Math 1952 – Calculus II   Section 1

Lecture Time: 9:00am – 9:50am (every day)   Location: Boettcher Center Auditorium 102
   Monday through Thursday sessions will be lead by instructor, Friday session will be lead by TA

Instructor: Mei Yin   mei.yin@du.edu
   Office and Office Hours: Aspen Hall Middle 713B, 2:30pm – 4:00pm (MW), or by appointment

TA: Konrad Aguilar   konrad.aguilar@du.edu
   Office and Office Hours: Aspen Hall Middle 719A, 8:00am – 9:00am & 10:00am – 11:00am (MW) and 8:00am – 9:00am (TR)

COURSE DESCRIPTION

Calculus, which is covered at DU with the courses MATH 1951, 1952, 1953 and 2080, is the study of infinitesimal change. Whereas MATH 1951 is focused on the derivative, MATH 1952 is focused on integrals. Both of these concepts are defined in terms of a limit, which is a central idea that underlies all of Calculus. It turns out that these two special limits, the integral and the derivative, are closely related, and in particular the integral is tied to the idea of an antiderivative. This will force us to learn to 'undo' the derivative rules which we learned in 1951. Integrals have several important applications. The most fundamental is that an integral gives the area under the graph of a positive function on an interval. Beyond measuring area under the curve, we can use the integrals to compute many other important quantities such as the volume or surface areas of an object, the average value of a continuous function, the amount of work done by a force (as in physics) or the probability of a certain random event.

LEARNING OBJECTIVES

By the end of the course, you should be able to:

·        Be able to approximate the area under a curve using a Riemann sum or other techniques (Trapezoid Rule, Simpson's Rule). For certain functions, be able to determine whether your estimate is an overestimate/underestimate.

·        Give the definition of a Riemann integral as a limit, identify a limit of Riemann sums as a definite integral, and compute a Riemann integral by the definition.

·        Find the indefinite or definite integral of a basic function via antiderivatives.

·        Find the exact area under a curve or between curves, by computing the definite integral of a function on an interval.

·        Apply the fundamental techniques of integration in order to find the indefinite integral of more complicated functions: substitution, integration by parts, trigonometric substitution.

·        Be able to compute volumes of solids generated by rotating functions using integration.

·        Find the average value of a continuous function over an interval via integration.

·        Compute the surface areas of basic objects by integration.

·        Be able to apply the concept of integration to problems in physics, and economics.

REQUIRED MATERIALS

Textbook – The textbook for this course is Single Variable Calculus: Early Transcendentals, 8th edition, by Stewart, which will also be used in Math 1953. We will be using WebAssign for this course. If you purchased your book from the bookstore, you already received a license for this and will need a course key to log in. Otherwise, you will need to purchase a license. Note that these licenses come with an electronic copy of the book.

Calculator – Students may use a non-graphing, non-programmable calculator on quizzes or exams. Graphing calculators such as the TI-8x series will not be permitted.

GRADES

Your grades will be a weighted average of the following components.
 

Component
Points
Percentage

WebAssign Homework
45
12%

Written Assignments
45
6%

Quizzes
60
12%

Midterm 1
100
20%

Midterm 2
100
20%

Final Exam

150
30%

Total
500
100%

Note that the final exam will be comprehensive (covering the entire quarter).

WebAssign Homework – There will be a weekly assignment on the online homework system through WebAssign. By and large these will be sets of routine problems for you to practice with. You should work these on paper and enter the answers into the site. The system allows for you to get instant feedback as you practice. WebAssign homework will typically be due on Tuesdays. Each WebAssign homework score will count for 5 points and may cover multiple sections; the lowest score will be dropped.

To get started, go to http://www.webassign.net and create an account. To do this, go to the right-hand side of the page, and look for a link that says 'Enter Class Key.' (This is to the left of the words 'Log in.') Your class key for our session is du 9682 0084. With this, you should be able to create an account with your own username and password and start learning about the system.

Written Assignments – Each week a written assignment will be given, due the following Friday (the same day as the quiz). The purpose of these problems is twofold. First it gives you more practice and feedback on your handwritten work. Second, it allows you to address more conceptual questions that may not be compatible with entering a number into WebAssign. Each written assignment will count for 5 points; the lowest written assignment score will be dropped.

