Mathematics for Engineers

Citation

Croft, A., & Davison, R. (2025). Mathematics for Engineers (6th ed.). Pearson.

Chapter Summary

The sixth edition is listed by Pearson with twenty-four chapters, the same sequence of topics as the fifth edition: arithmetic and algebra first, then functions, trigonometry, complex numbers, matrices and vectors, calculus, differential equations and transforms. Pearson describes it as a practical, informal and accessible text that covers all the requirements of a first-year engineering mathematics course, together with introductory material for more advanced topics, and that combines traditional learning methods with interactive examples in which the reader takes part in the calculations.

Chapters 1–4: Arithmetic; Fractions; Decimal numbers; Percentage and ratio

The foundation chapters, giving a base in number work so that the book can be started by students whose arithmetic needs revision.

Chapters 5–8: Basic algebra; Functions and mathematical models; Polynomial equations, inequalities, partial fractions and proportionality; Logarithms and exponentials

Algebra and the idea of a function, presented together with mathematical models. Chapter 7 gathers techniques for polynomial equations, inequalities, partial fractions and proportionality, and Chapter 8 introduces logarithms and exponential functions.

Chapters 9–10: Trigonometry; Further trigonometry

Trigonometry takes two chapters, an introductory one and one of further trigonometry, before complex numbers and calculus make use of it.

Chapter 11: Complex numbers

Complex numbers are covered in a single chapter, placed before matrices and calculus.

Chapters 12–14: Matrices and determinants; Using matrices and determinants to solve equations; Vectors

Matrix and determinant algebra, a separate chapter on solving systems of equations with them, and a chapter on vectors.

Chapters 15–18: Differentiation; Techniques and applications of differentiation; Integration; Applications of integration

The calculus core: differentiation and integration each have an introductory chapter and a chapter on techniques and applications.

Chapters 19–21: Sequences and series; Differential equations; Functions of more than one variable and partial differentiation

Sequences and series, then differential equations, then calculus of several variables with partial derivatives.

Chapters 22–24: The Laplace transform; Statistics and probability; An introduction to Fourier series and the Fourier transform

The closing chapters introduce the Laplace transform, statistics and probability, and, as the title signals, Fourier series and the Fourier transform.

Key Concepts

Chapters 1–10: Foundations

• Functions and mathematical models: functions used to describe engineering quantities.
• Partial fractions, inequalities and proportionality: the algebraic toolkit of Chapter 7.
• Logarithms and exponentials: the functions behind growth, decay and many engineering relationships.

Chapters 11–14: Complex numbers, matrices and vectors

• Complex numbers: numbers with real and imaginary parts.
• Matrices and determinants: representing and solving systems of linear equations.
• Vectors: quantities with magnitude and direction.

Chapters 15–24: Calculus and further methods

• Differentiation and integration: single-variable calculus with techniques and applications.
• Differential equations and partial differentiation: equations linking a function to its derivatives, and rates of change of functions of several variables.
• Laplace and Fourier transforms: methods introduced at the end for later engineering courses.

Critical Analysis

Strengths

• One book from arithmetic to transforms. The contents run from fractions and decimals to Laplace transforms and Fourier series, so a single text can support students with a weak start and carry them through a first-year syllabus.
• Gentle ordering of prerequisites. Algebra and functions precede trigonometry, complex numbers and matrices, which precede calculus, differential equations and transforms; each block rests on the one before it.
• Calculus given room. Differentiation and integration each take two chapters, one introductory and one on techniques and applications.
• Interactive examples. Pearson describes examples that invite the reader to participate in the calculations, which suits independent study.

Limitations

• Introductions at the top end. Fourier series and the Fourier transform appear in a single closing chapter, so students who need them in depth will need a second-level text.
• Single chapters for large topics. Sequences and series, and statistics and probability, each receive one chapter; modules treating these in depth need further material.
• Edition identification. Print, eText and regional editions carry different ISBNs and dates, so the edition named on a course list should be checked against the chapter list above.

Where It Fits in the Course

Croft and Davison is one of the two first-year books in the engineering mathematics list. Stroud and Booth's Engineering Mathematics covers a similar syllabus through a programmed, self-paced format in which the reader completes each step before moving on. Croft and Davison is written in conventional chapters with worked examples, and it goes further at the end with an introduction to Fourier series and transforms. Students who want to be led line by line may find Stroud easier; those who prefer reading an explanation and then practising are better served here. Using both is reasonable, with Stroud's frames for extra practice on any topic that moves too fast.

The other books belong to later stages. Glyn James's Advanced Modern Engineering Mathematics is the second-level British text that takes matrix methods, transforms, vector calculus and complex variables further, the natural next step after Chapters 11–24. Kreyszig's Advanced Engineering Mathematics is a broad reference of applied mathematics, Riley, Hobson and Bence's Mathematical Methods for Physics and Engineering is a large reference for physical sciences and engineering, and Bender and Orszag's book on asymptotic and perturbation methods is a graduate text.

How to Use This Book

The book is aimed at first-year engineering students. School mathematics is enough to start, since the opening chapters revise arithmetic and algebra.

• Foundation (as needed): Chapters 1–10. Students with a solid background can skim Chapters 1–4 and test themselves on Chapters 5–10; those whose algebra or trigonometry is weak should work through them carefully, because every later chapter depends on them.
• Core first-year course: Chapters 11–21, covering complex numbers, matrices, vectors, differentiation and integration, series, differential equations and partial differentiation.
• By syllabus: Chapters 22–24 on the Laplace transform, statistics and probability, and Fourier methods. Many modules cover only some of these.

Work through the interactive examples with pen and paper before reading each solution, and do the exercises regularly rather than saving them for revision.