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Notes on Diffy Qs (Lebl)
Edfinity is supported by the National Science FoundationInfo
This is an online homework companion to Notes on Diffy Qs: Differential Equations for Engineers by Jiri Lebl. It comprises hundreds of algorithmic problems carefully organized into problem sets mapped to textbook sections. Use this course as-is, or customize at any level. You can mix-and-match problems from other catalog courses, add problems from the Edfinity problem repository, or write your own
How to use this course
- Homework: Assign high quality problems with hints and personalized feedback to develop problem-solving skills.
- Testing: Create summative secure online quizzes and tests in minutes.
- Supplementary resources: Embed videos, class notes, and applets alongside assignments.
- Intervention: Use rich analytics to identify and monitor at-risk students for timely intervention.
- Analytics: Drill down into student performance and identify problematic or difficult topics.
- Flipped classroom: Assign pre-class assignments. Save precious class time for discussions.
- Emporium classes: Use Edfinity for individual/group work for large enrollment sections in labs.
Interactive, algorithmic problems
Algebraic, graphing, open response; randomized variants, hints, and tips
Algebraic, graphing, open response; randomized variants, hints, and tips
Adaptive learning and personalization
Each student receives personalized support
to fill learning gaps.
Each student receives personalized support
to fill learning gaps.
Corequisite course structures
Use pre-built corequisite content,
or create your own.
Use pre-built corequisite content,
or create your own.
LMS integration and accessibility
Connect to your LMS in minutes. VPAT here.
Connect to your LMS in minutes. VPAT here.
WeBWorK-compatible
Import and author WeBWorK problems.
Import and author WeBWorK problems.
Syllabus
- Edfinity Demo
- Sec 0.2: Introduction to differential equations
- Sec 0.3: Classification of differential equations
- Sec 1.1: Integrals as solutions
- Sec 1.2: Slope fields
- Sec 1.3: Separable equations
- Sec 1.4: Linear equations and the integrating factor
- Sec 1.5: Substitution
- Sec 1.6: Autonomous equations
- Sec 1.7: Numerical methods
- Sec 1.8: Exact equations
- Sec 1.9: First order linear PDE
- Sec 2.1: Second order linear ODEs
- Sec 2.2: Constant coefficient second order linear ODEs
- Sec 2.3: Higher order linear ODEs
- Sec 2.4: Mechanical vibrations
- Sec 2.5: Nonhomogeneous equations
- Sec 2.6: Forced oscillations and resonance
- Sec 3.1: Introduction to systems of ODEs
- Sec 3.2: Matrices and linear systems
- Sec 3.3: Linear systems of ODEs
- Sec 3.4: Eigenvalue method
- Sec 3.5: Two dimensional systems and their vector fields
- Sec 3.6: Second order systems and applications
- Sec 3.7: Multiple eigenvalues
- Sec 3.8: Matrix exponentials
- Sec 3.9: Nonhomogeneous systems
- Sec 4.10: Dirichlet problem in the circle and the Poisson kernel
- Sec 4.1: Boundary value problems
- Sec 4.2: The trigonometric series
- Sec 4.3: More on the Fourier series
- Sec 4.4: Sine and cosine series
- Sec 4.5: Applications of Fourier series
- Sec 4.6: PDEs, separation of variables, and the heat equation
- Sec 4.7: One dimensional wave equation
- Sec 4.8: D’Alembert solution of the wave equation
- Sec 4.9: Steady state temperature and the Laplacian
- Sec 5.1: Sturm-Liouville problems
- Sec 6.1: The Laplace transform
- Sec 6.2: Transforms of derivatives and ODEs
- Sec 6.3: Convolution
- Sec 6.4: Dirac delta and impulse response
- Sec 6.5: Solving PDEs with the Laplace transform
- Sec 7.1: Power series
- Sec 7.2: Series solutions of linear second order ODEs
- Sec 7.3: Singular points and the method of Frobenius
- Sec 8.1: Linearization, critical points, and equilibria
- Sec 8.2: Stability and classification of isolated critical points
- Sec 8.3: Applications of nonlinear systems
- Sec 8.4: Limit cycles
- Sec A.1: Vectors, mappings, and matrices
- Sec A.2: Matrix algebra
- Sec A.3: Elimination
- Sec A.4: Subspaces, dimension, and the kernel
- Sec A.5: Inner product and projections
- Sec A.6: Determinant
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