Course Info

Title: MAT 136H: Calculus I
Semester: Fall 2022
Credits: 4
Section: Honors
Time: 9:10-10:0AM MWThF
Location: AMB 146

Instructor Info

  Dana C. Ernst, PhD
  AMB 176
  11:15-12:15PM MWF, 10:15-12:15 Th


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.

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 calculus at NAU is Calculus: Early Transcendentals (NAU Version) by David Guichard (Whitman College). This book is available for free in PDF or HTML format. I’ll loosely follow the book. 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. If you are interested in purchasing a print textbook, I recommend Calculus: Early Transcendentals (3rd edition or later) by Rogawski and Adams.

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 antiderivative of elementary polynomial, exponential, logarithmic and trigonometric functions.
  • Use substitution to find the antiderivative 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 almost every class meeting, and students are expected to complete each assignment before the due date. 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.


There will be 4 midterm exams, which are tentatively scheduled for the following Fridays: September 23, October 14, November 4, and December 2. These dates are subject to change. Details will be provided at least a week prior to each exam. Each exam will be worth 15% of your overall grade. There will also be a cumulative final exam, which will be on Wednesday, December 14 at 7:30-9:30AM. The final exam is 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. You are not allowed to use a calculator on any of the exams.

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, syllabus, webpage). This includes broken links on my website. 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 exam. You can earn at most five percentage points per exam. 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.
4 Midterm Exams 60% Each midterm exam is worth 15% of your overall grade.
Final Exam 20% The final exam is cumulative.

Department of Mathematics & Statistics Policies

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

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. However, you are not allowed to use a calculator on any of the exams.

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! Lastly, free tutoring is available through the Math Achievement Program.

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

Important Dates

Here are some important dates:

  • September 5: Labor Day (no classes)
  • September 8: Last day to drop a course (without a “W”)
  • September 10: Department Picnic
  • October 28: Last day to withdraw from a course (with a “W”)
  • November 11: Veteran’s Day (no classes)
  • November 24-25: Thanksgiving Holiday (no classes)
  • December 14: Final Exam (7:30-9:30AM)

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.

University Policies

Academic Integrity: NAU expects every student to firmly adhere to a strong ethical code of academic integrity in all their scholarly pursuits. The primary attributes of academic integrity are honesty, trustworthiness, fairness, and responsibility. As a student, you are expected to submit original work while giving proper credit to other people’s ideas or contributions. Acting with academic integrity means completing your assignments independently while truthfully acknowledging all sources of information, or collaboration with others when appropriate. When you submit your work, you are implicitly declaring that the work is your own. Academic integrity is expected not only during formal coursework, but in all your relationships or interactions that are connected to the educational enterprise. All forms of academic deceit such as plagiarism, cheating, collusion, falsification or fabrication of results or records, permitting your work to be submitted by another, or inappropriately recycling your own work from one class to another, constitute academic misconduct that may result in serious disciplinary consequences. All students and faculty members are responsible for reporting suspected instances of academic misconduct. All students are encouraged to complete NAU’s online academic integrity workshop available in the E-Learning Center and should review the full Academic Integrity policy available here.

Copyright Infringement: All lectures and course materials, including but not limited to exams, quizzes, study outlines, and similar materials are protected by copyright. These materials may not be shared, uploaded, distributed, reproduced, or publicly displayed without the express written permission of NAU. Sharing materials on websites such as Course Hero, Chegg, or related websites is considered copyright infringement subject to United States Copyright Law and a violation of NAU Student Code of Conduct. For additional information on ABOR policies relating to course materials, please refer to ABOR Policy 6-908 A(2)(5).

Course Time Commitment: Pursuant to Arizona Board of Regents guidance (ABOR Policy 2-224, Academic Credit), each unit of credit requires a minimum of 45 hours of work by students, including but not limited to, class time, preparation, homework, and studying. For example, for a 3-credit course a student should expect to work at least 8.5 hours each week in a 16-week session and a minimum of 33 hours per week for a 3-credit course in a 4-week session.

Disruptive Behavior: Membership in NAU’s academic community entails a special obligation to maintain class environments that are conductive to learning, whether instruction is taking place in the classroom, a laboratory or clinical setting, during course-related fieldwork, or online. Students have the obligation to engage in the educational process in a manner that does not interfere with normal class activities or violate the rights of others. Instructors have the authority and responsibility to address disruptive behavior that interferes with student learning, which can include the involuntary withdrawal of a student from a course with a grade of “W”. For additional information, see NAU’s Disruptive Behavior in an Instructional Setting policy located here.

