ask your own questions, look for your own examples, discover your own proofs. Is the hypothesis necessary? Is the converse true? What happens in the classical special case? What about the degenerate cases? Where does the proof use the hypothesis?

Purpose and Goals

The primary objective of this course is to aid students in becoming confident and competent in solving problems that require techniques developed in calculus. Successful completion of MAT 136 provides students with skills necessary for upper division mathematics courses, such as MAT 137: Calculus II. In general, calculus is a study of functions. The main tools are differentiation, which measures instantaneous change in a function, and integration, which gauges the cumulative effect of that change. The crowning achievement of first semester calculus is the Fundamental Theorem of Calculus, which explains how differentiation and integration are related. Students will have a working understanding of limits and continuity. Students will also be able to utilize various techniques to differentiate and integrate numerous functions including trigonometric functions. In addition, students will understand and be able to apply the Mean Value Theorem, the First and Second Derivative Tests, and the Fundamental Theorem of Calculus in both theoretical problems and applications. Also, the purpose of any mathematics class is to challenge and train the mind. Learning mathematics enhances critical thinking and problem solving skills.

Aside from the obvious goal of wanting you to learn calculus, one of my principle ambitions is to make you independent of me. Nothing else that I teach you will be half so valuable or powerful as the ability to reach conclusions by reasoning logically from first principles and being able to justify those conclusions in clear, persuasive language (either oral or written). Furthermore, I want you to experience the unmistakable feeling that comes when one really understands something thoroughly. Much “classroom knowledge” is fairly superficial, and students often find it hard to judge their own level of understanding. For many of us, the only way we know whether we are “getting it” comes from the grade we make on an exam. I want you to become less reliant on such externals. When you can distinguish between really knowing something and merely knowing about something, you will be on your way to becoming an independent learner. Lastly, it is my sincere hope that all of us (myself included) will improve our oral and written communications skills.

Learning Outcomes

Upon successful completion of the course, you will be able to:

  • Demonstrate an understanding of the concepts of limit, derivative and integral in writing, and graphically.
  • Calculate, or approximate as appropriate, the limit of a function using appropriate techniques including l’Hospital’s rule.
  • Find the derivative of elementary polynomial, exponential, logarithmic and trigonometric functions.
  • Use rules of differentiation including the power rule, product rule, quotient rule, chain rule, and implicit differentiation to compute the derivative of a function. Obtain expressions for higher order derivatives of a function.
  • Interpret the derivative as the instantaneous rate of change and as the slope of the tangent line.
  • Apply the derivative to find the line tangent to a function at a point and the linearization of a function at a point.
  • Apply the derivative to analyze graphical behavior of a function, motion problems, other rate problems, and optimization problems.
  • Construct a definite integral as the limit of a Riemann sum and use the sum to approximate a definite integral.
  • Find the anti-derivative of elementary polynomial, exponential, logarithmic and trigonometric functions.
  • Use substitution to find the anti-derivative of a composite function.
  • Evaluate a definite integral and interpret an indefinite integral as a definite integral with variable limit(s) in order to evaluate it.
  • Apply the definite integral to analyze the area under a curve and motion problems.
  • Apply the Fundamental Theorem of Calculus.
  • Apply differentiation and integration in setting up and critically evaluating hypotheses in the fields of science, engineering and technology.

The impediment to action advances action. What stands in the way becomes the way.

Rights of the Learner

As a student in this class, you have the right:

  1. to be confused,
  2. to make a mistake and to revise your thinking,
  3. to speak, listen, and be heard, and
  4. to enjoy doing mathematics.

You may encounter many defeats, but you must not be defeated.

Commitment to the Learning Community

In our classroom, diversity and individual differences are respected, appreciated, and recognized as a source of strength. Students in this class are encouraged and expected to speak up and participate during class and to carefully and respectfully listen to each other. Every member of this class must show respect for every other member of this class. Any attitudes or actions that are destructive to the sense of community that we strive to create are not welcome and will not be tolerated. In summary: Be good to each other. I would appreciate private responses to the following question: Are there aspects of your identity that you would like me to attend to when forming groups, and if so, how?

Students are also expected to minimize distracting behaviors. In particular, every attempt should be made to arrive to class on time. If you must arrive late or leave early, please do not disrupt class. Please turn off the ringer on your cell phone. I do not have a strict policy on the use of laptops, tablets, and cell phones. You are expected to be paying attention and engaging in class discussions. If your cell phone, etc. is interfering with your ability (or that of another student) to do this, then put it away, or I will ask you to put it away.


There are two types of homework assignments: Daily and Weekly. Unless a student has a documented excused absence, late homework will not be accepted. There are many resources available to assist you with doing your homework (e.g., office hours, Discord, free tutoring at numerous places across campus). Your combined homework score is worth 20% of your overall grade. You are allowed and encouraged to work together on homework. However, each student is expected to turn in their own work.

Daily Homework: Homework will be assigned each class meeting, and students are expected to complete each assignment before the next class period. The majority of the Daily Homework assignments are to be completed via WeBWorK, which is an online homework system. You should log in with your NAU credentials. There will likely be some growing pains associated with getting used to the online homework system, so we should all plan to be patient with each other as we get used to the system.

Weekly Homework: Mathematics is about so much more than cranking out answers to assigned exercises. Having the ability to appropriately convey a mathematical argument is equally as important as “getting the right answer.” In fact, I would argue that it is one of the most important reasons for learning mathematics. Each week, you will be required to submit carefully written solutions to a selection of problems. The Weekly Homework will be graded for more than the correct answer. In particular, intermediate steps will be graded, as well as your ability to present a complete solution. Moreover, your write-ups should be neatly written and make proper use of mathematical notation. Your lowest Weekly Homework score will be dropped. You will need to capture your handwritten work digitally and then upload a PDF to BbLearn. There are many free smartphone apps for doing this. I use TurboScan on my iPhone.


