MA251.02V Fall 21: Calculus I Syllabus

9:00-9:50 MWF 023 Fernandez Center
9:25-10:40 Tues 237 Fernandez Center

9:25-10:15 Thurs 237 Fernandez Center
(Enrichment Hour)

Dr. Lisa Oberbroeckling (o-burr-brek-ling) Office:301c Knott Hall Phone: 410-617-2516

E-mail: loberbro "at" loyola "dot" edu OR loberbroeckling "at" loyola "dot" edu

Zoom Room: https://loyola.zoom.us/my/loberbro or PMI: 410 617 2516

Moodle: moodle.loyola.edu

WeBWorK: https://webwork.loyola.edu/webwork2/MA251-Fa21-OBER

Office Hours: 10:15-12 MF, 10:15-11 W. Also by appointment (see my schedule)

I reserve the right to make changes to the syllabus at any time during the term by announcing them in class and on the webpage. You are responsible for knowing not only what is discussed/announced in class but also what is posted on Moodle.

Prerequisites

MA109, score of 76 or higher on ALEKS, or one year of high school calculus.

Course Description

A rigorous approach to Calculus for all majors. Topics include limits, definition, interpretation, and applications of the derivative; differentiation rules; antiderivatives; definition of definite and indefinite integrals; and the Fundamental Theorem of Calculus. Degree credit will not be given for both MA151 and MA251.

Department Learning Aims

• Calculate Accurately: Students will be able to calculate accurately using algebra, calculus, or higher-level mathematics.
• Write Proofs: Students will be able to write proofs of theorems.
• Interpret Accurately: Students will be able to accurately interpret mathematical or statistical information in relation to procedures, concepts, or applications.
• Program Quantitatively: Students will be able to write computer programs or run computer packages to perform quantitative tasks.

Text

Required: Calculus, Volume 1 by openstax.

Calculators

A graphing calculator is not required but may be useful FOR HOMEWORK. You need nothing fancier than a TI-83 or its equivalent. DESMOS.COM is just as useful for homework. YOU MAY NOT USE GRAPHING CALCULATORS ON QUIZZES OR EXAMS.

Homework

This course will emphasize problem solving and some applications of mathematics. Homework problems will be assigned from each section that we cover. You will be asked to do homework on the computer through WeBWorK. The WeBWorK counts towards your grade. Even though I will not be collecting any of the homework assigned from the book, it is important for you to be able to do all of the problems and understand the concepts behind them.

Quizzes

There will be short quizzes every Tuesday at the end of class unless told otherwise. They will cover the material on the week's homework problems (both textbook and WeBWorK problems) and examples done during class. I will only answer brief questions before the quiz; questions should be taken care of in previous classes or office hours. There are no make-ups on quizzes.

Exams

There will be 2 in-class exams during the term. They are tentatively scheduled on Tuesday, October 12 and Tuesday, November 9. Other information about the exams will be announced in class as each exam approaches.

Final Exam

The final exam is cumulative and is on Thursday, December 16 at 9 AM. This exam will be a final opportunity to complete or master a Learning Target. In addition, the overall points of the exam will determine a +/- to the grade. Below 70% on the final and you earn a -; above 85% and you earn a +.

Engagement Score

There will be activities in class periodically that will count toward this score. In addition, your attendance, engagement, and any activities assigned or done during Enrichment Hour count toward this score.

Extra Credit

Do not count on extra credit in this course to boost your grade. I make it a policy to not give extra credit on an individual basis so do not ask for it, especially at the end of the semester.

Honor Code

All students of the University are expected to understand the meaning of the Loyola University Honor Code. Ignorance of the Code is not a valid reason for committing an act of academic dishonesty. The following constitute violations of the Code and are defined in the Community Standards Handbook: cheating, stealing, lying, forgery, plagiarism and the failure to report a violation.\\[1ex]I expect you to work with others on homework (by collaborating, not copying!). I will ask you to sign a pledge on exams but not on other turned-in work (like quizzes) although I will expect the same honesty on all of them. Any questions or concerns should be directed immediately to me.

Classroom Etiquette

When you come to class, I expect you to not only be in attendance physically but also mentally. That means no cell phones, no leaving class during lecture, no extraneous chatter, etc. If you know you must leave class, sit by the door to minimize the disruption. If cell phones and texting become a problem, I will confiscate the phone.

The goals of this course are best accomplished when in a setting of mutual respect. The study of mathematics does not usually lead to much controversy. That being said, we must all work to provide a safe environment that is conducive to learning. All are welcomed and encouraged to actively participate in the learning of analysis, regardless of gender, race, nationality, native language, sexual orientation, gender identity, political ideology, and especially personal mathematical history. Any student who feels she or he is experiencing a hostile environment should speak to me immediately.

