MATH 156 - Calculus I

Instructor: Roberto De Leo.     Term: Fall 2026.     Section 10.

Newton
Cauchy
When & Where: MWTF 11:10-noon at Mackey Building (Architecture), room G09

Office: Annex III, Room 226

Office Hours: MWF 10-11am or just email me and we will arrange for a zoom meetingx.

HU Email: roberto DOT deleo AT howard DOT edu

Preferred Email: roberto AT deleo DOT info

Textbook

I will refer in my lectures to the following open source textbook:
M. Boelkins, D. Austin, S. Schlicker, Active Calculus (HU version), CreateSpace Independent Publishing Platform (2018).

Other Textbooks

Studying from a single textbook is seldom a good idea. Below is a list of some other Calculus 1 textbook you might want to consult during the semester:
  1. G. Strang, Calculus VOl. 1, Open Stax
  2. D. Guichard, Calculus - Early Trascendentals, Lyryx
  3. G. Hartman, B. Heinold, T. Siemers, D. Chalishajar, J. Bowen, Apex Calculus, APex
  4. R. Holowinsky, J. Thiel, D. Lindberg, Mooculus Calculus, Mooculus

Videos

Here are a few series of very well done Video Lectures you might use in case you feel the need of hearing more about any of the topics we are going to cover:
  1. Calculus 1 at Grand Valley State University
  2. Calculus 1 full course by T. Basett

Homework

  • Homework will be assigned weekly but it will not be graded. The whole purpose of the homework will be for you to practice in view of the midterms.

    Grades policy

    Grades will be evaluated on the following bases:
    1. Weekly quizzes: 20%;
    2. Three midterms: 3x20%;
    3. Final exam: 20%.
    Grades will be regularly posted on canvas. At the end of the course, based on the total, you will get the following letter: A (90-100%), B (80-89%), C (70-79%), D (60-69%), F (0-59%).

    Important: You will not receive full credit if you only write only the answers. Please always explain your work and present solutions step by step.

    Tentative Syllabus

    • Week 1: Continuous functions, Limits.
    • Week 2: Limits, Derivatives.
    • Week 3: Derivatives rules, elementary derivatives.
    • Week 4: Product and quotient rules, chain rule.
    • Week 5: Inverse functions, derivatives of implicit functions.
    • Week 6: Using derivatives to find maxima and minima.
    • Week 7: Global optimization.
    • Week 8: Applied optimization.
    • Week 9: Riemann sums.
    • Week 10: Definite and indefinite integrals.
    • Week 11: Fundamental Theorem of Calculus.
    • Week 12: Integration by substitution.
    • Week 13: Applications of integral and numerical integration.
    • Week 14: Review.

    Collaboration

    Teamwork in learning is very important and will give you the occasion to interact with your classmates. You are encouraged in general to work with study partners and also to collaborate on homework. You are also encouraged to interact with chatgpt and the like to learn how to solve problems and to get as many practice problems you wish. On the other side, team working is not allowed during tests, make sure to learn everything before coming to class.

    Technology

    No electronic devices are allowed in class during tests, including non-graphical calculators, earbuds and the like.

    Our course is in-person

    In particular, all assessments MUST BE TAKEN IN PERSON.

    Academic Code of Student Conduct

    (please see Howard University handbook) No copying, unauthorized use of calculators, books, or other materials, or changing of answers or other academic dishonesty will be tolerated. Cheating will not be tolerated. Anyone caught cheating will receive an F for the course and may be expelled from the university.

    Grievance Procedure

    If you have any problems with the policies or rules of this course, discuss your concerns with your instructor. If you are still unable to come to a satisfactory arrangement, you may contact (depending on your status) the Course Coordinator Roberto De Leo, the Director of Undergraduate Studies, Dr. Sam Hopkins, and then, finally, the Chair of the Department, Dr. Bourama Toni.

