Introducing engineering students to numerical analysis and computing, this book covers a range of topics suitable for the first three years of a four year undergraduate engineering degree. The teaching of computing to engineers is hampered by the lack of suitable problems for the students to tackle, so much effort has gone into making the problems in this book realistic and relevant, while at the same time solvable for undergraduates.
Taking a balanced approach to teaching computing and computer methods at the same time, this book satisfies the need to be able to use computers (using both formal languages such as Fortran and other applications such as Matlab and Microsoft Excel), and the need to be able to solve realistic engineering problems.
David Walker, Michael Leonard and Martin Lambert are in the School of Civil, Environmental and Mining Engineering, and Andrew Metcalfe is in the School of Mathematical Sciences, all at the University of Adelaide, Australia. They are all active in teaching and research and the content of the book reflects a strong belief that the one should complement the other.
1 Introduction to Engineering Modelling and Analysis 2 Introduction to Computing Tools - Fortran, Pascal, Basic, and C 3 Introduction to Computing Tools - Spreadsheets 4 Introduction to Computing Tools - Matlab 5 Fortran 90/95 - Basic Concepts, Input and Output 6 Fortran 90/95 - Control Structures and Data Storage 7 Fortran 90/95 - Common Tasks 8 Roots of Equations - Introduction 9 Roots of Equations - Bracket Methods 10 Roots of Equations - Open Methods 11 Numerical Integration - Trapezoidal Rule 12 Numerical Integration - Simpson's Rules 13 Numerical Interpolation - Newton's Method 14 Numerical Interpolation - Polynomial Methods 15 Numerical Interpolation - Splines 16 Systems of Linear Equations - Introduction 17 Systems of Linear Equations - Gauss-Jordan and Gauss-Seidel Methods 18 Systems of Linear Equations - Thomas Algorithm 19 Numerical Solution of Ordinary Differential Equations - Introduction 20 Numerical Solution of Ordinary Differential Equations - Euler and Runge-Kutta Methods 21 Finite Difference Modelling - Introduction 22 Finite Difference Modelling - LaPlace's Equation Solutions 23 Finite Difference Modelling - Solution of Pure Convection 24 Finite Difference Modelling - Solution of Pure Diffusion 25 Finite Difference Modelling - Solution of Transport Equation 26 Finite Difference Modelling - Alternate Schemes 27 Probability Distributions - Introduction 28 Probability Distributions - The Normal and Lognormal Distributions 29 Probability Distributions - The Binomial Distribution and Return Periods 30 Probability Distributions - The Poisson Distribution 31 Probability Distributions - Testing Distributions using Probability Paper 32 Probability Distributions - Testing Distributions using Chi2 Test 33 Random Numbers - Theory and Generation 34 Monte Carlo - Introduction 35 Monte Carlo - Applications 36 Resonance 37 Spectral Analysis - Basic Concepts 38 Spectral Analysis - Discrete Fourier Transform 39 Spectral Analysis - Application of the Fast Fourier Transform 40 Spectral Analysis - Practical Aspects of Data Collection and Analysis 41 Linear Regression and Correlation 42 Parameter Estimation 43 Assorted Topics - The Error Function 44 Assorted Topics - Taylor Series 45 Assorted Topics - Complex Representation of Periodic Functions 46 Solutions to Selected Problems