Student Athletes

If you are a student athlete, please provide me with your travel letter indicating when you will need to miss class to participate in athletic events. While travel for athletics is an excused absence, you will need to make up any missed work. Absences only on the travel letter will be accommodated.

The Counseling Center

The Counseling Center supports the emotional well-being of the student body and is committed to a respectful understanding and honoring of the social, emotional, and cultural contexts represented by each individual student. The Counseling Center provides brief individual and group counseling, emergency and crisis intervention, and comprehensive referral services for those in need of longer-term therapy. We are currently providing both in-person and virtual services and this is subject to change in accordance with best health practices and state laws. Relevant updates and more information can be found on our webpage: www.loyola.edu/counselingcenter or by calling (410) 617-CARE (2273). To make an appointment, please call (410) 617-CARE (2273). For after-hours emergencies, please call our after-hours counselor at (410) 617-5530 or Campus Police at (410)617-5911. Let's Talk!

DSS Accommodations

If you are a student registered with Disability Support Services (DSS) who needs accommodations for this course, please make sure you ask DSS to send me a Faculty Notification Email (FNE). If DSS has already sent me your FNE, please schedule a brief meeting to discuss your accommodations during my office hours. If you are registered with DSS and need accommodations for this course, be sure to contact the DSS office as soon as possible. Students with a physical or mental condition experiencing barriers in this or another course, please go to the Disability Support Services' website to learn more about accommodations at Loyola. Also, you can contact DSS at DSS@loyola.edu or (410) 617-5387 to schedule a meeting.

Title IX

Title IX: Loyola University Maryland is committed to a learning and working environment free from sexual and gender-based misconduct including sexual harassment, sexual verbal abuse, sexual assault, domestic violence, dating violence, stalking, and sexual exploitation. Reports of such offenses are taken seriously and Loyola encourages students experiencing sexual misconduct to report the incident in accordance with the University's policy on Reporting Sexual Misconduct. Because of the University’s obligation to respond to reports of sexual misconduct, mandated reporters including faculty members, are required to report incidents of sexual misconduct to the Title IX coordinator even if the reporting party requests confidentiality. Information about confidential resources that are not required to report sexual misconduct to the Title IX coordinator may be found in the Notice Rights and Options for Sexual Misconduct policy. For more information about policies and resources or reporting options, please visit Community Standards, or Title IX . Loyola is also committed to an environment free of other forms of harassment and discrimination. For information about policies and reporting resources, please visit (harassment and discrimination policy.)

The Study

The Study is located on the third floor of Jenkins Hall and serves as Loyola University Maryland's academic support center. Our mission is to help Loyola students become successful, independent learners. We do this through a variety of free academic support services, such as peer and professional tutoring, academic success workshops, academic coaching, and time management and organization coaching. These services are available in person and online, and students can register for them through The Study's website at www.loyola.edu/thestudy.

Peer Tutoring for Math/Stats

Tutoring is also available in a drop-in basis at the Math/Stats Seminar Room in 303 Knott Hall. Times and days are TBA.

Food/Housing Insecurity and Textbook Needs

Any student who has difficulty securing their food, housing, or textbooks is urged to contact Christina Spearman, the Dean of Students, at cjspearman1@loyola.edu or 410-617-5171. Loyola may have resources available to help.

Grading

This course will use standards-based grading, which is system that you may not be used to. The two key ideas of standards-based grading are (1) no partial credit and (2) anything graded can be attempted more than once. The driving reason for standards-based grading is that it is better to master 80% of the course content than to complete all skills with 80% accuracy. A list of standards that you pass is a list of things you can leave this course saying "I know how to do that!" Problems and/or standards will be marked on a scale of:

E: Excellent

An exemplary response which is correct and communicates a very good understanding of the content and has only the most minor algebraic, conceptual, logical, numerical, symbolic, verbal, or visual flaws.

M: Meets Expectations

An adequate response which is essentially correct and communicates a satisfactory understanding of the content even though it contains some algebraic, conceptual, logical, numerical, symbolic, verbal, or visual flaws.

R: Reassessment Recommended

An uneven response which demonstrates misunderstanding of the content through several algebraic, conceptual, logical, numerical, symbolic, verbal, or visual errors.

F: Fragmentary

An incongruous or incomplete/missing response which demonstrates a significant misunderstanding of the content through numerous algebraic, conceptual, logical, numerical, symbolic, verbal, or visual errors.

To COMPLETE a Learning Target: Earn M or E level on that target during quiz or exam times.

To MASTER a Learning Target: Earn M or E level on that target a second time during quiz or exam times.

