Formulary for Engineering Mathematics

Abstract

Preface:

Most commonly, engineering students pursuing their bachelor's degree study engineering mathematics courses in their first year of studies. In these courses, students study calculus, algebra, vector analysis, complex analysis, differential equations, numerical methods, Laplace and Fourier transforms, basic statistics, and probability distributions. The number of students in engineering mathematics courses is always huge, and teachers are always asked about the basic material and some lecture notes where students could revise their previous mathematics skills they learned in high school. Before courses start, students are excited and a bit stressed about what new mathematical topics they will be taught and what is the most related background for those topics. To overcome these issues and keep a priority to facilitate the students as much as possible, this formulary is prepared.

This formulary is specially prepared for first-year engineering students, providing a quick overview of the formulas and topics they studied in high school. When the course starts, students will be familiar with the formulas they will be using in their courses. Sometimes, seeing a formula provides motivation to prove it or understand how it came into being. Thus, without asking the teacher, students learn the proofs of these formulas, fostering a culture of learning from each other. Such a culture helps students showcase their talents to others and fosters friendships. Additionally, it serves as a tool to reduce students' stress about passing engineering mathematics courses.

After completing engineering mathematics courses, this formulary can be useful for students' successive studies and can serve as a mathematical tool for their future degree pursuits. While this document doesn't contain all possible mathematics formulas related to the courses mentioned in the beginning, but it covers a significant portion of these courses.

This formulary contains definitions, rules, formulas, observations, and famous theorems. The best way to read this document is to go through each item and make sure you know or understand it. If a formula is new to you, I suggest trying to learn its proof from some source or from the lecture notes provided in each course. In some cases, highlight the item if you think it needs more attention or if you need to work on it for better understanding. If you are unable to learn the concept of a definition or proof of a formula, you are encouraged to ask the teacher or teacher assistant to explain it to you during the course.

I am grateful to Dr. Liyao Xie and Prof. Juho Ratava for their proofreading and comments. Moreover, I am thankful to Prof. Harri Eskelinen for his encouragement, support, and appreciation, which motivated me to write this document.

Barkat Bhayo Lahti, 2024