## Abstract

Mathematics is at the heart of most sub-specializations in engineering (from chemical engineering, civil and mechanical engineering, to electrical and electronic engineering, etc.) and also features significantly in the broader area of STEM (Science, Technology, Engineering and Mathematics) education. Chapter 1 is a foundational topic covering core aspects of engineering mathematics, including differentiation and integration, statistical methods, eigenvector and eigenfunctions and Laplace transforms. This chapter details step-by-step mathematical steps with accompanying visuals (e.g., graphs and diagrams) to guide readers through the solutions to common problems in engineering mathematics, including examples of applied mathematics in practical use-cases such as heat transfer and reaction engineering. This chapter also provides a useful summary of key mathematical formula and methods commonly used to solve engineering problems for one-stop easy reference suitable for both students and educators alike.

## Keywords

Eigenvalue Laplace transform Integration by parts Fourier expansion Characteristic roots Homogeneous ODE Hypothesis test*t*test Exact differential Symmetric matrix