Abstract: 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.
Publication Year: 1977
Publication Date: 1977-05-25
Language: en
Type: book
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Cited By Count: 51
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