    Americans with Disabilities Act

    Howard University is dedicated to fostering an accessible, inclusive, and supportive learning environment for all students. We are committed to ensuring that students with documented disabilities receive equal access to all course activities. If you require accommodations, please reach out to the Office of Student Accessibility (OSA) to discuss your needs in a confidential setting. The OSA is responsible for determining reasonable accommodations in both classroom and clinical settings. Please note that accommodations should be requested at the beginning of each semester and cannot be applied retroactively. To request accommodations, contact the OSA via email at accessibility@howard.edu or visit https://studentaffairs.howard.edu/Accessibility for more information.

    Statement on Sex and Gender-Based Discrimination, Harassment and Violence

    Howard's Policy Prohibiting Sex and Gender-Based Discrimination, Sexual Misconduct and Retaliation (aka, the Title IX Policy) prohibits discrimination, harassment, and violence based on sex, gender, gender expression, gender identity, sexual orientation, pregnancy, or marital status. With the exception of certain employees designated as confidential, note that all Howard University employees University - including all faculty members - are required to report any information they receive regarding known or suspected prohibited conduct under the Title IX Policy to the Title IX Office (TitleIX@howard.edu or 202-806-2550), regardless of how they learn of it. For confidential support and assistance, you may contact the Interpersonal Violence Prevention Program (202-836-1401) or the University Counseling Service (202-806-7540). To learn more about your rights, resources, and options for reporting and/or seeking confidential support services (including additional confidential resources, both on and off campus), visit titleix.howard.edu.

    Quizzes

    1. Quiz 1
    2. Quiz 2
    3. Quiz 3
    4. Quiz 4
    5. Quiz 5
    6. Quiz 6

    Lectures log

    WeekDaySectionsTopicsExercises
    1 17 AugCourse introduction.
    19 Aug1.1Some example of how to use AI as an effective learning tool.
    What is a Function.
    Rational and irrational numbers.    		Write as ratio of two integers the following numbers: 0.1, 0.1234, 0.111..., 0.999...,0.1232323...

    If you do not remember how to do this, review some old math textbook of yours or ask AI to explain you how to do that.
    20 Aug1.1.1What is an infinite set.
    Different types of infinities.
    What is a function and how to represent it.    		Consider a hotel with infinitely many rooms, each labeled by a natural number (1,2,3,...). Suppose the hotel has no vacancy but one more guest shows up. Find a way to make space for this new guy so that all previous guests still have a room and the new guy has his own room (building a new room is not allowed).
    Hence, a hotel with infinitely many rooms can accomodate new guests even when is 100% full!

    Spend some time thinking about how to accomplish this. This can be a hard problem to solve so if, after all that, you are unable to find a solution, look at this video, where it also explains what to do if infinitely many new guests show up!

