Course Syllabus
Syllabus Calculus SHU
Welcome
Welcome to Calculus SHU! We’re so glad you’re here.
Every lesson is designed to help you grow as a thinker, problem solver, and global learner. As a Mizzou Academy global student, you will complete lessons and assignments on your own schedule, interacting with course content, participating in interactives, and completing practice activities, as well as drafting and revising assignments, preparing for quizzes and assessments, and taking exams.
To stay on track, we recommend using a pacing guide. You can find more information about pacing in the Course Resources section, along with helpful tools, technology support, and tips for online learning success.
As you begin, remember that online learning requires both independence and communication. Be curious, stay organized, and don’t hesitate to reach out to your teacher if you need support.
We’re excited to learn with you, and we’re happy you’re part of our Mizzou Academy community!
Pacing
This course can be completed in as few as six weeks or take up to 6 months (180 calendar days). The six weeks are counted from the date of the first lesson submission and not the date of enrollment.
This course is asynchronous, meaning you can complete lessons and assignments at your own pace.
Most students spend approximately 10 hours per lesson interacting with course content, participating in interactive activities, and completing practice exercises, as well as drafting and revising assignments, preparing for quizzes and assessments, and taking exams. Your time may vary depending on your goals and learning style.
We encourage you to work at a consistent pace, allowing time to absorb new ideas, build skills, and reflect on what you’ve learned. Use a pacing guide to plan ahead, stay organized, and finish strong.
Course Description
In Calculus, Second Half Unit, you will find the area between curves, not just under a curve.
You will find the volume of geometric solids that do not have flat surfaces, such as the volume of material used in the Liberty Bell. Integration will be used to determine the amount of work a system performs, to find the center of a mass, and to find the pressure and force produced by a fluid. Your integration skills will be honed with more techniques, tables, and L’Hôpital’s Rule. The course will end with a study of series and sequences. This may cause you to delve into an individual study of fractals.
This course is composed of ten lessons. Each lesson contains the following sections:
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Purpose—States the general goal of the lesson.
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Objectives—Lists specific knowledge you will gain after completing the lesson and topics to keep in mind when studying for progress evaluations and exams.
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Reading Assignment—Lists required reading for the lesson.
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Commentary—The heart of the lesson. Elaborates on topics noted in the Objectives section, further develops readings from the Reading Assignment section, and may offer additional information not covered in the textbook or noted in the Objectives section.
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Study Questions and Practice Quizzes—Ungraded assignments that help you review important concepts in the lesson. Excellent preparation tools for progress evaluations and exams. Because study questions and practice quizzes will not be graded, do not send your answers to the Center. However, compare your answers to the answers provided in the Commentary section.
Course Essential Questions
Essential Question
How can we use advanced integration techniques and infinite series to solve complex differential equations and quantify the geometry of non-linear shapes?
Course Overview
Lesson |
Objectives |
Quiz |
Assignment |
|
1: Exponential Functions |
1.1. Differentiate and integrate natural exponential functions. 1.2. Differentiate and integrate exponential functions that have bases other than e. 1.3. Use exponential functions to model compound interest and exponential growth. 1.4. Use separation of variables to solve a simple differential equation. 1.5. Use exponential functions to model growth and decay in applied problems. |
20 multiple-choice questions |
No Assignment |
|
2: Differential Equations Involving Separation of Variable, Inverse Trigonometric Functions, Hyperbolic Functions |
2.1. Use initial conditions to find particular solutions of differential equations. 2.2. Recognize and solve differential equations that can be solved by separation of variables. 2.3. Recognize and solve homogeneous differential equations. 2.4. Use a differential equation to model and solve an applied problem. 2.5. Differentiate inverse trigonometric functions. 2.6. Integrate functions whose antiderivatives involve inverse trigonometric functions. 2.7. Use completing the square to integrate a function. 2.8. Differentiate and integrate hyperbolic functions. 2.9. Differentiate and integrate functions involving inverse hyperbolic functions. |
20 multiple-choice questions |
No Assignment |
|
3: Area of Region Between Two Curves and Volume |
3.1. Find the area of a region between two curves. 3.2. Find the area of a region between two intersecting curves. 3.3. Find the volume of a solid of revolution using the disk method. 3.4. Find the volume of a solid of revolution using the washer method. 3.5. Find the volume of a solid with a known cross section. 3.6. Find the volume of a solid of revolution using the shell method. |