Nondiscrimination and Anti-harassment: NAU prohibits discrimination and harassment based on sex, gender, gender identity, race, color, age, national origin, religion, sexual orientation, disability, veteran status and genetic information. Certain consensual amorous or sexual relationships between faculty and students are also prohibited as set forth in the Consensual Romantic and Sexual Relationships policy. The Equity and Access Office (EAO) responds to complaints regarding discrimination and harassment that fall under NAU’s Nondiscrimination and Anti- Harassment policy. EAO also assists with religious accommodations. For additional information about nondiscrimination or anti-harassment or to file a complaint, contact EAO located in Old Main (building 10), Room 113, PO Box 4083, Flagstaff, AZ 86011, or by phone at 928-523-3312 (TTY: 928-523-1006), fax at 928-523-9977, email at, or visit the EAO website located here.

Title IX: Title IX of the Education Amendments of 1972, as amended, protects individuals from discrimination based on sex in any educational program or activity operated by recipients of federal financial assistance. In accordance with Title IX, Northern Arizona University prohibits discrimination based on sex or gender in all its programs or activities. Sex discrimination includes sexual harassment, sexual assault, relationship violence, and stalking. NAU does not discriminate on the basis of sex in the education programs or activities that it operates, including in admission and employment. NAU is committed to providing an environment free from discrimination based on sex or gender and provides a number of supportive measures that assist students, faculty, and staff.

One may direct inquiries concerning the application of Title IX to either or both the Title IX Coordinator or the U.S. Department of Education, Assistant Secretary, Office of Civil Rights. You may contact the Title IX Coordinator in the Office for the Resolution of Sexual Misconduct by phone at 928-523-5434, by fax at 928-523-0640, or by email at In furtherance of its Title IX obligations, NAU promptly will investigate or equitably resolve all reports of sex or gender-based discrimination, harassment, or sexual misconduct and will eliminate any hostile environment as defined by law. The Office for the Resolution of Sexual Misconduct (ORSM): Title IX Institutional Compliance, Prevention & Response addresses matters that fall under the university’s Sexual Misconduct policy. Additional important information and related resources, including how to request immediate help or confidential support following an act of sexual violence, is available here.

Accessibility: Professional disability specialists are available at Disability Resources to facilitate a range of academic support services and accommodations for students with disabilities. If you have a documented disability, you can request assistance by contacting Disability Resources at 928-523-8773 (voice), ,928-523-8747 (fax), or (e-mail). Once eligibility has been determined, students register with Disability Resources every semester to activate their approved accommodations. Although a student may request an accommodation at any time, it is best to initiate the application process at least four weeks before a student wishes to receive an accommodation. Students may begin the accommodation process by submitting a self-identification form online here or by contacting Disability Resources. The Director of Disability Resources, Jamie Axelrod, serves as NAU’s Americans with Disabilities Act Coordinator and Section 504 Compliance Officer. He can be reached at

Responsible Conduct of Research: Students who engage in research at NAU must receive appropriate Responsible Conduct of Research (RCR) training. This instruction is designed to help ensure proper awareness and application of well-established professional norms and ethical principles related to the performance of all scientific research activities. More information regarding RCR training is available here.

Misconduct in Research: As noted, NAU expects every student to firmly adhere to a strong code of academic integrity in all their scholarly pursuits. This includes avoiding fabrication, falsification, or plagiarism when conducting research or reporting research results. Engaging in research misconduct may result in serious disciplinary consequences. Students must also report any suspected or actual instances of research misconduct of which they become aware. Allegations of research misconduct should be reported to your instructor or the University’s Research Integrity Officer, Dr. David Faguy, who can be reached at or 928-523-6117. More information about misconduct in research is available here.

Sensitive Course Materials: University education aims to expand student understanding and awareness. Thus, it necessarily involves engagement with a wide range of information, ideas, and creative representations. In their college studies, students can expect to encounter and to critically appraise materials that may differ from and perhaps challenge familiar understandings, ideas, and beliefs. Students are encouraged to discuss these matters with faculty.

Dana C. Ernst

Mathematics & Teaching

  Northern Arizona University
  Flagstaff, AZ
  Google Scholar
  Impact Story

Current Courses

  MAT 226: Discrete Math
  MAT 320: Foundations
  MAT 431: Analysis

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 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.