Quizzes – There will be a quiz every week on Fridays, except during weeks when there is a midterm. Quiz problems will be based on the assigned homework (WebAssign & written). Each quiz will count for 10 points; the lowest quiz score will be dropped.

Midterms – There will be two in-class 50 minute midterm exams.

·        Midterm 1 – Friday, January 27.

·        Midterm 2 – Friday, February 24.

Final Exam – There will be a cumulative final exam on Thursday, March 16, 8-9:50am.

Grading Scale – Point totals in the following ranges will correspond to the following grades. Any modifications to this (which would be minor) will be to the benefit of the student.
 

Point Range
Percentage
Grade

465-500
93-100%
A

450-464
90-92.9%
A-

435-449
87-89.9%
B+

415-434
83-86.9%
B

400-414
80-82.9%
B-

385-399
77-79.9%
C+

365-384
73-76.9%
C

350-364
70-72.9%
C-

335-349
67-69.9%
D+

315-334
63-66.9%
D

300-314
60-62.9%
D-

0-299
0-59.9%
F
 
TENTATIVE SCHEDULE WEEK BY WEEK


Week
Sections Covered

Jan 2 – Jan 6
4.9 – Antiderivatives
5.1 – Areas and Distances

Jan 9 – Jan 13
5.2 – The Definite Integral

5.3 – The Fundamental Theorem of Calculus

Jan 16 – Jan 20
5.4 – Indefinite Integrals and the Net Change Theorem

5.5 – The Substitution Rule

Jan 23 – Jan 27
6.1 – Areas between Curves

6.2 – Volume

MIDTERM 1

Jan 30 – Feb 3
6.3 – Volumes by Cylindrical Shells

6.4 – Work

Feb 6 – Feb 10
6.5 – Average Value of a Function

7.1 – Integration by Parts

Feb 13 – Feb 17
7.2 – Trigonometric Integrals

7.3 – Trigonometric Substitution

Feb 20 – Feb 24
7.4 – Integration of Rational Functions by Partial Fractions

7.5 – Strategy for Integration

MIDTERM 2

Feb 27 – Mar 3
7.7 – Approximate Integration

8.1 – Arc Length

Mar 6 – Mar 10
8.2 – Area of a Surface of Revolution

8.5 – Probability

Mar 13 – Mar 17
Review

FINAL EXAM

OFFICE HOURS/MATH CENTER

Students are encouraged to come to office hours or go to the Math Center. A great deal of learning mathematics comes outside of the classroom and your professor enjoys having students come to office hours to talk about the material.

The Math Center https://portfolio.du.edu/mathcenter provides a place to study, to do homework, and to ask questions. Students are encouraged to work with other students in the same class. When students have questions, assistants at the Math Center will give them hints and will guide them to find the answer. Working in small groups and having discussions with other students is one of the most effective ways to learn mathematics.

DISABILITY SERVICES

If you have a disability/medical issue protected under the Americans with Disabilities Act (ADA) and Section 504 of the Rehabilitation Act and need to request accommodations, please visit the Disability Services Program website at http://www.du.edu/disability/dsp. You may also call (303) 871-2372, or visit in person on the 4th floor of Ruffatto Hall; 1999 E. Evans Ave., Denver, CO.

INCLUSIVE LEARNING ENVIRONMENT

In this class, we will work together to develop a learning community that is inclusive and respectful. Our diversity may be reflected by differences in race, culture, age, religion, sexual orientation, socioeconomic background, and myriad other social identities and life experiences. The goal of inclusiveness, in a diverse community, encourages and appreciates expressions of different ideas, opinions, and beliefs, so that conversations and interactions that could potentially be divisive turn instead into opportunities for intellectual and personal enrichment.

A dedication to inclusiveness requires respecting what others say, their right to say it, and the thoughtful consideration of others' communication. Both speaking up and listening are valuable tools for furthering thoughtful, enlightening dialogue. Respecting one another's individual differences is critical in transforming a collection of diverse individuals into an inclusive, collaborative and excellent learning community. Our core commitment shapes our core expectation for behavior inside and outside of the classroom.

HONOR CODE/ACADEMIC INTEGRITY

All work submitted in this course must be your own. You are encouraged to work together on homework, but make sure that working together does not turn into copying another student's answer. For consequences of violating the Academic Misconduct policy, refer to the University of Denver website on the Honor Code (http://www.du.edu/honorcode).