There will be 3 midterm exams, which are tentatively scheduled for the following days: September 4, October 2, and October 30 November 2. These dates are subject to change. Each exam will consist of an in-class portion and a take-home portion. Details will be provided at least a week prior to each exam. Each exam will be worth 20% of your overall grade. There will also be a cumulative final exam, which will be on Saturday, November 21 at 12:30-2:30PM. The final exam is also worth 20% of your overall grade. Make-up exams will only be given under extreme circumstances, as judged by me. In general, it will be best to communicate conflicts ahead of time.

I must not fear.
Fear is the mind-killer.
Fear is the little-death that brings total obliteration.
I will face my fear.
I will permit it to pass over me and through me.
And when it has gone past I will turn the inner eye to see its path.
Where the fear has gone there will be nothing.
Only I will remain.


As per university policy, attendance is mandatory in all 100-level courses, and in particular, I am required to record attendance each class session. Regular attendance is vital to success in this course, but you will not explicitly be graded on attendance. You are responsible for all material covered in class. You can find more information about NAU’s attendance policy on the Academic Policies page.

Extra Credit

The only thing I will award extra credit for is finding typos on course materials (e.g., course notes, quizzes, syllabus, webpage). This includes broken links on the webpage. However, it does not include the placement of commas and such. If you find a typo, I will add one percentage point to your next quiz. You can earn at most two percentage points per quiz and at most five percentage points over the course of the semester. They’re is a typo right here.

Basis for Evaluation

In summary, your final grade will be determined by your scores in the following categories.

Category Weight Notes
Homework 20% A combination of Daily and Weekly Homework.
3 Midterm Exams 60% Each exam is worth 20% of your overall grade.
Final Exam 20% The final exam is cumulative.

Department and University Policies

You are responsible for knowing and following the Department of Mathematics and Statistics Policies (PDF) and other University policies listed here (PDF). More policies can be found in other university documents, especially the NAU Student Handbook (see appendices) and the website of the Office of Student Life.

As per Department Policy, cell phones, MP3 players and portable electronic communication devices, including but not limited to smart phones, cameras and recording devices, must be turned off and inaccessible during in-class tests. Any violation of this policy will be treated as academic dishonesty.

About Calculators and Other Technology

I am a huge fan of technology and believe that when it is used appropriately, it can greatly enhance one’s learning experience. However, when learning, technology should never replace one’s own amazing cognitive abilities. When we are discussing concepts in class or when you are doing homework, you should feel free to use whatever resources you feel will help you understand the concepts better. So, feel free to use things like Sage, Wolfram|Alpha, Mathematica, your graphing calculator, etc. when doing homework. You will likely be able to use a calculator during exams. We will lay out some guidelines prior to the first exam.

Moreover, be warned that I am much more interested in the process by which you arrived at your answer than the answer itself. An answer to a homework or exam question that is correct but lacks justification may be worth little to no points. If you understand a concept, then barring a silly computational error, the correct answer comes along for the ride. Yet, getting the correct answer does not imply that you understand anything!

Getting Help

There are many resources available to get help. First, you are allowed and encouraged to work together on homework. However, each student is expected to turn in their own work. You are strongly encouraged to ask questions in our Discord discussion group, as I (and hopefully other members of the class) will post comments there for all to benefit from. You are also encouraged to stop by during my office hours and you can always email me. I am always happy to help you. If my office hours don’t work for you, then we can probably find another time to meet. It is your responsibility to be aware of how well you understand the material. Don’t wait until it is too late if you need help. Ask questions!

Alone we can do so little; together we can do so much.

Important Dates

Here are some important dates:

  • Friday, August 21: Last day to Drop courses without a “W”
  • Monday, September 7: Labor Day (no classes)
  • Monday, October 19: Last day to drop individual courses without a petition
  • Wednesday, November 11: Veteran’s Day (no classes)
  • Wednesday, November 11: Last Day to withdraw from all classes in session
  • Thursday, November 19: Reading Day (no classes)
  • Saturday, November 21: Final Exam (12:30-2:30PM)

Changes to the Syllabus

Any changes to this syllabus made during the term will be properly communicated to the class.

If you want to sharpen a sword, you have to remove a little metal.

Dana C. Ernst

Mathematics & Teaching

  Northern Arizona University
  Flagstaff, AZ
  Google Scholar
  Impact Story

Current Courses

  MAT 411: Abstract Algebra
  MAT 690: Genome Combinatorics

About This Site

  This website was created using GitHub Pages and Jekyll together with Twitter Bootstrap.

  Unless stated otherwise, content on this site is licensed under a Creative Commons Attribution-Share Alike 4.0 International License.

  The views expressed on this site are my own and are not necessarily shared by my employer Northern Arizona University.

  The source code is on GitHub.

Land Acknowledgement

  Flagstaff and NAU sit at the base of the San Francisco Peaks, on homelands sacred to Native Americans throughout the region. The Peaks, which includes Humphreys Peak (12,633 feet), the highest point in Arizona, have religious significance to several Native American tribes. In particular, the Peaks form the Diné (Navajo) sacred mountain of the west, called Dook'o'oosłííd, which means "the summit that never melts". The Hopi name for the Peaks is Nuva'tukya'ovi, which translates to "place-of-snow-on-the-very-top". The land in the the area surrounding Flagstaff is the ancestral homeland of the Hopi, Ndee/Nnēē (Western Apache), Yavapai, A:shiwi (Zuni Pueblo), and Diné (Navajo). We honor their past, present, and future generations, who have lived here for millennia and will forever call this place home.