Modern Engineering Mathematics

Content: Table of ContentsChapter 1: Numbers, Algebra and Geometry1.1    Introduction1.2    Number and arithmetic1.3    Algebra1.4    Geometry1.5    Numbers and accuracy1.6    Engineering applications1.7    Review exercises Chapter 2: Functions2.1    Introduction2.2    Basic definitions2.3    Linear and quadratic functions2.4    Polynomial functions2.5    Rational functions2.6    Circular functions2.7    Exponential, logarithmic and hyperbolic functions2.8    Irrational functions2.9    Numerical evaluation of functions2.10    Engineering application: a design problem2.11    Review exercises Chapter 3: Complex Numbers3.1    Introduction3.2    Properties3.3    Powers of complex numbers3.4    Loci in the complex plane3.5    Functions of a complex variable3.6    Engineering application: alternating currents in electrical networks3.7    Review exercises Chapter 4: Vector Algebra4.1    Introduction4.2    Basic definitions and results4.3    The vector treatment of the geometry of lines and planes4.4    Engineering application: spin-dryer suspension4.5    Engineering application: cable stayed bridge4.6    Review exercises Chapter 5: Matrix Algebra5.1    Introduction5.2    Definitions and properties5.3    Determinants5.4    The inverse matrix5.5    Linear equations5.6    Rank5.7    The eigenvalue problem5.8    Engineering application: spring systems5.9    Engineering application: steady heat transfer through composite materials5.10    Review exercises  Chapter 6: An Introduction to Discrete Mathematics6.1    Introduction6.2    Set theory6.3    Switching and logic circuits6.4    Propositional logic and methods of proof6.5    Engineering application: expert systems6.6    Engineering application: control6.7    Review exercises Chapter 7: Sequences, Series and Limits7.1    Introduction7.2    Sequences and series7.3    Finite sequences and series7.4    Recurrence relations7.5    Limit of a sequence7.6    Infinite series7.7    Power series7.8    Functions of a real variable7.9    Continuity of functions of a real variable7.10    Engineering application: insulator chain7.11    Engineering application: approximating functions and Pade approximants7.12    Review exercises Chapter 8: Differentiation and Integration8.1    Introduction8.2    Differentiation8.3    Techniques of differentiation8.4 Higher derivatives8.5    Applications of optimization problems8.6    Numerical differentiation8.7    Integration8.8    Techniques of integration8.9    Applications of integration8.10    Numerical evaluation of integrals8.11    Engineering application: design of prismatic channels8.12    Engineering application: harmonic analysis of periodic functions8.13    Review exercises Chapter 9: Further Calculus9.1    Introduction9.2    Improper integrals9.3    Some theorems with applications to numerical methods9.4    Taylor\'s theorem and related results9.5    Calculus of vectors9.6    Functions of several variables9.7    Taylor\'s theorem for functions of two variables9.8    Engineering application: deflection of built-in column9.9    Engineering application: streamlines in fluid dynamics9.10    Review exercises Chapter 10: Introduction to Ordinary Differential Equations10.1    Introduction10.2    Engineering examples10.3    The classification of differential equations10.4    Solving differential equations10.5    First-order ordinary differential equations10.6    Numerical solution of first-order ordinary differential equations10.7    Engineering application: analysis of damper performance10.8    Linear differential equations10.9    Linear constant-coefficient differential equations10.10  Engineering application: second-order linear constant-coefficient differential   equations10.11   Numerical solution of second-and higher-order differential equations10.12   Qualitative analysis of second-order differential equations10.13   Review exercises Chapter 11: Introduction to Laplace Transforms11.1    Introduction11.2    The Laplace transform11.3    Solution of differential equations11.4    Engineering applications: electrical circuits and mechanical vibrations11.5    Review exercises Chapter 12: Introduction to Fourier Series12.1    Introduction12.2    Fourier series expansion12.3    Functions defined over a finite interval12.4    Differentiation and integration of Fourier series12.5    Engineering application: analysis of a slider-crank mechanism12.6    Review exercises Chapter 13: Data Handling and Probability Theory13.1    Introduction13.2    The raw material of statistics13.3    Probabilities of random events13.4    Random variables13.5    Important practical distributions13.6    Engineering application: quality control13.7    Engineering application: clustering of rare events13.8    Review exercises Appendix I Tables Answers to Exercises Index