MATH-113-M002 Calculus 2
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Calculus 2 (MATH-113-M002)
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Please read the information in this syllabus carefully before you begin this course! The syllabus
covers the prerequisites, learning outcomes, course requirements, grading information, and
other information vital to getting through this course.
Successful completion of MATH 113 requires a basic knowledge of the concepts covered in
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 students
should already know how to do:
1. Limits
a. Explain, intuitively and graphically, the concept of the limit of a function.
b. Recognize the correct definition of a limit, and be able to use the definition of a limit to prove simple limit statements.
c. Recall and use limit theorems to evaluate limits.
d. Explain and use one-sided limits, limits at infinity, and infinite limits.
e. Apply limits to the description of the asymptotes of a function.
f. Find for functions which are not defined at .
2. Continuity
a. Recognize the definition of continuity at a point.
b. Explain the graphical interpretation of continuity.
c. Understand different types of discontinuities and which can be rewritten so as to be continuous.
d. Use continuity in evaluating limits of composite functions.
e. Apply the extreme value and intermediate value theorems.
f. State these two theorems correctly.
3. Derivatives
a. Explain and apply the graphical interpretation of a derivative as slope.
b. Explain and apply the dynamic interpretation of the derivative as the rate of change.
c. Define a derivative, and compute the derivative of a function.
d. 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).
e. Recognize and use the common notations for a derivative.
f. Recall and use the relationship between differentiability and continuity.
g. Use implicit differentiation to find the first derivative of an implicitly-defined function.
h. Explain and use the interpretations of the second derivative.
i. Compute derivatives of a higher order.
j. Be proficient in all the differentiation techniques, including the product rule and the chain rule.
4. Rolle’s theorem and the mean value theorem
a. Recall and explain the meaning of Rolle’s theorem and the mean value theorem.
b. Use the derivative to describe the monotonicity of a function.
c. Use the second derivative to describe the concavity of a function.
d. Use the first and second derivative tests to classify extrema.
e. Use the derivatives to find critical points, inflection points, and local extrema.
f. Use derivatives to aid in sketching by hand the graph of a function.
g. Solve optimization problems.
h. Solve related rates problems.
i. Use l’Hôpital’s rule to evaluate limits.
5. Definite integrals
a. Explain and apply the graphical interpretation of the definite integral as area.
b. Explain and apply the dynamic interpretation of the definite integral as total change (given the velocity or acceleration, find the displacement.)
c. Recognize a correct definition of the definite integral.
d. Recall and use the definition of the definite integral as a limit of Riemann sums (that is, find what is a certain limit of Riemann sums in terms of an integral).
e. Recognize an integral that corresponds to a sequence of Riemann sums.
f. Recall and use linearity and interval properties of definite integrals.
g. Explain that interval properties are properties pertaining to the interval of integration like and
h. Recall and explain the fundamental theorem of calculus.
i. 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.
j. Use the fundamental theorem of calculus to evaluate definite integrals by antidifferentiation.
k. Use a simple substitution to find an antiderivative.
NOTE: In order to assess readiness, and before students can access 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.
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, and polar coordinates. This course contributes to all the expected learning outcomes of
the Mathematics BS.
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 a 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 , , , and
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.
This course uses online resources and the following textbook:
Single Variable Calculus, Early Transcendentals, Volume 2, 9th Edition by James Stewart
(with WebAssign). Thomson Brooks/Cole (Cengage), 2021.
ISBN: 9780357631478, 0357631471
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 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.
A calculator is not required for this course but you may wish to have one. While graphing and
programmable calculators may be used for the homework, please not that only a scientific
calculator is allowed during the exams. Graphing and programmable calculatros are not allowed
during the exams.
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– 16 |
Chapter 10 |
Lessons 17– 20 |
Chapter 11 |
Lessons 21– 31 |
This course includes three core components: a pretest, online homework, and the exams.
Preparation Time
Adequately-prepared students should expect to spend a minimum of 48 hours of work for each
credit hour. For this course, this adds up to a minimum of 192 hours for this course. 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. Online students typically need to spend more time on the
class due to the fact that they do not attend any lectures.
Assignments
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 may also study online resources, like K- 12 or Khan Academy, or you
may use a search engine like Google or Yahoo to find resources. The textbook used for this
course does not have the preliminary chapters, 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 closed notes.
You may take the pretest twice; the highest score will be counted towards your grade. Please
be aware that you will not be ableto continue in the course or receive access to the
WebAssign homework until the pretest is completed andsubmitted.
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.
Homework
Each lesson has a graded homework assignment, and all homework will be done through
WebAssign. You 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 hard copy 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:
a. You can click on “Preview” to make sure you entered in your problem correctly.
b. 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, but understand that
homework problems have a limit of 10 attempts.
Since the homework is separate from this course, your final homework score will need to be
transferred to this course. This is done only once, after the last lesson and before you request
the final exam.
This means that you could take the midterms without doing any homework, but it is highly
unlikely that you will acheive a passing grade without doing the homework first. Before you
request an exam, you should make sure that 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 or you request that your final homework score be
transferred to your course. To submit your score before you request the final, complete and
submit the WebAssign Homework Score Transfer Request.
There will be three midterm exams and a final exam for the course.
Exam 1 will cover chapters 6– 7 in the textbook, and corresponds to lesson 1– 12 in the
course.
Exam 2 will cover chapters 8 and 10 in the textbook, and corresponds to lessons 13– 20 in
the course.
Exam 3 will cover chapter 11 in the textbook, and corresponds to lessons 21– 31 in the
course.
The final exam will cover all lessons.
Each exam has has ten to fifteen multiple-choice questions (worth 40% of the total exam
score) and six to nine free response questions (worth 60% of the total exam score). A
scientific calculator is allowed. Graphing and programmable calculators are not allowed.
Exam |
Textbook |
Your Course |
|
Midterm 1 |
Chapters 6 and 7 |
Lessons 1– 12 |
|
Midterm 2 |
Chapters 8 and 10 |
Lessons 13– 20 |
|
Midterm 3 |
Chapter 11 |
Lessons 21– 31 |
|
Final |
Chapters 6, 7, 8, 10, and 11 |
Lessons 1– 31 |
Note: Before you request the final, you need to complete and submit the WebAssign Homework
Score Transfer Request. Once this is done, you will not be able to change your homework
grade.
Your grade in this course will be based on these assignments and exams.
Assignment or Exam |
Format/Grading |
Percent of Total Grade |
Pretest |
Computer |
2% |
Overall WebAssign Homework |
Computer |
28% |
3 Proctored Midcourse Exams |
Online/Mixed |
45% |
1 Proctored Final Exam* |
Online/Mixed |
25% |
*You must pass the final exam to earn credit for the course; you may retake it once, for a fee,
upon request.
Your homework grade is a cumulative score. It will be posted only once from WebAssign into
your course gradebook. When you are ready to take the final exam, complete and submit the
WebAssign Homework Score Transfer Request. 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.
2022-07-20