9-10 MWF
Solution techniques for several types of ordinary differential equations are developed and applied to problems in physics, geometry, and other sciences. Topics include first order equations (separable, homogeneous, exact, and linear), higher-order linear equations with constant coefficients, the Laplace transform, systems of linear equations, and power series solutions. AAS: Mathematics elective. IAI: MTH 912 Mathematics.
MATH 2524 with a grade of C or better or equivalent - Must be completed prior to taking this course.
General Education Outcomes are the knowledge, skills, abilities, attitudes, and behaviors that students are expected to develop as a result of their overall experiences with any aspect of the college, including courses, programs, and student services, both inside and outside of the classroom. The General Education Outcomes specifically learned in this course are:
- Critical Thinking
This course is used as an extension of the calculus sequence and will be used as a foundation for modeling and computing rates of change across several disciplines.
Faculty Contact Information
10-12 MWF
Email is the best way to get hold of me: aharwood@kcc.edu
Course Information
At the end of this course, students will be able to:
- Solve first and second order differential equations
- Apply first and second order differential equations to situations including, but not limited to electricity, engineering, physics, and chemistry.
- Solve a differential equation using the Laplace transform.
- Find a power series solution to a linear differential equation with variable coefficients and no singular point.
- Solve linear systems of differential equations by the methods of elimination and eigenvalues.
- Basic Definitions and Terminology
- Initial Value Problems
- Separable Variables
- Solutions by Substitution
- Exact Equations
- Linear Equations
- A Numerical Method
- Preliminary Theory
- Homogeneous Linear Equations with Constant Coefficients
- Undetermined Coefficients – Annihilator Approach
- Variation of Parameters
- Cauchy-Euler Equations
- Introductions to Systems of Differential Equations
- Linear Models
- Non-Linear Models
- Undamped Systems
- Free Damped
- External Forces
- LRC Circuits
- Solutions About Ordinary Points
- Definition of the Laplace Transform
- Inverse Transforms and Transforms of Derivatives
- First and Second Translation Theorems
- Operational Properties II, Convolutions, Periodic Functions
Textbook: A First Course in Differential Equations with Modeling Applications 11 th Edition, by D. G. Zill; Cengage, 2016
Calculator · A graphing calculator is required for this course · We will be using the TI-84+ in lecture, but any graphing calculator is appropriate (83,86,89,Nspire). There are calculators to borrow for free from the library, if needed.
Quizzes-
There will be quizzes approximately once every two weeks, typically Fridays. Quizzes will assess material from the current week and material previously taught. Quizzes can be taken early, if arrangements are made with your professor. Quizzes cannot be made-up afterward. The 2 lowest quiz scores will be dropped.
Project –
Teams of two students will work on a project concerning a topic in the list below, topics that . The students may pick their teams. During week 16, the students will present their project in 15-minute presentations.
Topics can be chosen from the following:
1) The Runge-Kutta Method
2) Dirac Delta Function
3) Picard’s Method
4) Power Series Solutions about Singular Points
5) Estimating Time of Death using Newton’s Law of Cooling
6) An introduction to Delay Differential Equations
7) An introduction to Fourier Series
Most of these topics (except #5) are academic in nature. #5 is an experiment. Each topic can only be used by one group. Topics and groups will be picked and approved on or close to February 1st. The instructor will then give guidelines and scoring rubrics for the topics picked.
Comprehensive Final Exam-
The final exam is comprehensive. It is worth 20% of your final grade and will be during week 17.
Quizzes - 60%
Comprehensive Final Exam- 20%
Project – 20%
90% - 100% A
80% - 89% B
66% - 79% C
56% - 65% D
0% - 55% F
Liberal Arts & Sciences
Dean, Jennifer Huggins; 815-802-8484; R310; jhuggins@kcc.edu; Division Office- W102; 815-802-8700
Attendance
Attendance is mandatory. To be successful in this course, a student must attend class every day. You are responsible for work missed due to absence. There will be no distinction between “excused” and “unexcused” absences. Attendance will not be counted for a grade, but will factor into your overall success in the class.
**Note: Math can be taught in the classroom, but can only be learned through practice, critical thinking, and more practice. Please ask questions to help further your understanding, either in class or during office hours. Advanced mathematics requires your knowledge of algebraic procedures but also creative, critical thinking that needs to be developed. You are expected to be in attendance during each class period.
Cell Phones, Other Distractions
Please refrain from using cell phones for calls, texting, etc… while in class. If it is an emergency, please leave the classroom. Using cell phones or other electronic devices on or during the taking of tests/quizzes will be considered cheating and will be subject to the guidelines below.
Cheating/Plagiarizing
Students found cheating on any assessments will earn a grade of zero on the assessment after the first occurrence and a grade of F for the entire course after the second occurrence. Using AI tools, such as ChatGPT and photomath, will be considered cheating.
Calculator Usage
Graphing calculators will be required throughout this course, except on specific items chosen
Integrity and Respect for everyone involved in the course is expected. If you have any questions about expectations, please let your professor know.
Week 1 | 1.1 Basic Definitions and Terminology 1.2 Initial Value Problems |
2 | 2.2 Separable Variables, Exact Equations 2.4 Exact Equations |
3 | 2.3 Solutions by Substitution 2.5 Linear Equations |
4 | 2.6 A Numerical Method |
5 | 4.1 Preliminary Theory |
6 | 4.3 Homogeneous Linear Equations with Constant Coefficients Differential Operations Addendum |
7 | 4.5 Undetermined Coefficients--Annihilator Approach 4.7 Cauchy-Euler Equations |
8 | 4.7 Cauchy-Euler Equations 4.9 Solving Systems of Linear DEs by Elimination, Eigenvalues and Eigenvectors |
9 | 3.1 Linear Models 3.2 Non-Linear Models |
10 | 5.1 Linear Models: IVPs |
11 | 5.1 Linear Models: IVPs |
12 | 6.2 Solutions about Ordinary Points with Power Series Solutions |
13 | 7.1 Definition of the Laplace Transform 7.2 Inverse Transforms and Transforms of Derivatives |
14 | 7.3 Operational Properties I 7.4 Operational Properties II |
15 | 7.3 Operational Properties I 7.4 Operational Properties II |
16 | Project Presentations |
17 | Final Exam |
College Policies, Resources and Supports
For information related to the Student Code of Conduct Policy, Withdrawal Policy, Email Policy, and Non- Attendance/Non-Participation Policy, please review the college’s Code of Campus Affairs and Regulations webpage, which can be found at catalog.kcc.edu under the Academic Regulations & Conduct Guide.
KCC offers various academic and personal resources for all students. Many services are offered virtually, as well as in person. Please visit Student Resources - Kankakee Community College to access student resources services such as:
- Clubs and organizations
- Counseling and referral services
- Office of disability services
- Student complaint policy
- Transfer services
- Tutoring services, etc.
The materials on this course are only for the use of students enrolled in this course for purposes associated with this course. Further information regarding KCC's copyright policy is available at https://kcc.libguides.com/copyright.
|Course syllabus/calendar is subject to change.