## 1/f Noise, Modelling planets - Paul Bourke

Introduction: Course outline, relevance to modern engineering activities in everyday life and in technology; Structured fluids and their flow characteristics including non-Newtonian features and their measurement in simple shear, oscillatory shear and elongation flow; Constitutive equations; Conservation equations (Mass, Momentum, Energy); Simple model flows with and without heat transfer; Melting and mixing of polymers; Polymer forming processes – extrusion, calendaring, coating, fiber spinning.

Vectors and tensor analysis: review of vector algebra and calculus, tensors w.r.t. to general linear homogeneous transformations, tensors in 4-dimensional space time; Matrices and linear vector spaces: vector spaces, eigenvalues and eigenvectors, diagonalization and triangularization of matrices, orthogonal transformations and rotations; Complex analysis: analytic functions, power series, complex integration, Cauchy's theorem, Taylor and Laurent series, Jordan's lemma, analytic continuation, method of steepest descent, Gamma functions; Calculus of variation: functionals and functional derivatives, extremization problem involving functions, Euler equations ; Ordinary differential equations and special functions: Linear differential equations (first and second order), power series method; Integral transforms and Generalized functions: Fourier and Laplace transforms, applications of integral transforms, Generalized functions: Dirac delta function, generalized eigenfunction expansion; Partial differential equations (PDE's) : Some important PDE's, solution using separation of variables, types of PDE's and boundary conditions; Green's functions: ordinary and partial differential operators, Solutions of boundary value problems using Green's function; Group theory: representation of group, symmetry and degeneracy, Lie groups and Lie algebra, Unitary and Orthogonal groups and their representations .

## Courses of Study | IIT Gandhinagar

Computational physics and science, algorithms; Representation of numbers, machine precision, series summation; Errors, uncertainties, round offs, recursion relations method; Visualization of data; Non-thermal Monte Carlo techniques, random numbers and sequences, random walk problems, application to radio-active decay; Numerical Integration and Differentiation, Higher Dimensional Integration, Quantum Monte-Carlo methods; Function optimization, steepest descent, conjugate gradient, Golden ratio search, Variational Methods in Quantum mechanics; Matrix computing, system of equations, eigenvalue problems, large matrices, linear algebra packages; Data fitting: Lagrange interpolation, cubic splines, least-squares method, singular value decomposition; Ordinary differential equations: Euler's rule, Runge-Kutta methods, solving for equations of motion, non-linear oscillations with and without forcing, precision considerations, energy and momentum conservations; Quantum eigenvalue problem for a particle in a box; Time series analysis in Physics, Fourier analysis, discrete Fourier transforms, sampling and aliasing effects, Fast Fourier Transforms; Molecular Dynamics, non-interacting gas in a box, extracting thermodynamic variables from simulations; Introduction to high-performance computing hardware and parallel computing: distributed memory programming, parallelizing strategy, high level view of message passing, high throughput computing models.

## Electrical & Systems Engineering | Washington …

Conservation of mass, momentum and balance of energy in differential and integral forms; Forced convection external flows, boundary layer equations: differential and integral techniques; high speed flows; internal flows; developing and fully developed flows; natural convection, boiling and condensation

## Engineering Courses - Concordia University

Prandtl and Nusselt number correlations; Derivation of differential and integral energy equation. Thermal boundary layer; Analogy between heat and momentum transfer. ; Heat transfer in pipe flows; Thermal entry length; Correlations for some common configurations; Free convection from plate: Governing equations and non-dimensionalization. Similarity and integral solutions for vertical plate; Free convection for other cases; Mixed convection. Heat Exchangers. Applications and classification of heat exchangers; Design analysis using LMTD method; Performance analysis using - NTU method. Introduction to boiling and condensation;

## Kuwait Journal of Science - Kuwait University

Review of Linear Algebra: Vector spaces, linear transformations, eigenvalues and eigenvectors, diagonalization; Inner product spaces, Gram-Schmidt orthonormalization, spectral theorem for real symmetric matrices. Systems of ODEs: Homogeneous and nonhomogeneous linear systems; Eigenvalue method. Nonlinear systems: qualitative approach; linearization. Series solutions of differential equations: Frobenius method, equations of Legendre and Bessel. Sturm-Liouville problems: orthogonality of eigenfunctions and eigenfunction expansions. Fourier series, Fourier integrals and Fourier transforms: basic results. Partial Differential Equations: Classification of linear second order PDEs in two variables; Modeling: vibrating string, heat conduction; solutions using Fourier series, Fourier integrals and Fourier transforms.