Calculus II

I.     Course Prefix/Number: MAT 251

       Course Name: Calculus II

       Credits: 4 (4 lecture; 0 lab)

II.    Prerequisite

MAT 250 with minimum grade of C.

III.   Course (Catalog) Description

Course is second in calculus and analytic geometry. Content focuses on differentiation and integration of transcendental functions such as inverse trigonometric functions; hyperbolic functions and inverse hyperbolic functions; applications of the definite integral; sequences and series; power series representations; parametric and polar coordinates; techniques of integration and improper integrals. Calculators/computers used when appropriate.

IV.   Learning Objectives

  1. Use integration in applications.
  2. Apply more advanced integration techniques.
  3. Analyze sequences and infinite series.
  4. Analyze and use power series representations.
  5. Solve parametric and polar equations.
  6. Use technology to evaluate integrals, series, and to solve polar and parametric equations.

V.    Academic Integrity and Student Conduct

Students and employees at Oakton Community College are required to demonstrate academic integrity and follow Oakton's Code of Academic Conduct. This code prohibits:

• cheating,
• plagiarism (turning in work not written by you, or lacking proper citation),
• falsification and fabrication (lying or distorting the truth),
• helping others to cheat,
• unauthorized changes on official documents,
• pretending to be someone else or having someone else pretend to be you,
• making or accepting bribes, special favors, or threats, and
• any other behavior that violates academic integrity.

There are serious consequences to violations of the academic integrity policy. Oakton's policies and procedures provide students a fair hearing if a complaint is made against you. If you are found to have violated the policy, the minimum penalty is failure on the assignment and, a disciplinary record will be established and kept on file in the office of the Vice President for Student Affairs for a period of 3 years.

Please review the Code of Academic Conduct and the Code of Student Conduct, both located online at

VI.   Sequence of Topics

  1. Recommended Review
    1. Apply L’Hopital’s Rule and methods of differentiation.
    2. Using basic integration and u-substitution to find the area between curves.
  2. Use integration in applications.
    1. Compute the area of a region bounded by two or more curves.
    2. Calculate the volume of a solid using the general slicing method and the volume of solid of revolution using disks and washers.
    3. Calculate the volume of a solid of revolution using the shell method.
    4. Calculate the arc length of a function.
    5. Calculate the area of a surface of revolution.
    6. Apply the slice and sum strategy in applications such as finding the mass of a straight rod with variable density, work done in the presence of a variable force and the force exerted by a fluid on a dam.
    7. Apply the properties of logarithms and exponentials in differentiation and integration.
    8. Use exponential functions in mathematical modeling.
    9. Analyze hyperbolic functions, their derivatives, anti-derivatives, inverses and other identities.
  3. Apply more advanced integration techniques.
    1. Review standard techniques in evaluating integrals.
    2. Evaluate definite and indefinite integrals using integration by parts.
    3. Integrate powers and products of trigonometric functions.
    4. Use the technique of trigonometric substitution.
    5. Integrate rational functions using the method of partial fractions.
    6. Use integration tables or CAS systems to evaluate integrals.
    7. Use the Midpoint Rule, Trapezoidal Rule and Simpson’s Rule to approximate values of definite integrals.
    8. Evaluate improper integrals, including those over discontinuities.
    9. Solve basic differential equations.
    10. Use technology to evaluate integrals.
  4. Analyze sequences and infinite series.
    1. Define and classify sequences and series.
    2. Determine the behavior of sequences.
    3. Evaluate geometric and telescopic series or determine that the series diverges.
    4. Apply the divergence and integral tests.
    5. Apply the ratio, root and comparison tests.
    6. Apply the alternating series test, to determine a bound for the remainder in an alternating series and to determine whether a series diverges, converges absolutely or converges conditionally.
    7. Use technology to analyze sequences and series.
  5. Analyze and use power series representations.
    1. Approximate functions with polynomials.
    2. Calculate the radius and interval of convergence of a power series.
    3. Analyze the power series representations of functions.
    4. Apply several uses of Taylor series.
  6. Solve parametric and polar equations.
    1. Solve parametric equations.
    2. Define polar coordinates and to analyze polar curves.
    3. Compute slopes of lines tangent to polar curves and areas of regions bounded by polar curves.
    4. Analyze conic section curves using polar coordinates.
    5. Use technology to graph and solve polar and parametric equations.

VII.  Methods of Instruction

(To be completed by instructor)

Methods of presentation can include lectures, discussion, experimentation, audio-visual aids, small-group work and regularly assigned homework. Calculators/computers will be used when appropriate. Use of a computer algebra system is recommended. Mathematica is available for use at the College at no charge.
Course may be taught as face-to-face, hybrid or online course.

VIII. Course Practices Required

(To be completed by instructor)

IX.   Instructional Materials

Note: Current textbook information for each course and section is available on Oakton's Schedule of Classes.

Within the Schedule of Classes, textbooks can be found by clicking on an individual course section and looking for the words "View Book Information".

Textbooks can also be found at our Mathematics Textbooks page

A graphics calculator is required.  A TI-83/84 or higher numbered model will be used for instructional purposes.

X.    Methods of Evaluating Student Progress

(To be determined and announced by the instructor)

Evaluation methods can include grading homework, chapter or major tests, quizzes, individual or group projects, calculator/computer projects and a final examination.

The following applies to the online section of this course only:
This online course requires that students take their exams as directed by their instructor: either on campus at Oakton's Testing Center, at an authorized testing center with a face-to-face monitor, or remotely through a pre-approved testing service.   (To be customized by instructor.)

XI.   Other Course Information

If you have a documented learning, psychological, or physical disability you may be entitled to reasonable academic accommodations or services. To request accommodations or services, contact the Access and Disability Resource Center at the Des Plaines or Skokie campus. All students are expected to fulfill essential course requirements. The College will not waive any essential skill or requirement of a course or degree program.

Oakton Community College is committed to maintaining a campus environment emphasizing the dignity and worth of all members of the community, and complies with all federal and state Title IX requirements.

Resources and support for
  • pregnancy-related and parenting accommodations; and
  • victims of sexual misconduct
can be found at

Resources and support for LGBTQ+ students can be found at

Electronic video and/or audio recording is not permitted during class unless the student obtains written permission from the instructor. In cases where recordings are allowed, such content is restricted to personal use only. Any distribution of such recordings is strictly prohibited. Personal use is defined as use by an individual student for the purpose of studying or completing course assignments.

For students who have been approved for audio and/or video recording of lectures and other classroom activities as a reasonable accommodation by Oakton’s Access Disabilities Resource Center (ADRC), applicable federal law requires instructors to permit those recordings. Such recordings are also limited to personal use. Any distribution of such recordings is strictly prohibited.

Violation of this policy will result in disciplinary action through the Code of Student Conduct.