Quizzes or Learning Targets that receive a Reassessment Recommended grade may be reattempted in two different ways. One way is to request a retake of that quiz during a later quiz or assessment period (request must be made in advance). A second way is to reattempt a quiz during office hours (in person or online), by working out quiz problems while I watch and assess your work. Reattempts of quizzes in either form will cover the same Learning Target and have similar problems but will not be identical to past quizzes.

Reattempts of Learning Targets done in office hours are subject to some restrictions:

• You must schedule a 15-minute appointment for quiz reattempts.
• You may schedule no more than two such appointments per week.
• You may attempt no more than two retakes during any one 15-minute appointment.
• The 15-minute length of the appointment is firm; no extra time will be allowed, including if a student arrives late to the appointment.
• Failing to appear for an appointment may result in a ban from office hours quiz retakes.
• Office hours appointments are available on a first-come, first-served basis.

WeBWorK Advice

• If you have problems with WeBWorK, contact me through Moodle, email, phone or in person right away.
• Download and print the generated PDF hardcopies of the problem sets.
• Keep your work in a notebook or some other organized way as if you were turning it in.
• Read and do the Intro problem set.
• Don't guess; it is neither efficient nor effective.
• Give exact values or 4 or 5 significant digits for (floating point) numerical answers.
• If I go through a problem in class or you are working with others, don't just go through and try and change the numbers in yours to match my or your friend's numbers.
• Use Preview Answers.
• Keep track of the time and date due!
• Form a study group.

GENERAL SUGGESTIONS:

• This course will test your study and time management skills. The homework WILL be time consuming so DO NOT put off the homework until the night before they are due. I cannot and will not give extensions on these due dates.
• Organize your work for WeBWorK in a folder or notebook, clearly labeled.
• Participate in class, ASK QUESTIONS, make use of my office hours. If you get behind or stuck, see me or work with other students RIGHT AWAY.
• Form a study group. Learning math is best as a social activity. Working together on homework is allowed, as long as everyone contributes. I've also found that the best way to learn material is to try and explain it to someone else (SHAMELESS PLUG: become a tutor!). And hopefully that someone else can then explain another problem to you.
• READ THE BOOK. Lectures will be much more understandable. It will be important to READ the book, not just look at the highlighted boxes because I will not be able to cover all of the details or show nearly enough examples in class.
• If you think you'll need extra help, get it as soon as possible. Do not wait until right before an exam! There are tutoring services available -- many are FREE.

Learning Targets (by Section)

1. Demonstrate fluency with functions and their representations.

   Chapter 1: Functions

   • Use numbers, algebra, graphs, and words to describe functions.
   • Use functions to model situations from science and business.
   • Classify and create new functions using arithmetic and composition of basic functions; power, polynomial, rational, trigonometric, inverse, exponential, and logarithmic.
   • Describe a function's global and local behavior, noting especially the function's domain and range.

2. Calculate, interpret, and communicate about limits.

   Section 2.1: A Preview of Calculus

   • Calculate an average rate of change from context, using correct units and meaning.
   • Explain the meaning of an average rate of change in context.
   • Describe the visual representation of average rates of change using secant lines.
   • Determine and explain when average rates of change are under- or over-estimates.
   • Accurately describe average rates of change as approximations for the instantaneous rate of change.
   • Demonstrate how interval size affects the approximation accuracy of average rates of change.

   Sections 2.2: The Limit of a Function

   • Use limits to distinguish the behavior of a function near a given input from the value of the function at that input.
   • Define and describe one-sided, two-sided, and infinite limits.

   Sections 2.3: The Limit Laws

   • Calculate limits using algebra, arithmetic, graphs, and technology.
   • Evaluate limits using laws: constant multiple, sum, difference, product, quotient, composition.
   • Determine the value of a limit using the Squeeze Theorem.

   Section 2.4: Continuity

   • Describe the three kinds of discontinuities.
   • Determine where a function is continuous or discontinuous, and classify any of its discontinuities.
   • Verify examples which illustrate the truth or falsity of the Intermediate Value Theorem.

3. Define, analyze, calculate, and interpret derivatives.

   Section 3.1: Defining the Derivative

   • Interpret the derivative at a point as the limit of average rates of change on shrinking intervals.
   • Calculate the slope of the tangent line.
   • Interpret the value of the derivative as the slope of the tangent line at a point.
   • Use both Leibniz and Lagrange notation for derivatives.

   Section 3.2: The Derivative as a Function

   • Recognize when a function is not differentiable and include a precise explanation why.
   • Describe the logical and conceptual implications of continuity and differentiability.
   • Given a function, be able to sketch the derivative function.
   • Use the derivative to describe and interpret features of local minimum and maximum values.
   • Define and calculate the derivative function.

