MATH 156 - Calculus I

Newton

Cauchy

When & Where: MWTF 9-10am on Blackboard Collaborate Ultra

Office: Academic Support Building B, Room 214

Office Hours: just email me anytime and we will arrange for a zoom meeting time.

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 2.0, CreateSpace Independent Publishing Platform (2018).
The book is available for free in HTML and PDF formats or in paper for about 20$ at Amazon.

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
5. • J. Marsden & A. Weinstein, Calculus III, Caltech
   • J. Marsden & A. Weinstein, Calculus III Students' Guide, Caltech

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

Graded Homework will be assigned weekly on Webwork.

I will usually provide you a short list of ungraded homework from the suggested textbook. While Webwork problems will usually be straightforward problems, these ungraded ones will be usually harder and are more meant to make you think more about and understand more the topics of the corresponding sections. The list of those problems is in the lectures log below.

Grades policy

Grades will be evaluated on the following bases:

1. Weekly homework: 30%;
2. Two midterms: 2x25%;
3. Final exam: 20%.

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%).

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

Especially with online classes, teamwork is very important and will give you the occasion to interacct with your classmates. You are encouraged in general to work with study partners and also to collaborate on homework. On the other side, you must write your solutions yourself, in your own words, and you must list all collaborators and outside sources of information.
It is a serious violation of academic integrity to copy an answer without attribution.

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 the Director of Undergraduate Studies, Dr. Jill McGowan, and, if still unsatisfied, the Chair of the Department, Dr. Bourama Toni.

Americans with Disabilities Act

Howard University is committed to providing an educational environment that is accessible to all students. In accordance with this policy, students in need of accommodations due to a disability should contact the Office of the Dean for Special Student Services (202-238-2420, bwilliams@howard.edu) for verification and determination of reasonable accommodations as soon as possible after admission and at the beginning of each semester as needed.

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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.

COVID-19 STATEMENT

The wearing of a face mask as well as compliance with other health protocols while on campus or in the classroom is mandatory. Students will be directed to leave the classroom if a face mask is not worn properly to cover the nose and mouth. Any student who refuses or fails to comply with the University's requirements and precautions against COVID-19, and any other measures the University advances for the safety and protection of the Howard Community, will constitute a violation of the University's Student Code of Conduct and could result in sanctions up to and including expulsion from the University

Lectures log

Week	Day	Sections	Topics	Exercises
1	22 Aug		Course introduction.
	24 Aug		To be recovered
	25 Aug		To be recovered
	26 Aug	1.1	Motivation: average and instantaneous velocity.	1.1: 1, 3, 4, 5
2	29 Aug	1.2	The notion of limit.	1.2: 1, 3, 4, 5, 6
	31 Aug	1.3	Derivative at a point.
	1 Sep	1.4	The Derivative as a function.	1.4: 2, 3, 6
	2 Sep	1.5	Using the derivative.
3	5 Sep	Labour day	.
	7 Sep	1.5	Comparing Forward and backward difference with central difference
	8 Sep	1.6	Where to read the increase/decrease intervals and concavity of the graph of a function
	9 Sep	1.6	Going over two activities at the end of 1.6
4	12 Sep	1.7	Left and right limits. Limits containing infinity. Continuity.
	14 Sep	1.7, 1.8	Differentiability. Linear approximations of functions.
	15 Sep	1.8	Linear approximations of functions.
	16 Sep	2.1	Derivative of monomials and exponentials. Linearity of the derivative.
5	19 Sep	2.2	Derivatives of sine and cosine.
	21 Sep	2.3	Product rule
	22 Sep	2.4	Quotient rule. Order of infinitesimals.
	23 Sep	2.4, 2.5,	Other trig functions, composition of functions
6	Sep 26	2.5	Chain rule.
	Sep 28	2.5	Chain rule.
	Sep 29	2.6	Derivative of inverse functions.
	Sep 30	2.6	Derivative of inverse functions.
7	Oct 3	2.6, 2.7	Derivatives of inverse functions. Derivatives of implicit functions.
	Oct 5	Practice test	Solving the practice test
	Oct 6	Practice test	Solving the practice test
	Oct 7	Midterm 1
8	Oct 10	Mental Health day
	Oct 12	2.7	Derivatives of implict functions
	Oct 13	2.7	Implicit Differentiation
	Oct 14	2.8	de L'Hopital's rule
9	Oct 17	3.1	Critical points of a function
	Oct 19	3.1	An example of studying a function
	Oct 20	3.1	Study of the family $h(x)=x^2+\cos(kx)$.
	Oct 21	3.2	Study of the family $p(x)=x^3-ax$.
10	Oct 24	3.2	Study of the family $L(t)=\frac{A}{1+ce^{-kt}}$
	Oct 26	3.3	Global Optimization
	Oct 27	3.4	Applied Optimization
	Oct 28	3.5	Related Rates
Extra Homework #2 Consider the family of functions $f_a(x)=e^x+\frac{1}{2}ax^2$, where $a$ is a real number and answer the following questions: Find $f'_a(x)$ and determine the critical numbers for $f_a(x)$. Construct a first derivative sign chart for $f_a(x)$. What can you say about the overall behavior of $f_a(x)$ if $a>0$? What if $a<0$? In each case, describe the relative extremes of $f_a(x)$. Find $f''_a(x)$ and construct a second derivative sign chart for $f_a(x)$. What does this tell you about the concavity of $f_a(x)$ if $a>0$? What if $a<0$? Sketch and label typical graphs of $f_a(x)$ for the cases where $a>0$ and $a<0$. Label all inflection points and local extrema. Use a graphing utility to test your results. Write several sentences to describe your overall conclusions about how the behavior of $f_a(x)$ depends on $f_a(x)$.
11	Oct 31	Practice test	Soving the practice test.
	Nov 2		Review
	Nov 3	4.1	Finding the distance covered $\Delta s$ from the velocity function $v(t)$.
	Nov 4	4.2	Riemann sums
12	Nov 7	Midterm 2
	Nov 9	4.2	Riemann sums
	Nov 10	4.3	The Definite Integral
	Nov 11	Veteran's day
13	Nov 14	4.3	The Definite Integral
	Nov 16	4.4	The Fundamental Theorem of Calculus
	Nov 17	5.1	Graph of the antiderivative
	Nov 18	5.1, 5.2	The second fundamental theorem of calculus
14	Nov 21	5.2	Second FTC
	Nov 23	5.3	Integration by substitution
	Nov 24	Thanksgiving
	Nov 25	Thanksgiving
15	Nov 28	notes	Review
	Nov 30		Midterm 3
	Dec 1	6.1	Using Definite Integrals to Find Area and Length
	Dec 2	6.2, 6.3	Volume, Density, Mass, and Center of Mass
	Dec 3	Notes	Review: solving Spring 2022 Calc 1 final
	Dec 4