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Please read the information in this syllabus carefully before you begin this course! The syllabus covers the learning outcomes that a student is expected to master in MATH 113, prerequisites, course requirements, grading information, and other vital information that you will need to know to get through this course.

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Successful completion of MATH 113 requires a basic knowledge of the concepts of MATH 112 (Calculus 1). These topics are not reviewed in the course. Students are expected to have competency in these areas before starting MATH 113. Here are the skills that are important for students to already know how to do:

  1. Limits
    1. Explain intuitively and graphically the concept of the limit of a function.
    2. Recognize the correct definition of a limit and be able to use the definition of a limit to prove simple limit statements.
    3. Recall and use limit theorems to evaluate limits.
    4. Explain and use one-sided limits, limits at infinity, and infinite limits.
    5. Apply limits to the description of the asymptotes of a function.
    6. Find lim x a f ( x ) for functions which are not defined at a.
  2. Continuity
    1. Recognize the definition of continuity at a point.
    2. Explain the graphical interpretation of continuity.
    3. Understand different types of discontinuities and which can be rewritten so as to be continuous.
    4. Use continuity in evaluating limits of composite functions.
    5. Apply the Extreme Value and Intermediate Value theorems.
    6. State these two theorems correctly.
  3. Derivatives
    1. Explain and apply the graphical interpretation of a derivative as slope.
    2. Explain and apply the dynamic interpretation of the derivative as the rate of change.
    3. Define a derivative and compute the derivative of a function.
    4. Use the differentiation formulas to find the derivative of any elementary function (polynomial, rational, root, exponential, logarithmic, trigonometric, inverse trigonometric, and hyperbolic functions, as well as all combinations and compositions thereof).
    5. Recognize and use the common notations for a derivative.
    6. Recall and use the relationship between differentiability and continuity.
    7. Use implicit differentiation to find the first derivative of an implicitly defined function.
    8. Explain and use the interpretations of the second derivative.
    9. Compute derivatives of a higher order.
    10. Be proficient in all the differentiation techniques, including the product rule and chain rule.
  4. Rolle’s theorem and the mean value theorem
    1. Recall and explain the meaning of Rolle’s theorem and the mean value theorem.
    2. Use the derivative to describe the monotonicity of a function.
    3. Use the second derivative to describe the concavity of a function.
    4. Use the first and second derivative tests to classify extrema.
    5. Use the derivatives to find critical points, inflection points, and local extrema.
    6. Use derivatives to aid in sketching by hand the graph of a function.
    7. Solve optimization problems.
    8. Solve related rates problems.
    9. Use l’Hôpital’s rule to evaluate limits.
  5. Definite integrals
    1. Explain and apply the graphical interpretation of the definite integral as area.
    2. Explain and apply the dynamic interpretation of the definite integral as total change (given the velocity or acceleration, find the displacement.)
    3. Recognize a correct definition of the definite integral.
    4. Recall and use the definition of the definite integral as a limit of Riemann sums (that is, find what a certain limit of Riemann sums is in terms of an integral).
    5. Recognize an integral that corresponds to a sequence of Riemann sums.
    6. Recall and use linearity and interval properties of definite integrals.
    7. Explain that interval properties are properties pertaining to the interval of integration like a b f ( x ) x = - b a f ( x ) x and a b f ( x ) x + b c f ( x ) x = a c f ( x ) x .
    8. Recall and explain the Fundamental Theorem of Calculus.
    9. Find derivatives of functions defined as definite integrals with variable limits, including situations which will require the use of other rules of differentiation in conjunction with the Fundamental Theorem of Calculus.
    10. Use the Fundamental Theorem to evaluate definite integrals by antidifferentiation.
    11. Use a simple substitution to find an antiderivative.

NOTE: In order to assess readiness and before students can get access to the homework through WebAssign, each student is required to take a pretest that covers the above material. This pretest is free. Each student is allowed only 2 attempts and the pretest will count towards the student’s course grade.

