Along with the version of Lyman Porter and Edward Lawler, Vroom's formulation is generally considered as representing major contributions to expectancy theory, having stood the test of time and historical scrutiny. In this theory, he suggested that motivation is largely influenced by the combination of a person's belief that effort leads to performance, which then leads to specific outcomes, and that such outcomes are valued by the individual. His most well-known books are Work and Motivation, Leadership and Decision Making and The New Leadership. Reed, Applied Mathematics in Chemical Engineering, McGraw–Hill, 1957.Vroom's primary research was on the expectancy theory of motivation, which attempts to explain why individuals choose to follow certain courses of action and prefer certain goals or outcomes over others in organizations, particularly in decision-making and leadership. Naylor, Differential Equations of Applied Mathematics, Wiley, 1966. Collins, Mathematical Methods for Physicists and Engineers, Reinhold, 1968. Stakgold, Green’s Functions and Boundary Value Problems, Wiley, 1998. Sagan, Boundary and Eigenvalue Problems in Mathematical Physics, Dover, 2012. Orszag, Advanced Mathematical Methods for Scientists and Engineers, McGraw–Hill, 1984. Keener, Principles of Applied Mathematics, Addison–Wesley, 1988. Kreyszig, Advanced Engineering Mathematics, Wiley, 1983. Amundson, Linear Operator Methods in Chemical Engineering with Applications to Transport and Chemical Reaction Systems, Prentice Hall, 1985. Amundson, First Order Partial Differential Equations, Volume I, Prentice Hall, 1986. Murfphy, The Mathematics of Physics and Chemistry, Van Nostrand, 1943. Crank, The Mathematics of Diffusion, Oxford University Press, 1956. Jeffreys, Mathematical Methods in Chemical Engineering, Academic Press, 1977. Amundson, Mathematical Methods in Chemical Engineering: Matrices and their Applications, Prentice Hall, 1966. Strang, Introduction to Applied Mathematics, Wellesley–Cambridge Press, 1986. Numerous examples and applications will be the core of the course. That is, it will emphasize the mathematical interpretation and the corresponding formulation of the relative physical phenomena, avoiding any rigorous mathematical analysis.
The course will be adapted to the engineering point of view. Prerequisite for this course is knowledge of Advanced Calculus, Matrix Theory, Linear Algebraic Systems and Ordinary Differential Equations. Main characteristics of vibration, radiation, wave propagation and scattering problems. Wave Theory: Modeling the physical behavior of initial and boundary value problems governed by hyperbolic equations.Solutions of transient diffusion problems. Fundamental solution and infinite speed of propagation. Diffusion Theory: Mathematical characteristics of non–invertible physical phenomena governed by parabolic equations.Stokes Flow: The mathematical peculiarities of elliptic equations of the fourth order.Solution of inviscid flow and steady state problems. Potential Theory: Modeling of time invariant physical problems in isotropic and anisotropic spaces.Green’s Functions: The fundamental solutions of partial differential equations.Examples from chemical engineering problems. Partial Differential Equations: The methods of characteristics.Introduction to Perturbation Theory: Regular and singular perturbation theory, inner and outer solutions.Diagonal representations and Jordan canonical forms. Generalized eigenvectors and eigenspaces. Spectral Theory: Characteristic quantities, algebraic and geometric multiplicity of eigenvalues, direct sum decomposition of vector spaces and of linear operators.Kernel and range spaces, rank, nullity and invertibility. Linear Operators: Matrix representation, similarity, change of bases.Structure of Vector Spaces: Subspaces, generating systems, span, linear independence, bases, dimension, codimension.
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