Math 142: Calculus II, Fall 2023

University of Rhode Island

Course Description and Goals

Math 142 continues the study of calculus where Math 141 left off. Topics include techniques and applications of integration, improper integrals, calculus using polar coordinates, sequences and series, Taylor polynomials, and differential equations.

The primary aim of Math 142 is to prepare students for further study in mathematics, basic sciences, or engineering by introducing them to techniques of integration, sequences, and series, and how to apply these to solve real-world problems and thereby develop new problem solving and critical reasoning skills. The course goals are:

• To provide a thorough introduction to methods of integration, infinite sequences and series.
• To provide a thorough introduction to applications of integration, especially in Physics.
• To provide an introduction to differential equations, mathematical modeling and numerical issues.

Textbook

Calculus: Single Variable, 8th edition Deborah Hughes-Hallett, Andrew Gleason, William McCallum, et al. ISBN: 1119379334 ISBN-13: 978-1119379331 You will NOT need a WileyPLUS access code this semester!

Course Schedule

Course Sections

Online Mini-Lectures

The following videos give brief explanations of topics related to the course.

Prerequisite review

Completing the Square (Needed for Section 7.4; thanks to Chris Staniszewski)

Polynomial Long Division (Needed for Section 7.4; thanks to Chris Staniszewski)

Limits of Rational Functions (Needed for Sections 7.6, 9.4)

Supplementary videos

Triangles and Trig Substitution (Supplement for Section 7.4)

Partial Fractions (Supplement for Section 7.4)

Improper Integrals (Supplement for Section 7.6)

Graphing Polar Equations and polar axes (Supplement for Section 8.3)

Work (Supplement for Section 8.5)

Fourier Series (Supplement for Section 10.5)

How to succeed in Math 142

Math 142 has a reputation for being a very challenging course, but you can succeed -- it just takes hard work and persistence. Here are some things you can do to help yourself out:

• Come to class! This means every day! Missing Tuesday's class will make it much harder to keep up in Wednesday's class, which will make it harder to keep up on Thursday, and so on...before you know it, things may have snowballed out of control.
• Do the homework right away! Working through the homework immediately after the corresponding lecture will help solidify your comprehension of the material -- which will make it much easier to follow the next lecture.
• Visit your instructor's office hours! You don't need to make an appointment; just stop by and ask questions. They're there to help!
• Find or start a study group! Many students find studying in a group more effective than studying alone. The AEC also provides assistance for students who would like group tutoring; see below for details.

Tutoring

The Academic Enhancement Center (AEC) also provides several free resources for students, including informal individual walk-in tutoring, weekly group tutoring, and general academic coaching. For more information on what the AEC can do for you, please check out their website.

For students who would like occasional individual help, but who can't make it to their instructor's office hours, the AEC employs trained tutors who will be glad to explain course material and answer questions. Walk-in tutoring hours haven't been determined yet, but they'll be posted soon!

Students seeking something more structured may be interested in the AEC's weekly tutoring groups. Tutoring groups are made up of 2-6 students and a trained tutor, who will meet on a weekly basis to discuss course material. This is a more structured environment than walk-in tutoring, and attendance is expected. Students who'd like to start a tutoring group should check out the AEC's website for more information.

Small groups of students may also make one-time appointments to meet with AEC tutors; refer to the AEC website for details.

Grading

The course grade will be based on online homework, section-specific coursework, three midterm exams, and a final exam.

Letter grade cutoffs may be lowered if deemed necessary (although this is not likely and should not be expected).

Homework

Homework for this course will be submitted through the online system Edfinity. To enroll in your section's Edfinity course, log into your Edfinity account (if you happen to have one already), and then click the relevant link below:

Please work through each homework assignment as soon as possible after the relevant lecture(s)! If you wait until the last minute, you risk running into technical problems that may keep you from finishing on time. In addition, working through the homework immediately will reinforce your understanding of the material and is a great way to study. You won't save any time by putting it off, so you might as well do it right away!