    21 Aug1.1.1 - 1.1.4
    2.1.1    		Combining functions (in particular, look at function composition).
    A close look at the position function of a moving body.
    Average velocity.    		For each pair of functions $f(x),g(x)$ below, write $f(g(x))$ and $g(f(x))$.
    1. $f(x)=5x,g(x)=\sqrt{x}$;
    2. $f(x)=\displaystyle\frac{1}{x},g(x)=1+2x^3$;
    3. $f(x)=1-x^2,g(x)=1+x^2$;
    4. $f(x)=e^x, g(x)=\ln(x)$
    2 24 Aug2.1.1In depth discussion of Preview Activity 2.1.1, using also Wolfram Alpha and chatgpt.
    This example shows the geometric meaning of average velocity, the relation between average and instantaneous velocity and the need for introducing the concept of limit.
    Look here for an interactive applet where you can slide points on a space-time graph and see 'live' how the average velocity changes.    		Write your solutions for activity 2.1.3.
    26 Aug2.1.2, 2.1.3, 2.1.4More examples on the concept of limit and instantaneous velocity.Solve problems 1, 2, 3 of Exercises 2.1.5 in the textbook.
    27 Aug2.2.1,2.2.2More elementary examples of limits.
    The notion of limit.    		Solve problems 9, 11 of Exercises 2.1.5 in the textbook.
    28 Aug
    2.2.2,2.2.4    		A formal definition of limit.Solve problems 4, 5, 8 of Exercises 2.1.5 in the textbook.
    3 31 AugQuiz 1
    2.2.4    		A formal definition of limit.Verify, using the formal definition of limit, that $\;\displaystyle\lim_{x\to2}x^2=4$ and $\;\displaystyle\lim_{x\to\pi}\sin x=0$
    In case you forgot how to solve inequalitites and/or trig, do review it from your College Algebra old textbook or with the support of AI! You can also re-learn that from tons of youtube videos such as this and/or this. Be proactive!!
    2 Sep2.3.1,2.3.2Limits involving infinity.
    The derivative of a function at a point.    		Solve problems 1, 3, 4, 5, 10 from Exercises 2.3.4 in the textbook.
    3 Sep2.4.1,2.4.2How to use the derivative of a function to get information on its graph.
    What the derivative is not able to tell us about the graph.
    Functions are not differentiable at corners.
    The derivative of $f(x)=x^2$.
    Comparison between the graph of a function and the graph of its derivative.    		Solve problems 1, 2, 3, 7, 9, 12 from Exercises 2.4.4 in the textbook.
    4 Sep2.5.1,2.5.2Some example of how to sketch the graph of the derivative of a function from the graph of the function.
    Units of the derivative function.
    		Solve problems 1, 2, 5 from Exercises 2.5.5 in the textbook.
    4 7 SepLabour Day
    9 Sep2.5.1,2.5.2Interpreting, estimating and using the derivative.Solve problems 4, 6 from Exercises 2.5.5 in the textbook.
    10 Sep2.5.3,2.6.1, 2.6.2, 2.6.3How to estimate the derivative.
    The second derivative and its meaning.    		Solve problems 9 from Exercises 2.5.5 and 2, 6 from Exercises 2.6.6 in the textbook.
    11 Sep2.6.4, 2.7.1, 2.7.2Concavity. Review of limits.Solve problems 8,9,10 from Exercises 2.6.6 and problems 1,2 from Exercises 2.7.6 in the textbook.
    5 14 Sep2.7.3, 2.7.4, 2.8.2Continuity. Differentiability. Tangent line to a graph.Solve problems 4,5,8,9 from Exercises 2.7.6
    16 Sep2.8.3Linearization.Solve problems 1,2,4,5,7 from Exercises 2.8.5 in the textbook.
    17 Sep2.8.3, 3.1.3Linearization.
    Derivative of a monomial.    		Solve problems 8,9,10 from Exercises 2.8.5 in the textbook.
    18 SepConvocation, no class
    6 21 SepMidterm #1.
    23 Sep3.1.3,3.1.4Derivative of a monomial. Derivative of a sum of two functions and derivative of a constant times a function. The Neper number. Derivative of the exponential.Solve problems 1,2,3,9 from Exercises 3.1.6 in the textbook.
    24 Sep3.1.3Derivative of exponential functions.Solve problems 6,11 from Exercises 3.1.6 in the textbook.
    25 Sep3.1.4Mainly went over a lot of exercises over the whole lecture.
    7 28 Sep3.2.1,3.2.2Definition and derivative of $\cos x$ and $\sin x$.Solve problems 1,2,3,5 from Exercises 3.2.4 in the textbook.
    30 Sep3.3Product and quotient rules for derivativesSolve problems 1,3,4,5,11,14 from
    1 OctWent over some important exercises
    2 OctWent over some important exercises
    8 5 Oct3.4Derivatives of $\tan x$, $\cot x$, $\sec x$, $csc x$Solve problems 1,8,9,10 from Exercises 3.4.4 in the textbook.
    7 OctWent over some exercises
    8 Oct3.5The chain ruleSolve problems 1,2,3,4,7,14 from Exercises 3.5.6
    9 OctMidterm #2
    9 12 OctHoliday
    14 Oct
    15 Oct
    16 Oct
    10 19 Oct
    21 Oct
    22 Oct
    23 Oct
    11 26 Oct
    28 Oct
    29 Oct
    30 Oct
    12 2 Nov
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    6 Nov
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