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MATH226 - Calculus II

Course Details

Course Code: MATH226 Course ID: 4085 Credit Hours: 3 Level: Undergraduate

This is the second course of a three part Calculus sequence. It is designed to extend the concepts learned in Calculus I to the concepts and techniques of integral calculus. Topics include the basics of integration (anti-derivatives, substitution, and the Fundamental Theorem), applications of integration (motion, area), L’Hopital’s Rule (indeterminate quotients, indeterminate forms), elementary function inverses (inverse functions, Calculus of inverses, trigonometry function inverses, Calculus of these inverses), techniques of integration (tables, powers of Sine and Cosine, other Trigonometric powers, by parts, trigonometric substitution, and numerical analysis), improper integrals, integral applications (average value, volumes by cross-sections, disk & washers, shells, arc lengths, and work). (Prerequisite: MATH225)


Course Schedule

Registration Dates Course Dates Session Weeks
05/21/21 - 10/29/21 11/01/21 - 02/20/22 Fall 2021 Session K 16 Week session
06/28/21 - 12/03/21 12/06/21 - 03/27/22 Fall 2021 Session C 16 Week session
07/27/21 - 12/31/21 01/03/22 - 04/24/22 Winter 2022 Session A 16 Week session
08/31/21 - 02/04/22 02/07/22 - 05/29/22 Winter 2022 Session K 16 Week session
09/28/21 - 03/04/22 03/07/22 - 06/26/22 Winter 2022 Session C 16 Week session
10/26/21 - 04/01/22 04/04/22 - 07/24/22 Spring 2022 Session A 16 Week session

Current Syllabi

After completing the course, you will be able to:

1. Use anti-derivatives.
2. Use the Fundamental Theorem of Calculus to solve problems of motion and area.
3. Solve indeterminate limits using L’Hopital’s rule.
4. Solve Calculus problems with exponential and logarithmic functions.
5. Evaluate inverse trig functions.
6. Integrate functions uses techniques for powers, partial fractions, by parts, and trigonometric substitution.
7. Use numerical integration to approximate integrals using the trapezoidal rule.
8. Solve improper integrals.
9. Apply integration to problems involving average value, volumes, arc lengths and work.

Staying on task and adhering to the published schedule are typically among the most challenging aspects of completing an academic course successfully. This is especially true for on-line and part-time non-resident programs. To avoid the pitfall of falling behind, students in this course should complete the assigned reading, and exercises in the Thinkwell environment. Students should also complete the Suggested Practice Problems as set forth in the schedule provided in the Course Outline of this syllabus.

Student grades for the course will be based on active weekly forum entries, watching videos and completing Thinkwell exercises, completing weekly assignments, submitting five tests and one final examination. You must complete all items to successfully master all skills in this course.

The Week 1 Introduction Forum: During the first week of class each student must make a post to the Week 1 Introduction Forum. You are to use this Forum to introduce yourself and state your goals and objectives as they relate to our course. You are required to make a post to the Week 1 Introduction Forum in order to complete your enrollment in the course. Your post must be at least 250 words, and you must complete it by the end of the first week. This is a university requirement. To make a post to the Week 1 Introduction Forum, click on the Forum topic link, then click Post New Thread. In the title block of the dialog box that appears kindly insert your first and last name; compose your post in the message box; and then click Post Message.

Besides completing your enrollment in the course, the Week 1 Introduction Forum is designed to 1) build peer-to-peer relationships by introducing oneself and one’s background to the class; 2) to articulate individual student learning goals and/or expectations for the class. Therefore, in your introduction you may wish to touch upon the following:

  1. Who you are and how you would like to be addressed.
  2. Your academic major or program of study.
  3. Your current status in your program of study.
  4. Your academic goals including why you are taking this course and what you hope to achieve by completing it.
  5. Other information about yourself that you would like to share and might help others know you better.

Chapter Tests: The chapter tests will cover two short or one long chapter as they are completed. These tests will be taken on-line in the classroom. They will be open book and open note tests. However, you may not receive help from any other person. These tests will be assigned early in the week and will be due by the end of the week. The exact dates are noted later in this student guide. These tests will represent 60 percent of the student’s course grade.

There are practice exercises, some in Thinkwell and others in Sakai for each of the text chapters covered. These practice problems are focused on the reading and study material for each week. After completing your assigned reading and viewing the appropriate weekly videos, you should complete those problems in order to ensure you have mastered the material covered. They are not graded, but will be discussed through the weekly forums per student questions. If you do not feel that you have mastered the topics sufficiently, please feel free to explore additional problems which you can also introduce into our weekly forums. You can also post your solutions on a weekly forum for input from other students and me.

