General Information

Title: MAT 136: Calculus I
Semester: Spring 2014
Credits: 4
Section: 3
Time: MWThF at 9:10-10:00AM
Location: AMB 205

Instructor Information

Instructor: Dr. Dana C. Ernst
Office: AMB 119
Office Phone: 928.523.6852
Office Hours: MWThF at 10:00-11:00AM (or by appointment)

Course Information


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 course.


Our textbook will consist of a course pack called Calculus I Lecture Notes by J. Neuberger, N. Sieben, and J. Swift. The course pack is available for purchase at Alphagraphics (12 N. Beaver Street) for less then $10. In addition, you will occasionally be provided with other course materials. You are welcome to utilize other books covering first semester calculus.

I expect you to be reading the textbooks. I will not be covering every detail of either textbook and 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 whenever necessary by asking questions in class or posting questions to the course forum.


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.

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.


We will have two types of homework assignments.

  1. Daily Homework: Typically, Daily Homework will be assigned every class session and will be due on the day of our next class meeting. 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. We will discuss the use of WeBWorK more during the first few class sessions. In addition to the problems done online, you will also be asked to occasionally submit written work. With some exceptions, each exercise (WeBWork or written) from the Daily Homework will be worth a point. Unless a student has a documented excused absence, late Daily Homework will not be accepted. However, if necessary, the scores will be “curved.” There are many resources available to assist you with doing your homework (e.g., office hours, course forum, free tutoring at numerous places across campus). For this reason, I will spend little to no time explicitly covering the problems from the Daily Homework.
  2. 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. Each Weekly Homework assignment will be worth 10 points, regardless of the number of problems. You are allowed to submit up to two late Weekly Homework assignments with no penalty. Also, at least one of your lowest Weekly Homework scores will be dropped.

Your grade on the homework category is calculated by taking your total points and dividing by the total number of possible points. Your homework score is worth 12% of your overall grade. You are allowed and encouraged to work together on homework. However, each student is expected to turn in his or her own work.

Midterm Exams

There will be 4 midterm exams, which are tentatively scheduled for the following dates: Friday, February 7, Friday, February 28, Monday, March 31, and Friday, April 25. Each exam will be worth 15% of your overall grade. There will also be a cumulative final exam, which will be on Wednesday, May 7 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.

Gateway Quizzes

Sometime around Exam 2, we will have a skills-based quiz, called a Gateway Quiz. The quiz will consist of (roughly) 10 short computational problems. Within reason, the class will retake the quiz until everyone achieves a reasonable score.


As per university policy, attendance is mandatory in all 100-level courses, and in particular, I am required to record attendance each class session. Daily attendance is vital to success in this course! You are responsible for all material covered in class, regardless of whether it is in the textbook. Repeated absences may impact your grade (see the section on Achievements). You can find more information about NAU’s attendance policy on the Academic Policies page.

Presentations and Participation

Throughout the semester, class time will be devoted to students presenting problems to the rest of the class. In addition, we will occasionally make use of in-class activities whose purpose is to either reinforce/synthesize previously introduced concepts or to introduce new concepts via student-driven inquiry. If necessary, these activities will be explicitly graded.

I expect each student to participate and engage in class discussion. Moreover, I will occasionally ask for volunteers (or call on students) to present problems at the board. No one should have anxiety about being able to present a perfect solution to a problem. In fact, we can gain so much more from the discussion surrounding a slightly flawed solution. However, you should not volunteer to present a problem that you have not spent time thinking about. Your overall participation includes your willingness to present, engagement in and out of class, and consistent attendance record. Your grade for this category will be worth 8% of your overall grade and will be based on Achievements (see below).


This semester we will “gamify” good student behavior. Here is the gist. I’ve generated a list of items that I deem good student behavior. Every time you achieve one of the items on the list, you earn some points. The more points you earn, the higher your Presentation and Participation grade (worth 8% of your overall grade in the course). So, how do you earn achievement points? Here’s a list.

Points Description
2 Stop by my office hours to get help. This goes into effect after the first visit and you can earn points for this up to 4 times.
1 Attend class, arrive on time, and stay the whole class meeting.
1/2 Attend class but arrive late.
1/2 Attend class but leave early.
2 Attend a review session offered by our Peer TA. You can earn points for this multiple times.
4 Stop by the Math Achievement Program to get help. This is a one time offer and you must get a “prescription” form from me in advance for a tutor to sign.
4 Stop by the North Student Learning Center drop-in Math Lab. This is a one time offer.
4 Schedule a one-on-one tutoring appointment at one of the Student Learning Centers to get math help. This is a one time offer.
2 Find a typo anywhere on the course webpage, homework, exam, etc. These points are first come, first earned, but there is no limit to the number of times you can earn points for this.
5 Volunteer to present a problem to the class on presentation days.
3 Agree to present a problem to the class on presentation days after I’ve called on you.
2 Earn a non-secret Achievement in WeBWork. You can see list of possible non-secret Achievements by clicking on the appropriate link in the sidebar after logging in to WeBWorK.
3 Earn a secret Achievement in WeBWork. These shall remain a mystery.
2 Post a useful resource such as a video or link to a math-related website on our course forum.
2 Post a relevant question on our course forum.
2 Post a useful response to a question on the course forum that does not just give an answer away.
5 Earn at least an 8/10 on your highest score for a Gateway Quiz.
4 Attend a Friday Afternoon Mathematics Undergraduate Seminar (FAMUS). You can earn points for this multiple times.

Important: Any time I feel you are taking advantage of the spirit of this, I reserve the right to take away an achievement point.

To calculate your grade for the Presentation and Participation category, I will give the top 5 scores 100%. To calculate grades for the remaining students, I will divide each student’s total Achievement points by the average of the number of Achievement points earned by the top 6-15 students (i.e., I’ll ignore the top 5 students) and then convert to a percent.

Basis for Evaluation

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

Category Weight Notes
Homework 12% Your grade is determined by dividing your total points on homework assignment by the total possible points.
Presentations and Participation 8% Your grade is based on Achievement points as described above.
4 Midterm Exams 60% Each exam is worth 15%.
Final Exam 20% The final exam is cumulative.

Grade Determination

In general, you should expect the grades to adhere to the standard letter-grade cutoffs: A 100-90%, B 80-89%, C 70-79%, D 60-69%, F 0-59%.

Additional Information

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. 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.

Class Etiquette

Students are expected to treat each other with respect. Students are also expected to promote a healthy learning environment, as well as minimize distracting behaviors. In particular, you should be supportive of other students while they are making presentations. Moreover, 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.

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, on exams you will not be allowed to use a calculator.

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, I recommend that you work on homework in groups as much as possible. Second, you are strongly encouraged to ask questions in the course forum, 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. Lastly, free tutoring is available in AMB 137 through the Math Achievement Program.

Important Dates

Here are some important dates:

  • January 20: MLK Day, no classes
  • January 23: Last day to drop/add (no W appears on transcript)
  • February 3: Last day to withdraw from a course
  • Friday, February 7: Exam 1
  • Friday, February 28: Exam 2
  • Monday, March 31: Exam 3
  • Friday, April 25: Exam 4
  • Wednesday, May 7 at 7:30-9:30AM: Final Exam

Changes to the Syllabus

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

Closing Remarks

When does the learning happen? It might happen in class, but most likely it happens when you sit down to do your homework. Most of you can follow what happens on the board in class, but the question is, can you do it on your own? To learn best, you must struggle with mathematics on your own. It is supposed to be difficult. However, if you are struggling too much, then there are resources available for you. 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. You can also get help from each other. Get a study buddy! Help each other learn. 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!