Skip Navigation

Differential Equations (NCAA Approved)

Apply Now Enroll in this Course

Prerequisites: Qualifying math score and completion of AP Calculus BC. Completion of Linear Algebra or Multivariable Calculus preferred.

Course Format: Session Based. See calendar for session dates and application deadlines.

Course Length: 30 weeks

Recommended School Credit: One full year of high school credit equal to or greater than an AP class or one semester of college credit

Student Expectations: Students are strongly encouraged to work at least 1 hour a day, 5 days a week.

Course Code: DIFY

Course Description

Description

Differential Equations is an online course equivalent to the final course in a typical college-level calculus sequence. This course is a broad introduction to Ordinary Differential Equations, and covers all topics in the corresponding course at the Johns Hopkins Krieger School of Arts and Sciences. This course covers the entire syllabus from the Johns Hopkins one-semester, in-person Differential Equations course, plus several additional topics. Online interactives, homework and quizzes help to reinforce concepts taught in the class. Online course materials supplement the required textbook.

Online course materials, such as videos, notes, interactive webpages, and practice problems with solutions, are provided for the student. Students are expected to watch videos and review notes regularly. Each student is assigned to a CTY instructor to help them during their course.

In this course, participation in forums and synchronous online virtual sessions are required as part of the final grade. Discussion forums are located within the course where students will be required to respond to a given prompt and then comment on responses by other students. Online sessions, led by a CTY instructor, are held in Adobe Connect, which allows for video, voice, text, screen sharing, and whiteboard interaction. 

Students can contact their instructors via email with questions or concerns at any time. Live one-on-one online review sessions can be scheduled as well, to prepare for the graded assessments, which include quizzes, homework, projects, unit exams, and a cumulative final.

The textbook must be purchased separately.

Topics include:

  • First order differential equations
  • Linear differential equations
  • Series solutions of second order linear equations
  • The Laplace transform
  • First order systems (both linear and nonlinear)

For a detailed list of topics, click the "List of Topics" tab.

directional field

Materials Needed

A textbook purchase is required for this course:

Elementary Differential Equations by Boyce and DiPrima, 10th Ed.

Elementary Differential Equations textbook cover
ISBN-10: 0470458321
ISBN-13: 978-0470458327

For those students who plan to continue their studies of differential equations beyond this course, we recommend the text Elementary Differential Equations and Boundary Value Problems, which contains the entire content of the book listed above, as well as two extra chapters not covered in this course.

Only one of the textbooks listed on this page is required for this course.

Elementary Differential Equations and Boundary Value Problems textbook cover

ISBN-10: 0470458313
ISBN-13: 978-0470458310

List of Topics

Upon successful completion of the course, students will be able to demonstrate mastery over the following topics:

First Order Differential Equations

  • Separable Equations
  • First Order Linear Equations
  • Exact Equations
  • Euler's Method
  • Autonomous Equations
  • Existence & Uniqueness

Linear Differential Equations

  • Review of Matrices
  • The Wronskian
  • nth Order Linear Equations
  • Homogeneous Equations with Constant Coefficients
  • Complex Roots of the Characteristic Equation
  • Repeated Roots of the Characteristic Equation
  • Higher Order Homogeneous Equations
  • Undetermined Coefficients
  • Variation of Parameters

Advanced Solving Techniques

  • Review of Power Series
  • Solutions Near an Ordinary Point
  • Euler Equations and Regular Singular Points
  • Definition of Laplace Transform
  • Solving IVPs with the Laplace Transform
  • Step Functions
  • Discontinuous Forcing Functions
  • Impulse Functions
  • The Convolution Integral

Linear Systems of Differential Equations

  • Introduction to First Order Systems
  • Eigenvalues and Eigenvectors
  • First Order Linear Systems
  • Homogeneous Linear Systems with Constant Coefficients
  • Complex Eigenvalues
  • Repeated Eigenvalues
  • The Phase Plane
  • Fundamental Matrices
  • Nonhomogeneous Linear Systems

Nonlinear Systems

  • Autonomous Systems and Stability
  • Locally Linear Systems
  • Competing Species
  • Predator-Prey Relationships
  • Periodic Solutions and Limit Cycles

Back to top

Technical Requirements

This course requires a properly maintained computer with high-speed internet access and an up-to-date web browser (such as Chrome or Firefox). The student must be able to communicate with the instructor via email. Visit the Technical Requirements and Support page for more details.

This course uses an online virtual classroom for discussions with the instructor. The classroom works on standard computers with the Adobe Connect Add-in or Adobe Flash plugin, and also tablets or handhelds that support the Adobe Connect Mobile appStudents who are unable to attend live sessions will need a computer with the Adobe Connect Add-in or Adobe Flash plugin installed to watch recorded meetings. The Adobe Connect Add-in, Adobe Flash plugin, and Adobe Connect Mobile app are available for free download. Students who do not have the Flash plug-in installed or enabled on their browsers will be prompted to download and install the Adobe Connect add-in when accessing the virtual classroom.