   Section 3.3: Differentiation Rules

   • Apply the constant, constant multiple, power, sum, and difference rules.
   • Calculate and interpret the derivatives of products and quotients of functions.
   • Calculate and interpret the derivatives of power, polynomial, and rational functions.

   Section 3.4: Derivatives as Rates of Change

   • Calculate an average rate of change from context, using correct units and meaning.
   • Explain the meaning of an average rate of change in context.
   • Explain the meaning of values of the derivative as an applied instantaneous rate of change.

   Section 3.5: Derivatives of Trigonometric Functions

   • Calculate and interpret the derivatives of the standard and reciprocal trigonometric functions: sine, cosine, tangent, secant, cosecant, cotangent.
   • Recognize and utilize patterns in the derivatives of sine and cosine.

   Section 3.6: The Chain Rule

   • Calculate and interpret the derivatives of compositions of functions.
   • Combine the chain rule with other derivative rules.

   Section 3.7: Derivatives of Inverse Functions

   • Calculate and interpret the derivatives of inverse functions.
   • Recognize derivatives of standard inverse trigonometric functions.

   Section 3.8: Implicit Differentiation

   • Calculate and interpret the derivatives of non-functions.
   • Write the equation of the tangent line to a curve which is not a function.

   Section 3.9: Derivatives of Exponential and Logarithmic Functions

   • Calculate and interpret the derivatives of exponential and logarithmic functions.
   • Apply knowledge of the derivative to growth and decay situations.
   • Use logarithmic differentiation to calculate derivatives.

4. Apply derivatives to mathematical, social, and scientific settings.

   Section 4.1: Related Rates

   • Use the chain rule to solve for unknown rates of change in applied settings.
   • Describe relationships between units when using the chain rule.

   Section 4.3: Maximum and Minimum Values

   • Use the derivative to find minimum and maximum values of a function in context.
   • Find reasonable domains for functions in context, and identify extrema on these restricted domains.

   Section 4.4: The Mean Value Theorem

   • Verify concrete, applied, and abstract examples which illustrate the Mean Value Theorem.

   Section 4.5: Derivatives and the Shape of a Graph

   • Identify the intervals where a function is increasing, decreasing, concave up, and concave down.
   • Identify inflection points of a function.
   • Explain the meaning of values of the derivative in context (with words like increasing, decreasing, positive, negative, concave up, and concave down) using tables of data, graphs, or equations.
   • Use the First and Second Derivative Tests to classify critical numbers of a function.

   Section 4.6: Limits at Infinity and Asymptotes

   • Calculate the limit of a function as its input increases or decreases without bound.
   • Recognize a horizontal asymptote on the graph of a function.
   • Analyze a function and its derivatives to draw its graph.

   Section 4.7: Optimization

   • Model physical situations using algebraic equations.
   • Use extrema classification techniques and theorems to solve maximum/minimum problems.

   Section 4.8: l'Hopital's Rule

   • Use l'Hopital's rule to calculate limits which take on an indeterminate form.

   Section 4.10: Antiderivatives

   • Find the general antiderivative of a given function.
   • Explain the terms and notation used for an indefinite integral.
   • Use antidifferentiation to solve simple initial-value problems.

5. Define, analyze, calculate, and interpret integrals.

   Section 5.1: Areas and Distances

   • Use approximating Riemann sums to calculate accumulation and area using correct units.
   • Explain the method and meaning of a rectangular Riemann sum calculation in context.
   • Determine and explain when Riemann sums are underestimates or overestimates for the corresponding definite integral.
   • Demonstrate how interval size affects the accuracy of Riemann sum approximations.

   Section 5.2: The Definite Integral

   • Apply geometry and properties to determine the value of integrals.
   • Construct a notationally correct expression for the definite integral.
   • Explain the meaning of a definite integral in context.
   • Interpret a definite integral as an area, or when appropriate, a net area.

   Section 5.3: The Fundamental Theorem of Calculus

   • Identify and distinguish the two parts of the Fundamental Theorem of Calculus
   • Apply Part I of the Fundamental Theorem of Calculus in order to calculate derivatives.
   • Apply Part II of the Fundamental Theorem of Calculus in order to evaluate definite integrals.

   Section 5.4: Integration Formulas and the Net Change Theorem

   • Calculate indefinite integrals using the reverse of basic derivative rules.
   • Apply integration to find net change.

   Section 5.5: The Substitution Rule

   • Identify the substitution rule as the dual to the Chain Rule.
   • Apply the substitution rule to calculate both definite and indefinite integrals.