Complete Guide to Differential Equations Foundations for Data Science

This course covers the essentials of differential equations, focusing on different orders and linearity along with other common topics. With practical explanations and examples, instructor Megan Silvey guides you through the core concepts and skills required to work with first-, second-, and higher-order differential equations—just like a traditional university-level course. Along the way, develop a thorough understanding of complex differential equations such as nonlinear and partial differential equations. By the end of this course, you’ll also be prepared to navigate other key differential equations topics including series, systems, Laplace transforms, numerical methods, and boundary value problems.

Learning objectives
Classify different types of differential equations—ordinary and partial, linear and nonlinear, first-order and higher-order—and solve first-order differential equations using various methods such as separation of variables, integrating factors, and substitutions.
Demonstrate proficiency in solving second-order and higher-order linear differential equations, both homogeneous and nonhomogeneous, using techniques such as the characteristic equation, reduction of order, undetermined coefficients, and variation of parameters.
Apply the Laplace transform to solve differential equations and initial value problems, including those involving step functions, impulse functions, and convolution integrals.
Analyze and solve systems of differential equations using matrix methods, undetermined coefficients, and variation of parameters, and apply these skills to model real-world phenomena such as predator-prey relationships.
Solve basic partial differential equations using separation of variables and apply this knowledge to specific equations such as the heat equation, wave equation, and Laplace's equation.