Differential Equations: 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
- A First Course in Differential Equations with Modeling Applications, 11th ed., by Zill, with WebAssign
- Homework
- WebAssign, class key pasadena 1578 3237
- Final exam
- Mon 12/7, 1–3 pm
- Grades
- Posted in Canvas
About the Course
Course description
Ordinary first- and higher-order differential equations and modeling, with applications to the biological and physical sciences. Linear and nonlinear equations, initial-value problems, series solutions, Laplace transforms, systems of linear equations, and numerical solutions.
Prerequisite
Math 005B or Math 005BH.
Course content
Lectures, assignments, and assessments will be based on most of Chapters 2–9 of the textbook.
Student learning outcomes
Upon successful completion of this course, you will be able to:
- Apply the appropriate analytical technique for finding the solution of first-order ordinary differential equations.
- Apply the appropriate analytical technique for finding the solution of higher-order ordinary differential equations.
- Create and analyze mathematical models using ordinary differential equations.
- Solve linear systems of ordinary differential equations.
The detailed performance objectives for each outcome are listed under Course objectives and outline.
Materials
Textbook
A First Course in Differential Equations with Modeling Applications, 11th edition, by Zill, with WebAssign (ISBN 978-1-305-96572-0). 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
Grading
| Component | Weight | Notes |
|---|---|---|
| Homework | 15% | WebAssign; three 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 1578 3237 to join my course.
Most assignments are due on Thursdays and Saturdays 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 three 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 2–8), 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 9/14 | Exam 1: Chapters 2 and 3 |
| Mon 10/12 | Exam 2: Chapters 4 and 5 |
| Wed 11/4 | Exam 3: Chapters 8 and 6 |
| 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: Sections 7.1–7.5 |
| Mon 12/7, 1–3 pm | Final exam: Chapters 2–8 |
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: First-order equations
- 1aIdentify the type of a given first-order differential equation.
- 1bApply the existence and uniqueness theorems for first-order ordinary differential equations.
- 1cFind solutions to separable, linear, and exact ordinary differential equations and Bernoulli’s equation by separation of variables, substitutions, and numerical (including Euler’s) methods.
- 1dSolve ordinary first-order initial-value differential equations.
Outcome 2: Higher-order equations
- 2aIdentify the type of a given higher-order differential equation.
- 2bApply the existence and uniqueness theorems for higher-order ordinary differential equations.
- 2cSolve ordinary higher-order homogeneous and nonhomogeneous differential equations by reduction of order, undetermined coefficients, variation of parameters, elimination, and Laplace transforms.
- 2dFind power series solutions to ordinary differential equations.
- 2eSolve ordinary higher-order initial-value and boundary-value problems.
- 2fDetermine the Laplace transform and inverse Laplace transform of functions, and use them to solve differential equations.
Outcome 3: Mathematical models
- 3aUse first-order ordinary differential equations to develop mathematical models involving exponential growth and decay, mixtures, logistic growth, and circuits.
- 3bUse higher-order ordinary differential equations to develop mathematical models involving damped and undamped spring/mass systems and circuits.
- 3cExamine, solve, and interpret results obtained from these mathematical models.
Outcome 4: Linear systems
- 4aApply the existence and uniqueness theorems for systems of linear first-order ordinary differential equations.
- 4bFind eigenvalues and eigenvectors of linear systems.
- 4cApply the methods of undetermined coefficients and variation of parameters to linear systems.
Course content outline
- Solutions to First-Order Ordinary Differential Equations
- Separable equations/separation of variables
- Homogeneous equations
- Exact equations
- Linear differential equations
- Direction fields (slope fields)
- Existence and uniqueness theorems
- Substitutions
- Numerical (including Euler’s) methods
- Initial-value problems
- Bernoulli’s equation
- First-order difference equations
- Applications of First-Order Differential Equations
- Exponential growth and decay
- Mixtures
- Logistic growth
- Circuits
- Second- and Higher-Order Differential Equations
- Homogeneous equations
- Fundamental solutions
- Independence
- Wronskian of functions
- Nonhomogeneous equations
- Reduction of order
- Undetermined coefficients
- Variation of parameters
- Elimination
- Higher-order initial-value problems
- Boundary-value problems
- Cauchy-Euler equation
- Runge-Kutta method
- Applications of Higher-Order Differential Equations
- Damped spring/mass systems
- Undamped spring/mass systems
- Circuits
- Power Series Solutions
- Solutions about ordinary and singular points
- Bessel’s equation
- Legendre’s equation
- Method of Frobenius
- Laplace Transforms
- Transforms and inverse transforms
- Initial-value problems
- Properties of Laplace transforms: shifts and convolutions
- Systems of Ordinary Differential Equations
- Homogeneous linear systems
- Eigenvalues
- Eigenvectors
- Wronskian and linear independence of a homogeneous linear system
- Nonhomogeneous linear systems
- Undetermined coefficients
- Variation of parameters
- Homogeneous linear systems