Weekly Forums: The weekly discussion forum is for students to answer my session topic and for students to post their questions on course content for that week. Successful students find that this is an excellent resource.

The Cumulative Final Exam will be taken during the last week of the semester (25 points). It will be a three-hour exam. It will be open book and open notes and it will be on-line. It is highly recommended that you use a calculator. Students are required to submit the precise 3 hour time block that they will take the final exam during the last week of class. This time and date should be submitted during the 7th week of the semester. Unless the professor approves alternate arrangements, students should plan to take the final examination during the 16th week of the course.

Students’ final grades will be posted as soon as the instructor receives and evaluates the final exam. Official grades will continue to be issued by the University on the grade report form. Professors have 7 days from the end of the semester to submit their grades to the University.

Please see the Student Handbook to reference the University’s grading scale.

The points earned on the graded course assignments will determine the course grade. The final grade in the course will be based on total points. Grades will be assigned based on the following term composite scores:

NameGrade %
Forums 5.00 %
Introductory Forum 0.63 %
Forum Week 2 0.63 %
Forum Week 4 0.63 %
Forum Week 7 0.63 %
Forum Week 9 0.63 %
Forum Week 11 0.63 %
Forum Week 13 0.63 %
Forum Week 15 0.63 %
Assignments of Thinkwell Exercises 10.00 %
APUS Honor Code and Pledge 1.00 %
Assignment 1 2.00 %
Assignment 2 2.00 %
Assignment 3 2.00 %
Assignment 4 2.00 %
Assignment 5 2.00 %
Test Critiques 60.00 %
Test 1 Critique 12.00 %
Test 2 Critique 12.00 %
Test 3 Critique 12.00 %
Test 4 Critique 12.00 %
Test 5 Critique 12.00 %
Final Exam 25.00 %
Final Examination 25.00 %

Additional Resources

You will need, and are encouraged to use, a graphing calculator to successfully complete this course. At your discretion, you may use a scientific or graphing calculator, or the calculator on your computer that is capable of performing these functions. Microsoft2 has a free on-line calculator, as listed below. You may use these tools for all graded assignments and examinations during the course.

Tutorials3: These tutorials include 4-6 minute vignettes on many course topics for both Calculus I and Calculus II, written by the course lead and are focused on the weekly course objectives. In addition, students have also found Khanacademy4 and PatrickJMT5 tutorials helpful. Students may access these videos by clicking on Cntrl+Click on the link.

Web Sites

The following public domain web sites are useful. Please abide by the APUS University’s academic honesty policy when using Internet sources, as well. Note web site addresses are subject to change.

Site Name Website URL/Address
Thinkwell 1
On-line graphing calculator 2 Microsoft Mathematics 4.0
APUS WV tutorials 3
Khanacademy 4
PatrickJMT 5


There is no required traditional or on-line textbook for this course. Any traditional introductory calculus textbook from the library or on-line should cover the topics for this class.

If you would feel more comfortable with an on-line textbook, one is available in the library at APUS. To access, simply follow the instructions below:

1 While in the classroom, from the left menu tab click APUS Library.

2 Type in … "calculus", then click Search.

3 From the first entry, "#1 Sarah Channon 2009", click on Full text on-line

4 Click on PDF full text. Using the page number blank at the top of the page, type in the desired section:.

Calculus I

Introduction begins on page 3
Functions begins on page 6
Limits begins on page 23
Differentiation begins on page 39

Calculus II

Integration on page 85

Calculus III

Infinite series on page 155
Multivariable Calculus on page 172
Extensions on page 262

Alternately you could click this link Calculus by Sarah Channon, and click on the first title.

Thinkwell does have a book available which is a compilation of problems. There are no lessons included in this book. All of the problems, plus additional problems are already available on-line in Thinkwell. You will need to contact Thinkwell directly to make this purchase.

Thinkwell’s Calculus Exercises for Chapter’s 1-8, Edited by Raymond W. Reinhardt, Copyright 2010 by Thinkwell Corporation.

Book Title:Thinkwell Calculus Online Materials - Thinkwell will send a user name and password to your primary email address on the first day of class. Instructions provided inside the classroom.
Publication Info:Thinkwell
Unit Cost:$67.50
Electronic Unit Cost:$35.00

Previous Syllabi

Not current for future courses.