20 multiple-choice questions |
No Assignment |
|
4: Arc Length and Surfaces of Revolution, Work, Centroids, and Fluid Force |
4.1. Find the arc length of a smooth curve. 4.2. Find the area of a surface of revolution. 4.3. Find the work done by a constant and variable force. 4.4. Find the center of a mass in a one-dimensional and two-dimensional system. 4.5. Find the center of a mass of a planar lamina. 4.6. Use the Theorem of Pappus to find the volume of a solid of revolution. 4.7. Find fluid pressure and fluid force. |
20 multiple-choice questions |
No Assignment |
|
5: Integration |
5.1. fit an integrand to one of the basic integration rules. 5.2. find an antiderivative using integration by parts. 5.3. use a tabular method to perform integration by parts. 5.4. solve trigonometric integrals involving powers of sine and cosine. 5.5. solve trigonometric integrals involving powers of secant and tangent. 5.6. solve trigonometric integrals involving sine–cosine products with different angles. |
20 multiple-choice questions |
No Assignment |
Midterm Exam |
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6: Integration Using Substitution, Partial Fractions, and Tables |
6.1. solve an integral using trigonometric substitution. 6.2. use integrals to model and solve real-life applications. 6.3. use partial fraction decomposition with linear factors to integrate rational functions. 6.4. use partial fraction decomposition with quadratic factors to integrate rational functions. 6.5. evaluate an indefinite integral using a table of integrals. 6.6. evaluate an indefinite integral using reduction formulas. 6.7. evaluate an indefinite integral involving rational functions of sine and cosine. |
20 multiple-choice questions |
No Assignment |
|
7: L'Hôpital's Rule |
7.1 recognize limits that produce indeterminate forms. 7.2. apply L'Hôpital's Rule to evaluate a limit. 7.3. evaluate an improper integral that has an infinite limit of integration. 7.4. evaluate an improper integral that has an infinite discontinuity. |
20 multiple-choice questions |
No Assignment |
|
8: Sequences and Series |
8.1. list the terms in a sequence. 8.2. determine whether a sequence converges or diverges. 8.3. write a formula for the nth term of a sequence. 8.4. use properties of monotonic sequences and bounded sequences. 8.5. use properties of infinite geometric series. 8.6. use the nth-Term Test for Divergence of an infinite series. 8.7. use the Integral Test to determine whether an infinite series converges or diverges. 8.8. use properties of p-series and harmonic series. |
20 multiple-choice questions |
No Assignment |
|
9: Alternating Series |
9.1. use the Direct Comparison Test to determine whether a series converges or diverges. 9.2. use the Limit Comparison Test to determine whether a series converges or diverges. 9.3. use the Alternating Series Test to determine whether an infinite series converges. 9.4. use the Alternating Series Remainder to approximate the sum of an alternating series. 9.5. classify a convergent series as absolutely or conditionally convergent. 9.6. use the Ratio Test to determine whether a series converges or diverges. 9.7. use the Root Test to determine whether a series converges or diverges. |
20 multiple-choice questions |
No Assignment |
|
10: Power Series |
10.1. find Taylor and Maclaurin polynomial approximations of elementary functions. 10.2. find the radius and interval of convergence of a power series. 10.3. determine the endpoint convergence of a power series. 10.4. differentiate and integrate a power series. 10.5. find a geometric power series that represents a function. 10.6. construct a power series using series operations. 10.7. find a Taylor or Maclaurin series for a function. 10.8. find a binomial series. |
20 multiple-choice questions |
No Assignment |
Final Exam |
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Grades
Your final grade will be based on the number of points you earn on submitted work and exams. The available points are distributed as follows:
| Source | Available Points |
|---|---|
| Lesson Quizzes | 200 |
| Midterm Exam | 175 |
| Final Exam | 175 |
| Total | 550 |
Textbook & Technology Requirements
To fully participate, make sure you have:
- A computer that meets our Mizzou Academy technology requirements
- A microphone and webcam for recording audio and video assignments
- Any other required textbooks or materials for the course
Accessibility
If you anticipate barriers related to the format or requirements of this course, please let Mizzou Academy know as soon as possible. If disability-related accommodations are necessary (for example, a scribe, reader, extended time on exams, captioning), please contact Mizzou Academy.Canvas Technical Support
Canvas will be used as the primary platform for accessing course materials and assignments for this class.
- Access Canvas through the Tiger Portal https://mizzouacademy.missouri.edu/
- For assistance with Canvas, passwords, or other technical issues, submit a ticket by selecting Help from the Global Navigation menu on the left in Canvas. Additional information is provided in the following Canvas Guide: How do I get help with Canvas as a student?
- For questions about enrollment, access to courses, exam proctoring, or billing, contact our Support Services Team at (855) 256-4975 or mizzouacademy@missouri.edu.
Course Summary:
| Date | Details | Due |
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