Basic Differential Equations

Differential equations are very important in the mathematical modeling of physical systems. Many fundamental laws of physics and chemistry can be formulated as differential equations. In biology and economics, differential equations are used to model the behavior of complex systems.

For example, in economics, differential equations are used to analyze consumer surplus and producer surplus, and in biology, they are used to analyze the spread of diseases and viruses such as COVID-19. Differential equations are, perhaps, the most utilized mathematical technique to develop models and this course focuses on teaching First-Order Ordinary Differential Equations since they are the most basic form of differential equations to solve. Of course, differential equations do not stop at First-Order.

It goes to second and higher orders, it addresses the LaPlace Transformation and the Fourier Method, and Partial Differential Equations; which are all advanced methods in differential equations. This course has two fundamental purposes. (1) to facilitate the comprehension of the student behind the concept of differential equations, (2) to empower students to possess the necessary skills to solve differential equations of first-order.

For students to be successful in this course, they must, at least, have a strong background in differential calculus and integral calculus. By the end of this course, students must be able to solve the most basic differential equations and apply what they've learned in their respective fields of study.