Advanced Engineering Mathematics

This book is the second in a series and is aimed at second year undergraduate science and engineering students in universities, polytechnics and colleges. It would also be useful for students preparing the engineering council examinations in mathematics at part 2 standard. The present edition differs from its predecessor in the following respects: The text material has been reorganised into eleven chapters instead of the fourteen of the first edition. This reflects the revisions to the material; problem sets appear at the end of each chapter instead of at the end of each section. The problems have been modified and have included more up to date examples from engineering council examinations. The chapter on integral transforms has been extended to meet the needs of electrical engineering applications. There is more material on fourier transforms and the z-transform and discrete fourier transform are introduced; some material on vector field theory has been removed and the surviving subject-matter has been amalgamated with some of the material on integration. Part description.

Table of Contents:
Part 1 Linear algebra: introduction; vector spaces; linear transformations; The solution of simultaneous linear algebraic equations; schems for solution of linear equations; partitioned matrices. Part 2 Eigenvalue problems: algebraic determination of eigenvalues; further results on eigenvalues; quadratic forms and their reduction; boundary-value problems; finding the eigenvalue of largest modulus; determination of other eigenvalues. Part 3 Optimization: linear programming - graphical solution; the simplex algorithm; non-linear optimization; search techniques in one variable; functions of several variables - direct search methods; calculas approach to functions of several variables; methods using the gradient of a function. Part 4 Ordinary differential equations: one-step and multistep methods; predictor-corrector methods; linear difference equations; stability of numerical procedures; case study - surge tank; phase-plane diagrams; boundary-value problems. Part 5 Special functions: a problem in heat transfer; series solution of ordinary differential equations; the gamma function; bessel functions of the first and second kind; modifeied bessel functions; transformations of bessel's equation; an intoduction to legendre polynomials; solution of partial differential equations. Part 6 Fourier series approximations: approximation of a function by a trigonometic series; examples of fourier series; odd and even functions - half-range series; further features of fourier series; trigonometric series approximation of discrete data. Part 7 Partial differential equations: steady state temperature distribution in a plate; some basic ideas; separation of variables method; origin of some partial differential equations; parabolic equations - finite difference methods; elliptic equations. Part 8 Integral transforms: basic results on the laplace transform; finite fourier transforms; infinite fourier transforms; solution of heat conduction equation. Part 9 Integration and vector field theory: scalar and vector fields - differentiation and integration of vectors; the gradient of a scalar field; divergence of a vector field; line integrals; curl of a vector field; vector identities; double integration; further features of double integrals; triple integrals; green's theorem in the plane; surface integral-stokes' theorem; gauss divergence theorem. Part 10 Functions of a complex variable: analytic functions - the cauchy-riemann equations; standard functions of a complex variable; complex potential and conformal mapping; further conformal mappings; complex integrals; taylor and laurent series; the residue theorem; evaluation of real integrals; further applications of contour integration. Part 11 Statistical methods: tests of hypotheses; mean of a small sample - the t test; test of sample variance - the x2 distribution; sample variances - the f test; comparison of sample means; introduction to analaysis of variance; introduction to simple linear regression.