Single Variable Calculus II: Syllabus
Quick facts
- Instructor
- Dr. Matt Henes
- mthenes@pasadena.edu
- Phone
- (626) 585-7456
- Office
- V-216F
- Office hours
- Mondays and Wednesdays, 11:30 am–12:45 pm, in V-216F
Wednesdays 4–5 pm and Tuesdays/Thursdays 5–6 pm on Zoom (meeting ID 310 291 0470) - Textbook
- Calculus, 9th ed., by Stewart, Clegg, and Watson, with WebAssign
- Homework
- WebAssign, class key pasadena 7237 7031
- Final exam
- Mon 12/7, 3:15–5:15 pm
- Grades
- Posted in Canvas
About the Course
Course description
Differentiation and integration of trigonometric, exponential, logarithmic, hyperbolic functions, polar, and parametric equations; applications and techniques of integration; indeterminate forms and infinite sequences and series.
Prerequisite
Math 005A or Math 005AH.
Course content
Lectures, assignments, and assessments will be based on most of Chapters 6, 7, 8, 10, and 11, and some of Chapter 9.
Student learning outcomes
Upon successful completion of this course, you will be able to:
- Differentiate and integrate transcendental functions; evaluate limits in indeterminate form.
- Select appropriate techniques and correctly perform a specific integration.
- Solve application problems involving integration.
- Perform differentiation and integration on parametric and polar curves.
- Represent functions as power series, test these power series for convergence, and use the theory of power series in applications.
The detailed performance objectives for each outcome are listed under Course objectives and outline.
Materials
Textbook
Calculus, 9th edition, by Stewart, Clegg, and Watson, with WebAssign (ISBN 978-1-337-62418-3). Available at the PCC bookstore or through Cengage.
Required materials
- Either
- pencils, eraser(s), lined paper, and a 1½-inch (or larger) binder with dividers, or
- a tablet device
- A scientific calculator
How Instruction Works
Because this is a hybrid class, some of the instruction is delivered asynchronously through videos I have created. Links to the video playlists for each textbook section are in Canvas and on the Math 005B Hybrid course page of my website. The tentative schedule lists the date by which to watch each week’s videos.
Grading
| Component | Weight | Notes |
|---|---|---|
| Homework | 15% | WebAssign; four lowest scores dropped |
| Exams (4) | 60% | All four exam scores count |
| Final exam | 25% | Comprehensive; required to pass the class |
Homework
The best way to learn math is to do it. Homework is your opportunity to practice working problems and learn the math you’ll see in class. Homework for this course is assigned through WebAssign, so you’ll need to purchase access from the PCC bookstore or directly from Cengage at GetEnrolled.com. Use class key pasadena 7237 7031 to join my course.
Most assignments are due on Fridays and close at 11:59 pm on the day they are due. Math builds on itself, and one of the best ways to succeed in this course is to do homework regularly and turn assignments in on time. Though homework is a relatively small part of your grade, it is when most of your learning happens; the time you spend on assignments each week is an investment in your exam scores.
Your four lowest homework scores will be dropped (about 10 percent of the homework assignments).
Exams
Exams are your opportunity to show what you’ve learned, so they make up the largest part of your grade. There are four exams, tentatively scheduled for the dates listed under Exams and important dates. Please take these dates into account when planning your personal schedule.
Arranging make-up exams is difficult, so ideally everyone will take exams in class as scheduled. If something comes up, I’ll consider a make-up for a missed exam on a case-by-case basis. Because exams reflect what you’ve learned, and because this course prepares you for future STEM classes, all exam scores are included in your final grade.
Comprehensive final exam
The final exam covers material from the whole course (Chapters 6–10), so preparing for it reinforces the concepts you’ve learned throughout the term. You must take the final exam to pass the class.
Grade scale
Course grades are based on your performance on exams and homework, not on extra credit or outside factors such as GPA or transfer plans. Your letter grade will be no lower than the scale below gives.
| Grade | Course percentage |
|---|---|
| A | 90–100% |
| B | 80–89% |
| C | 73–79% |
| D | 60–72% |
| F | below 60% |
Checking your grades in Canvas
Class notes and grades are posted in Canvas. Please let me know about any discrepancies or mistakes in posted scores within one week of their posting so I can correct them promptly.
Exams and Important Dates
Exam dates are tentative.
| Date | Event |
|---|---|
| Mon 9/7 | Labor Day (no classes) |
| Mon 9/7 | Last day to add, or to drop without a “W” |
| Mon 9/21 | Exam 1: Chapter 6 |
| Mon 10/12 | Exam 2: Chapter 7 |
| Mon 11/9 | Exam 3: Chapter 11 |
| Wed 11/11 | Veterans Day (no classes) |
| Fri 11/13 | Last day to drop with a “W” |
| Thu 11/26–Sun 11/29 | Thanksgiving break (no classes) |
| Mon 11/30 | Exam 4: Chapter 8 through Section 10.2 |
| Mon 12/7, 3:15–5:15 pm | Final exam: Chapters 6–10 |
The tentative schedule lists the textbook sections and homework due dates for every week.