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BYU Course Outcomes

This course is designed for students majoring in the mathematical and physical sciences, engineering, or mathematics education and for students minoring in mathematics or mathematics education. Calculus is the foundation for most of the mathematics studied at the university level. The mastery of calculus requires well-developed skills, clear conceptual understanding, and the ability to model phenomena in a variety of settings. Calculus 2 develops techniques of integration, applications of integration, infinite sequences and series, parametric curves, polar coordinates, and conic sections. This course contributes to all the expected learning outcomes of the Mathematics BS. For a more detailed course description, visit the Math 113 Wiki page.

Course Learning Outcomes

Upon completion of MATH 113, you should be able to do the following:

  1. Find antiderivatives of a wide variety of functions, including polynomial, rational, irrational, trigonometric, inverse trigonometric, logarithmic, exponential, and hyperbolic functions and their combinations.
  2. Find these antiderivatives by hand, using the techniques of integration by substitution, integration by parts, integration by partial fractions, and trigonometric substitutions.
  3. Change limits in a definite integral when changing the variables.
  4. Demonstrate knowledge of the difference between an integral and an improper integral.
  5. Work with both types of improper integrals: those on an unbounded interval and those involving an unbounded integrand.
  6. Resolve questions of convergence for improper integrals using comparison tests, limit comparison tests, and direct application of the definition of what it means for an improper integral to converge.
  7. Use the definite integral to model and resolve problems in physics and geometry, including problems involving area between graphs of functions, mass, arc length, volumes, and surface area.
  8. Use the techniques of finding volumes by slicing and by shells.
  9. Recall and use a correct definition of limit of a sequence.
  10. Recall and use the definition of infinite series and know the difference between an infinite series and sequence.
  11. Use theorems about monotone sequences to assert the convergence of a sequence.
  12. Test a series of constants for conditional or absolute convergence and understand the meaning of absolute and conditional convergence.
  13. Find the sum of a convergent geometric series and apply it to practical problems.
  14. Compute Taylor polynomials centered at various points using the formula for Taylor series.
  15. Recall or compute Taylor series for basic functions, including remainder terms.
  16. Use the remainder term of a Taylor series to estimate the error in the approximation of the function.
  17. Use the Maclaurin series for the functions ex, ln(1 + x), sin(x), cos(x), and 1 1 - x .
  18. Find the radius of convergence and interval of convergence of a power series.
  19. Differentiate and integrate functions expressed as a sum of a power series and understand the statements of the theorems used to do this.
  20. Recall and compute binomial series.
  21. Use parametric equations to represent a wide variety of curves.
  22. Find arc lengths of parametric curves.
  23. Transform coordinates and curves between rectangular and polar coordinates.
  24. Find areas enclosed by polar curves.
  25. Find arc lengths of polar curves.
  26. Parameterize ellipses and circles.

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Course Materials

This course uses online resources and the textbook:

Be sure to get the textbook with WebAssign access. If you need to order WebAssign separately, you may do so from the website, but it is far less expensive to buy the textbook and WebAssign bundled together.

Webassign.net is the website where you will complete your homework
assignments for each lesson. You will need to buy an access code
to use WebAssign. You will use the username, institution and password
provided in your course to access the homework assignments after you have completed the pretest.


This course performs best in Mozilla Firefox; other browsers may not work as well.

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Course Organization

The lessons in the course correspond to certain chapters in the book. The following table shows which lessons go with each textbook chapter.

Textbook Chapters Lessons in Course
Chapter 6 Lessons 1-5
Chapter 7 Lessons 6-12
Chapter 8 Lessons 13-15
Chapter 10 Lessons 16-21
Chapter 11 Lessons 22-32

This course includes three core components: a pretest, online homework and the exams.


Summary: 1 computer-graded pretest (two attempts with no fee) and WebAssign Homework for each of the 32 lessons, completed through a separate web application (no resubmission allowed).


In order to assess readiness, each student is required to take a pretest on the prerequisite information. Students must take the pretest before they will have access to the WebAssign homework. To prepare for the pretest, you may use your book from MATH 112 or check one out from a library. You can also access online resources, like cK-12, Khan Academy, or use a search engine like Google or Yahoo to find resources. The textbook used for this course does not have the preliminary chapters, and so it cannot be used to prepare for the pretest.

Note: When you take the pretest, you are not allowed to use any resources; it is closed book and notes.

