This course is based on the book entitled “Basic Training in Mathematics” written by Prof. R. Shankar at Yale. The course is designed in response to the frequent need of materials science and engineering (MSE) students to apply basic math to their own research. The course covers fundamental topics in calculus, power series, and differential equations. It presents each topic in its simplest form but ensures a thorough treatment, allowing MSE students—and anyone in the physical sciences—to build a strong mathematical foundation.

Intended as a 6-week undergraduate-graduate course, the course offers an approach that MSE department might consider to better prepare students for advanced science studies. It is structured for self-study, addressing common student questions directly, making it a resource for both structured and independent learning. This early investment in mathematical preparation helps foster success in the materials science and engineering, where proficiency in mathematics can significantly impact future achievements.