Class Policies
Attendance and classroom expectations
- Attend regularly.
- Arrive on time, and don’t leave early.
- Silence your cell phone.
- No food or drinks, except bottled water.
- No visitors (including children).
Calculators
Scientific calculators are allowed on exams. Use of any other electronic device during an exam will be considered cheating.
Academic integrity
Academic integrity ensures that the grades I submit are meaningful. Any student caught cheating on an exam will receive a grade deduction for that exam, possibly a score of zero. I am required to report the violation to the Office of Student Life for potential further action. Under PCC policy, any form of academic dishonesty can be grounds for a grade of F and possibly dismissal from the college.
Photo ID
Please bring an official photo ID (such as a PCC ID card, driver’s license, or passport). IDs will be checked during the term to verify that the students in class are the ones officially enrolled. If I’m unable to verify your ID, I can’t assign a passing grade for the class.
Getting Help
- Office hours: come by V-216F or join on Zoom (see the times above).
- Tutoring: free tutoring is available at the Math Success Center (R-406) and, for student athletes, at the Zone (GM-112A).
- Accommodations: Disabled Student Programs and Services (DSPS, D-209) supports students with documented disabilities. Please let me know about any accommodations for which you qualify.
Course Objectives and Outline
These are the official course objectives and topics. Select a heading to expand it.
Student performance objectives
Objectives are grouped by the student learning outcome they support.
Outcome 1: Transcendental functions and indeterminate forms
- 1.1Find derivatives and integrals involving logarithmic, exponential, trigonometric, and hyperbolic functions and their inverses.
- 1.2Evaluate limits in a variety of indeterminate forms using L’Hospital’s Rule and algebraic techniques.
Outcome 2: Techniques of integration
- 2.1Perform different techniques of integration, including partial fractions, trigonometric integrals, trigonometric substitutions, and integration by parts.
- 2.2Utilize numerical integration techniques, including the Trapezoidal Rule and Simpson’s Rule.
- 2.3Evaluate improper integrals.
Outcome 3: Applications of integration
- 3.1Solve applied problems involving arc length, area of a surface of revolution, moments, center of mass, separable differential equations, and growth and decay.
- 3.2Revisit applications including work and volume.
Outcome 4: Parametric and polar curves
- 4.1Graph, integrate, and differentiate parametric and polar functions.
- 4.2Solve applied problems with parametric and polar functions, including finding tangent lines and computing area.
Outcome 5: Infinite series and power series
- 5.1Test infinite series for convergence using the integral, ratio, root, alternating series, and comparison tests.
- 5.2Find Taylor series for basic functions (trigonometric, exponential, logarithm, inverse trigonometric, root), and determine the radius and interval of convergence.
- 5.3Use Taylor series in applications, including integration and estimation.
Course content outline
- Exponential and Logarithmic Functions
- 1.1Inverse functions
- 1.2Natural logarithmic function
- 1.3Natural exponential function
- 1.4Differentiation and integration
- 1.5Growth and decay
- Transcendental Functions
- 2.1Trigonometric functions
- 2.2Inverse trigonometric functions
- 2.3Hyperbolic functions
- 2.4Inverse hyperbolic functions
- Techniques of Integration
- 3.1Integration by parts
- 3.2Trigonometric integrals
- 3.3Trigonometric substitution
- 3.4Partial fractions
- 3.5Rationalizing substitution
- 3.6Numerical integration
- Trapezoidal Rule
- Simpson’s Rule
- 3.7Applications of integration
- Arc length
- Area of a surface of revolution
- Moments and centers of mass
- Separable differential equations
- Define and Graph Curves Using Parametric Equations
- 4.1Compute rates of change along parametric curves
- 4.2Compute arc lengths of parametric curves
- 4.3Compute definite integrals of parametrically defined curves
- Define and Graph Curves Using Polar Equations
- 5.1Compute rates of change along polar curves
- 5.2Compute arc lengths of polar curves
- 5.3Compute definite integrals of polar functions
- 5.4Compute area of polar regions
- Indeterminate Forms
- 6.1L’Hospital’s Rule
- 6.2Improper integrals
- Infinite Sequences and Series
- 7.1Convergence of sequences
- 7.2Series
- 7.3Tests for convergence of series, including the Comparison, Limit Comparison, Alternating Series, Integral, Ratio, and Root tests
- 7.4Power series; radius and interval of convergence
- 7.5Representing functions as power series
- 7.6Differentiation and integration of power series
- 7.7Taylor and Maclaurin series
- 7.8Binomial series
- 7.9Applications of power series, including integration and estimation