You may take the pretest twice; the highest score will be counted towards your grade. Please be aware that you will not be able to continue in the course or receive access to the WebAssign homework until the pretest is completed and submitted.

Once you have completed and submitted the pretest, you will be able to proceed to the Homework Access Instructions in your course. These step-by-step instructions will lead you through accessing WebAssign and your MATH 113 homework. For further help accessing WebAssign, you will need to visit the WebAssign website.


Each lesson has a graded homework assignment, and all homework will be done through WebAssign and submitted online. Since this is an Independent Study course, there is no deadline for finishing homework or taking an exam; however, you must complete the course within one year from the date you registered. Students are advised to study each section and the homework carefully before attempting each exam.

Once you have completed the pretest, gained access to the homework in WebAssign and logged in, you should be able to see the homework assignments by section.

  1. Click on the first section name (for example, 8.3), and it will take you to a page from which you can access each individual question.
  2. Just above the questions there is a “Print Assignment” link where you can download a hardcopy of the questions for that section. It is suggested that you print out the homework and keep the questions and your work in a notebook that you can review when necessary.
  3. Once you have completed all of the homework questions on your worksheets, log in to the homework server and click on the homework set.
  4. Click on each individual link to go to that problem’s page. Enter your solution into the given box. You have some options here.
    1. You can click on “Preview” to make sure you entered in your problem correctly.
    2. If you didn’t, you can fix it before you proceed. If you feel your answer is right, click on the “Submit answer” button.
  5. After submitting your answer, you will be told if your answer is right or wrong. If it is wrong, you can review your work and try to correct it. Then you can submit it again.

NOTE: You can spend as long on a homework assignment as you wish, with the caveat that homework problems have a limit of 10 attempts.

Since the homework is separate from your Independent Study course, your final homework score will need to be entered into the Independent Study course manually by the Math 113 teaching assistant (TA). This is done only once, after the last lesson and before you request the final exam.

This means that a you could take the midterms without doing any homework, but it is highly unlikely that a passing grade will be achieved without doing the homework first. Before you request an exam, you should make sure your homework percentage is high. A high homework percentage does not guarantee a good score on an exam, but a low percentage nearly always translates to a failing grade on the test.

If you want to go back later and improve your homework score, you are welcome to do so until you reach your 10-try limit per problem and/or you request that your final homework score be transferred to your Independent Study course. To do this, and before you request the final, complete and submit the WebAssign Homework Score Transfer Request assignment so that your homework score will be posted.

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Summary: 3 proctored, instructor-graded midcourse exams and 1 proctored, instructor-graded final exam (one retake for each exam allowed for a fee). Your homework grade must be posted to your Independent Study course before you request the final exam. You must pass the final exam with (50% or higher) to pass the course. A scientific calculator is allowed but not a graphing or programmable calculator.

There will be three midterm exams and a final exam for the course.

The exams are only available to be taken in a paper format. Please plan for shipping time.

Exam Textbook Your Course
Midterm 1 Chapter 6 and 7 Lessons 1-12
Midterm 2 Chapters 8 and 10 Lessons 13-21
Midterm 3 Chapter 11 Lessons 22-32
Final Chapters 6, 7, 8, 10 and 11 Lessons 1-32

Note: Before you request the final, you need to complete and submit the WebAssign Homework Score Transfer Request assignment so that your homework score will be posted. Once this is done, you will not be able to change your homework grade.

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Course Duration

You have 12 months from the date of registration to complete this course. Please be aware, it is very unlikely you will be able to successfully complete this course in less than 3 months. If you need additional time, one 3-month extension is allowed for a fee.

Preparation Time

Adequately prepared students should expect to spend a minimum of three hours of work per week for each credit hour. For this course, this adds up to a minimum of twelve hours per week. A minimal time commitment is likely to lead to an average grade (B-/C+ or lower). Much more time may be required to achieve excellence. Independent Study students typically need to spend more time on the class due to the fact that they do not attend any lectures.

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Getting Help

Since this is an Independent Study course, you do not have a professor with office hours set aside for your questions. You can e-mail online113@mathematics.byu.edu for help, but it will be very difficult to give help over e-mail. Please do not e-mail the professor. The above e-mail will go to the TA who is assigned to this course. If you are close to a university or college, you may be able to find an open math lab there that you can go to for help. Otherwise, you will need to check the textbook for similar examples, or look for examples on the Web. You can also look at examples in this course.

