## Introduction

Engineering Mathematics I by Sergei Silvestrov & Milica Rancic is an essential textbook for students studying mathematics at an introductory level in engineering programs. This book covers the fundamental concepts of mathematics necessary for engineering students, including calculus, linear algebra, and ordinary differential equations. In this review, we will analyze the content of the book and its effectiveness in teaching engineering mathematics.

## Content

The book is divided into nine chapters, each covering a different topic in mathematics. The first two chapters introduce the basics of functions, limits, and continuity, as well as derivatives and their applications. The authors provide numerous examples and exercises to help students grasp the concepts covered in these chapters.

Chapters three and four cover integration and techniques of integration, respectively. The authors present the fundamental theorem of calculus and provide examples on how to use it to evaluate integrals. The chapters also cover substitution, integration by parts, and trigonometric integrals. The authors have provided a good balance between theory and practice, with many solved examples and exercises.

Chapters five and six are dedicate to vectors and matrices, respectively. The authors start with the basics of vectors, including dot and cross products, and then move on to vector functions and their derivatives. In the chapter on matrices, the authors introduce the concept of determinants, matrix algebra, and linear transformations. The authors have provided numerous examples and exercises to help students understand the material.

Chapter seven covers systems of linear equations, including Gaussian elimination and matrix inversion. The authors provide a step-by-step approach to solving systems of linear equations, and they have included many examples and exercises to help students practice. In chapter eight, the authors introduce the concepts of ordinary differential equations and provide an introduction to their solutions. This chapter includes examples and exercises, making it easy for students to understand the subject matter.

The final chapter covers Laplace transforms, which are essential in solving differential equations. The authors have included a detailed explanation of Laplace transforms, including the properties and theorems associated with them. The chapter also includes numerous examples and exercises, which help students to practice applying the concepts presented.

## Effectiveness

The book is well-written and easy to understand, with clear explanations and many examples. The authors have structured the book in a way that makes it easy for students to learn and understand the material. The book is ideal for self-study, with exercises at the end of each chapter that allow students to practice what they have learned.

The authors have also included a chapter on Laplace transforms, which is not always cover in introductory engineering mathematics courses. This inclusion makes the book more comprehensive, and students will find it useful in their future studies.

One area where the book could be improve is in the inclusion of more real-world applications. Although the authors provide many examples, these are mostly abstract, and there are few real-world applications. This limitation may make it difficult for some students to relate to the material, especially those who prefer a more practical approach to learning.

## Conclusion

Engineering Mathematics I by Sergei Silvestrov & Milica Rancic is a comprehensive textbook that covers the fundamental concepts of mathematics necessary for engineering students. The book is well-written, with clear explanations and many examples. The authors have structured the book in a way that makes it easy for students to learn and understand the material, and the exercises at the end of each chapter allow students to practice what they have learned.

Although the book could benefit from more real-world applications, it is an excellent resource for engineering students who want to gain a solid foundation in mathematics. Overall, Engineering Mathematics I is a valuable textbook that will benefit engineering students at an introductory level.