Higher Engineering Mathematics, 7th Edition

A practical introduction to the core mathematics principles required at higher engineering level

John Bird’s approach to mathematics, based on numerous worked examples and interactive problems, is ideal for vocational students that require an advanced textbook.

Theory is kept to a minimum, with the emphasis firmly placed on problem-solving skills, making this a thoroughly practical introduction to the advanced mathematics engineering that students need to master. The extensive and thorough topic coverage makes this an ideal text for upper level vocational courses.

Now in its seventh edition, Engineering Mathematics has helped thousands of students to succeed in their exams. The new edition includes a section at the start of each chapter to explain why the content is important and how it relates to real life. It is also supported by a fully updated companion website with resources for both students and lecturers. It has full solutions to all 1900 further questions contained in the 269 practice exercises.

Table of Contents

Section A: Number and algebra
Chapter 1. Algebra
Chapter 2. Partial fractions
Chapter 3. Logarithms
Chapter 4. Exponential functions
Chapter 5. Inequalities
Chapter 6. Arithmetic and geometric progressions
Chapter 7. The binomial series
Chapter 8. Maclaurin’s series
Chapter 9. Solving equations by iterative methods
Chapter 10. Binary, octal and hexadecimal numbers
Chapter 11. Boolean algebra and logic circuits

Section B: Geometry and trigonometry
Chapter 12. Introduction to trigonometry
Chapter 13. Cartesian and polar co-ordinates
Chapter 14. The circle and its properties
Chapter 15. Trigonometric waveforms
Chapter 16. Hyperbolic functions
Chapter 17. Trigonometric identities and equations
Chapter 18. The relationship between trigonometric and hyperbolic functions
Chapter 19. Compound angles

Section C: Graphs
Chapter 20. Functions and their curves
Chapter 21. Irregular areas, volumes and mean values of waveforms

Section D: Complex numbers
Chapter 22. Complex numbers
Chapter 23. De Moivre’s theorem

Section E: Matrices and determinants
Chapter 24. The theory of matrices and determinants
Chapter 25. Applications of matrices and determinants

Section F: Vector geometry
Chapter 26. Vectors
Chapter 27. Methods of adding alternating waveforms
Chapter 28. Scalar and vector products

Section G: Differential calculus
Chapter 29. Methods of differentiation
Chapter 30. Some applications of differentiation
Chapter 31. Differentiation of parametric equations
Chapter 32. Differentiation of implicit functions
Chapter 33. Logarithmic differentiation
Chapter 34. Differentiation of hyperbolic functions
Chapter 35. Differentiation of inverse trigonometric and hyperbolic functions
Chapter 36. Partial differentiation
Chapter 37. Total differential, rates of change and small changes
Chapter 38. Maxima, minima and saddle points for functions of two variables

Section H: Integral calculus
Chapter 39. Standard integration
Chapter 40. Some applications of integration
Chapter 41. Integration using algebraic substitutions
Chapter 42. Integration using trigonometric and hyperbolic substitutions
Chapter 43. Integration using partial fractions
Chapter 44. The t=tan θ/2 substitution
Chapter 45. Integration by parts
Chapter 46. Reduction formulae
Chapter 47. Double and triple integrals
Chapter 48. Numerical integration

Section I: Differential equations
Chapter 49. Solution of first-order differential equations by separation of variables
Chapter 50. Homogeneous first-order differential equations
Chapter 51. Linear first-order differential equations
Chapter 52. Numerical methods for first-order differential equations
Chapter 53. Second-order differential equations of the form a d2y/dx2 +b dy/dx + cy=0
Chapter 54. Second-order differential equations of the form a d2y/dx2 + b dy/dx + cy= f(x)
Chapter 55. Power series methods of solving ordinary differential equations
Chapter 56. An introduction to partial differential equations

Section J: Statistics and probability
Chapter 57. Presentation of statistical data
Chapter 58. Mean, median, mode and standard deviation
Chapter 59. Probability
Chapter 60. The binomial and Poisson distributions
Chapter 61. The normal distribution
Chapter 62. Linear correlation
Chapter 63. Linear regression
Chapter 64. Sampling and estimation theories
Chapter 65. Significance testing
Chapter 66. Chi-square and distribution-free tests

Section K: Laplace transforms
Chapter 67. Introduction to Laplace transforms
Chapter 68. Properties of Laplace transforms
Chapter 69. Inverse Laplace transforms
Chapter 70. The Laplace transform of the Heaviside function
Chapter 71. The solution of differential equations using Laplace transforms
Chapter 72. The solution of simultaneous differential equations using Laplace transforms

Section L: Fourier series
Chapter 73. Fourier series for periodic functions of period 2π
Chapter 74. Fourier series for a non-periodic function over range 2π
Chapter 75. Even and odd functions and half-range Fourier series
Chapter 76. Fourier series over any range
Chapter 77. A numerical method of harmonic analysis
Chapter 78. The complex or exponential form of a Fourier series