Calculus II

Math 2414: Calculus II

Go here for extra course assignments and study sheets.

Summer 2015

Synonym: 30761, Section: 002, Northridge 2244
Thursday 10:35 11:50 AM

Course Content:

Course Description: MATH 2414 Calculus 2 (4-4-0). A standard second course in calculus. Topics include integration of elementary functions; techniques of integration; integrals with infinite limits of integration; integrals of discontinuous integrands; applications of the definite integral; an introduction to differential equations; infinite series; analytical geometry; and other applications. Prerequisites: MATH 2413 with a C or better or the equivalent. (MTH 1864) Instructional Methodology: This course is taught primarily through a lecture format. Additional methods such as using projects or laboratories may be used by individual instructors. Course Rationale: This course is the second course in the traditional calculus sequence for mathematics, science and engineering students. It is part of what could be a four-semester sequence in calculus courses. The approach allows the use of technology and the rule of four (topics are presented geometrically, numerically, algebraically, and verbally) to focus on conceptual understanding.  At the same time, it retains the strength of the traditional calculus by exposing the students to the rigor of proofs and the full variety of traditional topics: integration, techniques of integration, applications of integration, infinite series and analytical geometry.


Please make sure you have the necessary prerequisites for this course. That means you need a C or better in a Calculus I (or an equivalent) course or an acceptable grade on placement tests. If we feel you are not prepared for this course, we may choose to withdraw you. If you have any questions about your preparation for the course, please come and talk to one of us about it.

Course Materials:

Textbook: Calculus: Concepts and Contexts, 4th ed., by James Stewart, Brooks/Cole 2010.  The text is sold in a full version and a shortened version, the Single Variableversion.  Either may be used for Calculus I and II.  Students who will go on to Calculus III will need the full version. Supplemental Material for Students: Student Solutions Manual by Jeffrey A. Cole, Study Guide by Dan Clegg Technology required: Technology required: You must have access to technology that enables you to (1) Graph a function. (2) Find the zeroes of a function. (3) Do numerical integration.


You should bring your homework to class every day.  It will be collected regularly.  There may also be in-class assignments or quizzes collected for a grade (as part of your homework/quiz/lab  grade). There will be a penalty on late homework. Homework that is more than a week late might not receive any credit.  If you do not follow the instructions that will be announced in class about how to organize and submit your homework, you may not receive full (or any) credit for it.


There will be 3 exams (worth 100 points each) and a comprehensive final (worth 150 pints) during the term. There may also be a few extra projects on calculus applications or computer labs assigned, as well as occasional in-class quizzes; these extra projects plus your homework and quizzes will count for 100 points.

If you take any test late for any reason, there will be a penalty of 10 points off your test grade, from the deadline for the test announced in class until the day graded tests are returned to the class. However, no late tests will be allowed after the graded tests are handed back in class and the final exam may not be taken late without prior instructors approval.

If you miss a test, you must try to take it during this lateperiod. If you miss this deadline as well, we may consider allowing you to make-up the test or hand in corrections on all tests and replace part of the missed test with your grade on the final, but only in the case of serious illness or emergency. Make-ups of any sort are solely at the discretion of the instructors.  All tests and assignments must be turned in on or before the last class meeting.

Grades will be assigned as follows:


90% or better and a grade of at least 80% on the final


60% - 69%


80% - 89% and a grade of at least 70% on the final


below 60%


70% - 79% and a grade of at least 60% on the final





Withdrawn by student or instructor prior to last withdrawal date on school calendar


Incomplete grades (I) will be given only in very rare circumstances. Generally, to receive a grade of "I", a student must have taken all tests, be passing, and after the last date to withdraw, have a personal tragedy occur which prevents course completion. An incomplete grade cannot be carried beyond the established date in the following semester. The completion date is determined by the instructor but may not be later than the final deadline for withdrawal in the subsequent semester.


Attendance is required in this course.  It is extremely important for you to attend class regularly. Although we may not take regular attendance, we MAY drop you from the course for excessive absences, although we make no commitment to do so.


It is the student's responsibility to initiate all withdrawals in this course.  The instructor may withdraw students for excessive absences (4) but makes no commitment to do this for the student. After the last day to withdraw, neither the student nor the instructor may initiate a withdrawal. It is the responsibility of each student to ensure that his or her name is removed from the roll should he or she decide to withdraw from the class.  The instructor does, however, reserve the right to drop a student should he or she feel it is necessary. The student is also strongly encouraged to retain a copy of the withdrawal form for their records.

