In this week’s installment we will once again try to unify many different concepts. Our mission (should we choose to accept it!) is to first develop the fundamental notions of a branch of math called Complex Analysis. While it can be a difficult topic to wrap one’s head around, it is incredibly powerful. After all, there is a saying among mathematicians that the shortest path … [Read more...] about Joukowski Airfoils: Where Complex Analysis Meets Aerospace Engineering
Derivatives are Opposite to Boundaries: The Generalized Stoke’s Theorem and its Applications in Physics and Aerospace Engineering
I hope all of my readers are doing well as midterm season approaches. In this week’s blog post, I will try to cover a lot of information in a short amount of space. First, I will be building up intuition for a math formula that has staggering importance. This formula is called the Generalized Stoke’s Theorem, and very well may be my favorite piece of math. Then, I will explore … [Read more...] about Derivatives are Opposite to Boundaries: The Generalized Stoke’s Theorem and its Applications in Physics and Aerospace Engineering
The Mathematics of Aerospace Engineering: Part 3 (Sequences, Series, & Taylor Polynomials)
In this week’s blog post, we continue our discussion of the mathematics of aerospace engineering (and all engineering fields in general). We will combine fundamental concepts in differential calculus with mathematical structures called sequences and series to create nice functions that can allow engineers and mathematicians to approximate the values of weird and wonky … [Read more...] about The Mathematics of Aerospace Engineering: Part 3 (Sequences, Series, & Taylor Polynomials)
The Mathematics of Aerospace Engineering: Part 2 (Multivariable Calculus & Intro to Partial Differential Equations)
Having studied math for more than fifteen years, one fact I have learned is that there is always more math to learn. In the case of aerospace engineering (and all other engineering disciplines), there is some really useful and interesting math that goes beyond single-variable calculus and ordinary differential equations. In this post, we will explore this new, difficult, and … [Read more...] about The Mathematics of Aerospace Engineering: Part 2 (Multivariable Calculus & Intro to Partial Differential Equations)
Ramjets, Scramjets, and Propulsion for High-Speed Flight
I hope that my readers had an amazing summer, and I look forward to discussing more aerospace engineering topics this fall. In this week’s blog post, I will explore a topic that I began to research this June: propulsion mechanisms for high-speed aircraft. In particular, we will explore ramjets and scramjets, which can propel aircraft and missiles into the hypersonic regime, or … [Read more...] about Ramjets, Scramjets, and Propulsion for High-Speed Flight