Differential Equations in a Nutshell
What are differential equations and what are they used for?
Differential equations show up in just about every branch of science, including classical mechanics, electromagnetism, circuit design, chemistry, biology, economics, and medicine.
From analyzing the simple harmonic motion of a spring to looking at the population growth of a species, differential equations come in a rich variety of different flavors and complexities.
Discover why differential equations are so important!
Build and explore real-world models with first-order equations.
Make a differential equation through experimentation.
Conquer first-order separable equations with a single technique.
Unravel secrets of the biological micro-world with first-order equations.
Learn to sketch integral curves like a pro by solving this chemistry challenge.
Improve your solution curves and add an important integration skill to your toolbox.
Practice your first-order skills while exploring this chemistry application.
Use differential equations to save the countryside from a vampire plague!
Learn the power of combining geometry and differential equations
Use a simple, geometric technique to draw integral curves on the phase plane.
Combine vectors and geometry into a technique for solving first-order problems.
Apply the integrating factor to a classic real-world problem.
Explore the meaning of the integrating factor in the context of physics.
Explore the potential for using first-order equations to make real-world models.
Drop in on a marooned astronaut who uses first-order equations to call for rescue.
Matrices and vectors unlock the gateway to higher-order equations.
Learn to visualize the essential features of equation pairs.
Learn how to use vector geometry as a powerful tool for exploring linear systems.
Gain hands-on experience with the matrix exponential in a familiar setting.
What do you do when you just don't have enough eigenvectors?
Practice your linear systems skills on a mind-altering robot sociology problem.
Make an atom smasher by combining physics with systems of equations.
Make a master formula for linear systems and complete your cyclotron.
Strengthen your grasp on linear systems while learning how medical NMRI works.
The workhorse of physics, engineering, and applied mathematics.
Uncover the deep connection between higher-order equations and systems.
Find out what second-order equations can do for electrical engineers.
Reach beyond second-order and uncover a master formula with the Wronskian matrix.
Solve a structural engineering problem with a third-order equation.
Can a building withstand an earthquake? Find out with fourth-order equations!
Retrieve a treasure from the briny depths with a third-order equation.
Answer a very common science question by applying the perturbation method.