Students who enroll for the third or subsequent time in a course taken since Fall, 2002, may be charged a higher tuition rate, for that course. State law permits students to withdraw from no more than six courses during their entire undergraduate career at Texas public colleges or universities.  With certain exceptions, all course withdrawals automatically count towards this limit.  Details regarding this policy can be found in the ACC college catalog.

The withdrawal deadline for Summer 2015 is August 3, 2015.

Classroom behavior:

Classroom behavior should support and enhance learning. Behavior that disrupts the learning process will be dealt with appropriately, which may include having the student leave class for the rest of that day. In serious cases, disruptive behavior may lead to a student being withdrawn from the class. ACC's policy on student discipline can be found in the Student Handbook on the web at:

Class participation:


All students are expected to actively participate in this class. This can include asking relevant questions in class, participating in class discussions and other in-class activities, helping other students, coming to office hours with questions, and doing other things that contribute to the class.

Keeping up:

Please, try to keep up with the homework and with the lecture in class. There just isn't much time to catch up. This means you have to be sure to allow yourself plenty of time to do the homework and to study.

Ask questions:

Please, please, please, if you don't understand something, or you aren't clear about something, or if you think we (or the book) have made a mistake (it has been known to happen), or if you have any other questions, please ask. Don't let confusion accumulate. If you don't want to ask in class, come to our office hours (or call) and ask. It is much easier to ask a question now than to miss it on the test.  We expect all students to participate in class discussions and other activities. Trust us, you will get much more out of the class if you become actively involved in it.

Always show your work:

It is much more important that you understand the processes involved in solving problems than that you just give me the right answer. If we see from your work that you understand what you are doing, we will usually give partial credit for a problem, even if you made a mistake somewhere along the line. If you don't show your work (unless we believe you could reasonably do it in your head), we may not give you full credit, even if the answer is right. If you can really do something in your head, that's great, but when in doubt, write it down.  It is also very important that you write what you mean. We will correct your notation the first few times, but we will start counting it wrong if you continue to write things incorrectly. In addition, please write clearly and legibly. If we can't read it, we won't grade it.

Time required and outside help:

To do homework and study requires two or three times as much time outside of class as the time you spend in class in order to succeed in this course. If you need more out-of-class help than you can obtain in your instructor's office hours, free tutoring is available in any of ACC's Learning Labs.

ACC main campuses have Learning Labs which offer free first-come, first-serve tutoring in mathematics courses. The locations, contact information and hours of availability of the Learning Labs are posted at:




Upon successful completion of this course, students will:

1.     Use the concepts of definite integrals to solve problems involving area, volume, work, and other physical applications.

2.     Use substitution, integration by parts, trigonometric substitution, partial fractions, and tables of anti-derivatives to evaluate definite and indefinite integrals.

3.     Define an improper integral.

4.     Apply the concepts of limits, convergence, and divergence to evaluate some classes of improper integrals.

5.     Determine convergence or divergence of sequences and series.

6.     Use Taylor and MacLaurin series to represent functions.

7.     Use Taylor or MacLaurin series to integrate functions not integrable by conventional methods.

8.     Use the concept of polar coordinates to find areas, lengths of curves, and representations of conic sections.


ACC College Policies

Statement on Scholastic Dishonesty

A student attending ACC assumes responsibility for conduct compatible with the mission of the college as an educational institution.  Students have the responsibility to submit coursework that is the result of their own thought, research, or self-expression.  Students must follow all instructions given by faculty or designated college representatives when taking examinations, placement assessments, tests, quizzes, and evaluations.  Actions constituting scholastic dishonesty include, but are not limited to, plagiarism, cheating, fabrication, collusion, and falsifying documents.    Penalties for scholastic dishonesty will depend upon the nature of the violation and may range from lowering a grade on one assignment to an Fin the course and/or expulsion from the college.  See the Student Standards of Conduct and Disciplinary Process and other policies at


Student Rights and Responsibilities

Students at the college have the rights accorded by the U.S. Constitution to freedom of speech, peaceful assembly, petition, and association. These rights carry with them the responsibility to accord the same rights to others in the college community and not to interfere with or disrupt the educational process. Opportunity for students to examine and question pertinent data and assumptions of a given discipline, guided by the evidence of scholarly research, is appropriate in a learning environment. This concept is accompanied by an equally demanding concept of responsibility on the part of the student. As willing partners in learning, students must comply with college rules and procedures.


Statement on Students with Disabilities

Each ACC campus offers support services for students with documented disabilities.  Students with disabilities who need classroom, academic or other accommodations must request them through the Office for Students with Disabilities (OSD).   Students are encouraged to request accommodations when they register for courses or at least three weeks before the start of the semester, otherwise the provision of accommodations may be delayed.  


