Modern Engineering Mathematics

This book provides a complete course for first-year engineering mathematics. Whichever field of engineering you are studying, you will be most likely to require knowledge of the mathematics presented in this textbook. Taking a thorough approach, the authors put the concepts into an engineering context, so you can understand the relevance of mathematical techniques presented and gain a fuller appreciation of how to draw upon them throughout your studies.Table of Contents Chapter 1: Numbers, Algebra and Geometry 1.1 Introduction 1.2 Number and arithmetic 1.3 Algebra 1.4 Geometry 1.5 Numbers and accuracy 1.6 Engineering applications 1.7 Review exercises Chapter 2: Functions 2.1 Introduction 2.2 Basic definitions 2.3 Linear and quadratic functions 2.4 Polynomial functions 2.5 Rational functions 2.6 Circular functions 2.7 Exponential, logarithmic and hyperbolic functions 2.8 Irrational functions 2.9 Numerical evaluation of functions 2.10 Engineering application: a design problem 2.11 Review exercises Chapter 3: Complex Numbers 3.1 Introduction 3.2 Properties 3.3 Powers of complex numbers 3.4 Loci in the complex plane 3.5 Functions of a complex variable 3.6 Engineering application: alternating currents in electrical networks 3.7 Review exercises Chapter 4: Vector Algebra 4.1 Introduction 4.2 Basic definitions and results 4.3 The vector treatment of the geometry of lines and planes 4.4 Engineering application: spin-dryer suspension 4.5 Engineering application: cable stayed bridge 4.6 Review exercises Chapter 5: Matrix Algebra 5.1 Introduction 5.2 Definitions and properties 5.3 Determinants 5.4 The inverse matrix 5.5 Linear equations 5.6 Rank 5.7 The eigenvalue problem 5.8 Engineering application: spring systems 5.9 Engineering application: steady heat transfer through composite materials 5.10 Review exercises Chapter 6: An Introduction to Discrete Mathematics 6.1 Introduction 6.2 Set theory 6.3 Switching and logic circuits 6.4 Propositional logic and methods of proof 6.5 Engineering application: expert systems 6.6 Engineering application: control 6.7 Review exercises Chapter 7: Sequences, Series and Limits 7.1 Introduction 7.2 Sequences and series 7.3 Finite sequences and series 7.4 Recurrence relations 7.5 Limit of a sequence 7.6 Infinite series 7.7 Power series 7.8 Functions of a real variable 7.9 Continuity of functions of a real variable 7.10 Engineering application: insulator chain 7.11 Engineering application: approximating functions and Pade approximants 7.12 Review exercises Chapter 8: Differentiation and Integration 8.1 Introduction 8.2 Differentiation 8.3 Techniques of differentiation 8.4 Higher derivatives 8.5 Applications of optimization problems 8.6 Numerical differentiation 8.7 Integration 8.8 Techniques of integration 8.9 Applications of integration 8.10 Numerical evaluation of integrals 8.11 Engineering application: design of prismatic channels 8.12 Engineering application: harmonic analysis of periodic functions 8.13 Review exercises Chapter 9: Further Calculus 9.1 Introduction 9.2 Improper integrals 9.3 Some theorems with applications to numerical methods 9.4 Taylor's theorem and related results 9.5 Calculus of vectors 9.6 Functions of several variables 9.7 Taylor's theorem for functions of two variables 9.8 Engineering application: deflection of built-in column 9.9 Engineering application: streamlines in fluid dynamics 9.10 Review exercises Chapter 10: Introduction to Ordinary Differential Equations 10.1 Introduction 10.2 Engineering examples 10.3 The classification of differential equations 10.4 Solving differential equations 10.5 First-order ordinary differential equations 10.6 Numerical solution of first-order ordinary differential equations 10.7 Engineering application: analysis of damper performance 10.8 Linear differential equations 10.9 Linear constant-coefficient differential equations 10.10 Engineering application: second-order linear constant-coefficient differential equations 10.11 Numerical solution of second-and higher-order differential equations 10.12 Qualitative analysis of second-order differential equations 10.13 Review exercises Chapter 11: Introduction to Laplace Transforms 11.1 Introduction 11.2 The Laplace transform 11.3 Solution of differential equations 11.4 Engineering applications: electrical circuits and mechanical vibrations 11.5 Review exercises Chapter 12: Introduction to Fourier Series 12.1 Introduction 12.2 Fourier series expansion 12.3 Functions defined over a finite interval 12.4 Differentiation and integration of Fourier series 12.5 Engineering application: analysis of a slider-crank mechanism 12.6 Review exercises Chapter 13: Data Handling and Probability Theory 13.1 Introduction 13.2 The raw material of statistics 13.3 Probabilities of random events 13.4 Random variables 13.5 Important practical distributions 13.6 Engineering application: quality control 13.7 Engineering application: clustering of rare events 13.8 Review exercises Appendix I Tables Answers to Exercises Index