First Course in Engineering Mathematics

Abstract

Pursuing a Bachelor of Engineering at an engineering university can be challenging in the early years, with one barrier being the completion of mathematics courses (Engineering Mathematics). In engineering studies, students cannot ignore learning mathematics, as it will serve as an important tool in the rest of their studies.

Each student has own expectation about learning mathematics and it relies on his/her previous knowledge of mathematics learned at high school, learning culture, and some expectations from teacher. Some students expect from teacher that teacher should explain the problem step-by-step, and should not miss anything assuming that we know it already. Skipping the step could be sometimes hard for students to understand the whole explanation, and this way even easier stuff can be hard or complicated for them.

Engineering mathematics courses often have enrollment numbers in the hundreds, with students from all over the world bringing diverse mathematical backgrounds, learning cultures, and educational experiences. Adapting to a new learning environment and following unfamiliar instructions can be challenging for many of them. Consequently, each student tends to have a personal preference for how they would like to be taught, shaped by their unique prior experiences and learning styles.

With these considerations in mind, we have designed a foundation for engineering mathematics course that serves as a self-study resource for students and will function as a reference manual throughout the term. This course encourages students to independently learn certain concepts and proofs of theorems, fostering self-directed understanding. It is intended to provide a solid base for future engineering mathematics courses. The core topics include functions, trigonometric and hyperbolic functions, coordinate systems, limits, derivatives, integrals, and selected applications of these concepts.

Each topic is presented as simply as possible, including a definition, example, geometric interpretation, and formula derivation. We’ve kept the text concise, understanding that not all students are accustomed to learning independently from books. By studying this book, students will work to understand and grasp concepts on their own, which will help them develop the “learning to learn” skill.

Once student acquire the skill of learning to learn mathematics by reading a book, he/she will be able to teach him/herself in many situations without needing help in the early stages of learning mathematics topics. Reading the mathematical text and learning mathematics from a book is a lifelong skill, and we hope that through this book, students will develop and strengthen this valuable ability.