Students who have received approval for accommodations from OSD for this course must provide the instructor with the Notice of Approved Accommodationsfrom OSD before accommodations will be provided.   Arrangements for academic accommodations can only be made after the instructor receives the Notice of Approved Accommodationsfrom the student.  


Students with approved accommodations are encouraged to submit the Notice of Approved Accommodationsto the instructor at the beginning of the semester because a reasonable amount of time may be needed to prepare and arrange for the accommodations.   


Additional information about the Office for Students with Disabilities is available at


Safety Statement

Austin Community College is committed to providing a safe and healthy environment for study and work. You are expected to learn and comply with ACC environmental, health and safety procedures and agree to follow ACC safety policies. Additional information on these can be found at Because some health and safety circumstances are beyond our control, we ask that you become familiar with the Emergency Procedures poster and Campus Safety Plan map in each classroom. Additional information about emergency procedures and how to sign up for ACC Emergency Alerts to be notified in the event of a serious emergency can be found at


Please note, you are expected to conduct yourself professionally with respect and courtesy to all. Anyone who thoughtlessly or intentionally jeopardizes the health or safety of another individual will be dismissed from the days activity, may be withdrawn from the class, and/or barred from attending future activities.


You are expected to conduct yourself professionally with respect and courtesy to all. Anyone who thoughtlessly or intentionally jeopardizes the health or safety of another individual will be immediately dismissed from the days activity, may be withdrawn from the class, and/or barred from attending future activities.


Use of ACC email

All College e-mail communication to students will be sent solely to the students ACCmail account, with the expectation that such communications will be read in a timely fashion. ACC will send important information and will notify you of any college related emergencies using this account.  Students should only expect to receive email communication from their instructor using this account.  Likewise, students should use their ACCmail account when communicating with instructors and staff.  Instructions for activating an ACCmail account can be found at


Testing Center Policy

Under certain circumstances, an instructor may have students take an examination in a testing center.  Students using the Academic Testing Center must govern themselves according to the Student Guide for Use of ACC Testing Centers and should read the entire guide before going to take the exam.  To request an exam, one must have:


    ACC Photo ID

    Course Abbreviation (e.g., ENGL)

    Course Number (e.g.,1301)

    Course Synonym (e.g., 10123)

    Course Section (e.g., 005)

    Instructor's Name


Do NOT bring cell phones to the Testing Center.  Having your cell phone in the testing room, regardless of whether it is on or off, will revoke your testing privileges for the remainder of the semester.  ACC Testing Center policies can be found at


Student And Instructional Services

ACC strives to provide exemplary support to its students and offers a broad variety of opportunities and services.  Information on these services and support systems is available at:


Links to many student services and other information can be found at:


For help setting up your ACCeID, ACC Gmail, or ACC Blackboard, see a Learning Lab Technician at any ACC Learning Lab.


 Course Outline and Approximate Calendar:
Please note:  schedule changes may occur during the semester.
Any changes will be announced in class.










Whirlwind review of differential calculus





Review of integration and substitution





Numerical approximation of integrals





Integration by parts





Trigonometric integrals





Partial fractions





More partial fractions and Trig substitution





More Trig substitution





Integration using tables





Improper integrals





More improper integrals




Ch. 5

Review for Test 1, summary of methods of integration

Test 1Dates to be announced in class





Areas and integration





Volumes and slicing





Volumes of solids of revolution method of washers





Volumes of solids of revolution method of shells





Physics applications work





Physics applications hydrostatic force





Physics applications centroids and centers of mass





Even more physics so when do you really need to use an integral?









6.4, 6.5

Arc length and Average value of a function




Ch. 6

Review for Test 2





Intro the need to use one type of function to approximate another; sequences

Test 2 Dates to be announced in class





Series adding it all up, infinite sums





Testing for convergence the integral test and the comparison tests




8.3, 8.4

Other tests for convergence, alternating series





More alternating series, the ratio test





Power series infinite polynomials





Using power series to represent other functions





More power series





Taylor and Maclaurin series





More fun with Taylor series





Applications of Taylor polynomials and error terms, Review for Test 3




6.1, 6.4

Parametric equations in area and arc length




Appendix H.1

Curves in polar coordinates

Test 3 Dates to be announced in class




Appendix H.2

Area and length in polar coordinates





Modeling and differential equations





Slope fields and Eulers method





Solving separable equations




7.4, 7.5

Exponential growth and decay




Ch. 5, 6, 7, 8, App. H

Review for the final exam



Final Exam, Part 1 (in class)



Final Exam, Part 2 (in class)



This webpage was created by Marcus McGuff.
It was last updated on January 22, 2016 .