Late homework submissions will be accepted up until the end of the semester at a 50% penalty. (Please don't rely on this! It really is to your benefit to work through the homework as soon as you can; otherwise, you risk falling behind.) If you encounter circumstances that will keep you from submitting the homework on time, please explain the situation to your instructor ASAP; homework extensions may be granted on an individual basis at your instructor's discretion.

NOTE: this is our first semester using Edfinity, so there's a small chance you might run into issues with some question. If this happens, PLEASE LET US KNOW so we can fix it!

Exams

This class will have three midterm exams and one final exam, with the following dates, times, and locations. Each exam will consist entirely of free-response questions. (In past semesters, exams have used some multiple-choice questions, but that WILL NOT be the case this semester.)

The time, location, and modality of each exam is subject to change due to the ongoing pandemic.

General Exam Policies

• You must bring your URI Photo ID with you to each exam, and you must show it to a proctor as you hand in your exam.
• You may not take any books, bags, papers, or anything else to your seat. If you bring any of these items with you to the exam room, you must leave them at the front of the room.
• Proctors will not answer any questions regarding the content of the exam. In particular, you are expected to know and remember all relevant definitions and terminology.
• During the exam, you may not leave the room for any reason. Please remember to use the bathroom before the exam!
• No calculators of any kind may be used on exams.
• No cell phones, smart watches, MP3 players, or any electronic devices of any kind may be used or even accessible to you at any time during the exam. Any student found with any electronic device for any reason during the exam will be considered to be cheating.

Makeup Exam Policy

Makeup exams may be given for students who miss an exam due to an emergency or to an approved scheduling conflict (see below). Makeup exams must be scheduled after the original exam and will be administered as soon as is reasonably feasible.

If you miss any exam due to illness or emergency, you must contact your instructor within 24 hours. If you know that you will need to miss an evaluation due to religious observances or University-sanctioned events (including another class's exam), then you must contact your instructor at least 48 hours before the relevant evaluation.

In all cases, absences must be documented. Failure to provide documentation for an absence will result in a grade of zero for the exam.

Academic Accommodations

If you require academic accommodations and have documentation from Disability Services (874-2098), please get in touch with your instructor as soon as possible.

Math 142 Learning Outcomes

At the end of the course, the student should be competent in the following areas:

• Integration: Choose suitable techniques to analyze and compute indefinite and definite integrals. Techniques include substitution, integration by parts, partial fractions and trigonometric substitution. Approximate simple definite integrals using numerical integration techniques such as the midpoint and trapezoidal rules and Simpson's rule. Determine the convergence of standard improper integrals such as p-integrals and use these in comparison tests to determine the convergence or divergence of more complex improper integrals.
• Applications of Integration: Set up and evaluate integrals to compute the following quantities: areas and volumes by cross-sections including volumes of revolution (disc and washer methods), arc length (Cartesian and polar coordinates), area in polar coordinates, mass and center of mass of an object given its density, work. In many of these examples, it is important that the student check the units of their answer and whether the answer is physically meaningful.
• Probability: Be able to calculate simple probabilities, means, and medians using a probability density. Here also, the student needs to verify that the answers obtained are reasonable.
• Sequences and Series: Find a formula for the general term of a simple sequence given the first few terms. Determine whether a sequence converges or diverges. Recognize a geometric series and calculate the sum or show it diverges as appropriate. Analyze a series to determine whether or not it converges using the following tests: divergence test, comparison and limit comparison tests, ratio test, alternating series test. Apply these tests to determine whether a series is absolutely convergent. Students must also determine which of these tests and techniques is most appropriate for analyzing a given series.
• Power Series and Taylor Series: Calculate a Taylor polynomial for a desired function. Calculate a Taylor series and analyze the series to determine the radius of convergence. Apply the Lagrange Error Bound to bound the error in a Taylor polynomial approximation.
• Differential Equations and Modeling: Verify that a function is a solution of an ordinary differential equation. Draw a slope field for a differential equation and distinguish between different differential equations based on pictures of their slope fields. Use Euler’s method to compute simple approximate solutions to differential equations. Solve simple first-order differential equations using the method of separation of variables.