For those students who live near BYU, the BYU Math Lab is a great resource for getting one-on-one help. You can find information about the location and hours of the Math Lab at http://math.byu.edu/mathlab/.

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Grading and Assessment

Grades in this course are determined as follows:

Category Percent
Pretest 2%
Exam 1 15%
Exam 2 15%
Exam 3 15%
Overall WebAssign Homework 28%
Final 25%

Your homework grade is a cumulative score. Your homework grade will be posted only once from WebAssign into the Independent Study gradebook. When you are ready to take the final exam, complete and submit the WebAssign Homework Score Transfer Request assignment to request that your homework score be posted. Once you have done this, you will not be able to change your homework score. The homework score listed on the gradebook will become your final homework score. So, if you wish to improve your homework score, you must do it before you request the final exam.

You must pass the final (50% or higher) in order to pass the course.

Your overall grade will be determined by the following scale:

Grading Scale
A 90%–100% C 60%–64%
A− 85%–89% C− 55%–59%
B+ 80%–84% D+ 50%–54%
B 75%–79% D 45%–49%
B− 70%–74% D− 40%–44%
C+ 65%–69% E (fail) 39% or below

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Copyright Notice

The materials used in connection with this online course are only for the use of students enrolled in this course for purposes associated with this course and may not be retained or further disseminated. Any copying or further dissemination of these materials may be subject to applicable U.S. Copyright Laws. For questions or more information, please visit the BYU Copyright Licensing Office website.

“Members of the BYU community who willfully disregard this Copyright Policy or the BYU Copyright Guidelines place themselves individually at risk of legal action and may incur personal liability for their conduct. The unauthorized use or distribution of copyrighted material, including unauthorized peer-to-peer file sharing, may subject individuals to civil and criminal liabilities, including actual and statutory damages, costs and fees of litigation, fines, and imprisonment

Violations of the Copyright Policy may result in university disciplinary action including termination of university enrollment or employment.” (Emphasis added. Excerpt taken from the BYU Copyright Policy)

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University Policy - Title IX Statement

Preventing & Responding to Sexual Misconduct

In accordance with Title IX of the Education Amendments of 1972, Brigham Young University prohibits unlawful sex discrimination against any participant in its education programs or activities. The university also prohibits sexual harassment—including sexual violence—committed by or against students, university employees, and visitors to campus. As outlined in university policy, sexual harassment, dating violence, domestic violence, sexual assault, and stalking are considered forms of "Sexual Misconduct" prohibited by the university.

University policy requires all university employees in a teaching, managerial, or supervisory role to report all incidents of Sexual Misconduct that come to their attention in any way, including but not limited to face-to-face conversations, a written class assignment or paper, class discussion, email, text, or social media post. Incidents of Sexual Misconduct should be reported to the Title IX Coordinator at t9coordinator@byu.edu or (801) 422-8692. Reports may also be submitted through EthicsPoint at https://titleix.byu.edu/report or 1-888-238-1062 (24-hours a day).

BYU offers confidential resources for those affected by Sexual Misconduct, including the university’s Victim Advocate, as well as a number of non-confidential resources and services that may be helpful. Additional information about Title IX, the university’s Sexual Misconduct Policy, reporting requirements, and resources can be found at http://titleix.byu.edu or by contacting the university’s Title IX Coordinator.

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Accessibility Notice

BYU is committed to providing a working and learning atmosphere which reasonably accommodates persons with disabilities who are otherwise qualified to participate in BYU's programs and activities. In this spirit, BYU Independent Study aspires to improve web accessibility for users. While not required by law, the Web Content Accessibility Guidelines (WCAG) 2.0 Levels A and AA provide a wide range of helpful recommendations to make Web content more accessible. BYU Independent Study strives to apply WCAG 2.0 recommendations where feasible, but may deviate from any recommendations that would result in an undue hardship to BYU Independent Study or alterations to program and course content and objectives. If you have questions about accessibility, or if you need to report problems with any accessibility features please see our Accessibilities and Accommodations Web Page.

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