Everyday Engineering Examples
Eigenvalue equation and principle axis transformation, normal coordinates, forced oscillations and resonance, vibrations of molecules. Nonlinear oscillations and chaos. Motion in a central field. Equivalent one-body problem. Symmetries and conservations laws. Central forces in three dimensions.
Scattering in a central force field, Rutherford scattering. Rigid bodies. Orthogonal transformations, Euler angles, rigid body dynamics, spinning top. Recommended Reading H. Goldstein, C. Poole and J. Safko, Classical mechanics , 03rd edition, Addison-Wesley Landau and E. Lifshitz, Mechanics , 03rd edition, Butterworth Heinemann Rana and P. Arnold, V.
Mechanical Engineering - Introduction to Statics and Dynamics - Problem Book | Mechanics | Pendulum
Kozlov and A. Neishtadt, Mathematical aspects of classical and celestial mechanics , 03rd edition, Springer Jose and E. Saletan, Classical dynamics: a contemporary approach , Cambridge University Press Hilbert Spaces, Operators. Position, Momentum and Translation. Eigenvalue Problems. Emphasis on Linear Vector Spaces from a mathematical point of view.
Time Evolution Quantum Dynamics. Quantum Particles in Potential. Harmonic oscillator. Angular Momentum. Rotation in Quantum mechanics. Spherical Harmonics. Addition of Angular Momenta. Recommended Reading L.
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Sakurai, Modern quantum mechanics , Addison-Wesley Bjorken and S. Drell, Relativistic quantum mechanics , McGrawHill Shankar, Principles of quantum mechanics , 02nd edition, Springer Greiner and B. Muller, Quantum mechanics - Symmetries , 02nd edition, Springer Boundary value problems. Method of images. Eigenfunction expansions.
Series solution of PDE. Laplace equation in spherical and cylindrical coordinates.
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Special functions. Legendre polynomials, Associated Legendre functions and Spherical harmonics, Bessel functions. Multipole expansion. Electric fields in dielectrics.
Boundary value problems in dielectrics. Biot and Savart Law. Magnetic field in matter. Boundary conditions. B and H fields. Energy in the magnetic field. Maxwell equations. Displacement current. Scalar and vector potentials. Gauge transformations. Electromagnetic waves. Pointing vector. Electromagnetic waves in media. Relativistic formulation of electromagnetism.
Dipole radiation. Fields or moving charges. Retarded potentials. Recommended Reading J. Lifshitz, The Classical theory of fields , 04th edition, Pergamon Press Panofsky and M. Phillips, Classical electricity and magnetism , 02nd edition, Dover Publications Schwinger, L.
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DeRaad Jr. Milton, and W-Y. Greiner and J.
Reinhardt, Quantum electrodynamics , 04th edition, Springer Review of probability: one random variable, probability distributions, random walks, many random variables, central limit theorem, information, entropy and estimation. Recommended Reading K. Huang, Statistical Mechanics , 02nd edition, Wiley Lifshitz, Statistical Physics , 03rd edition, Butterworth-Heinemann Greiner, L.
Neise, H. Stocker, and D. Rischke, Thermodynamics and Statistical Mechanics , Springer Ma, Statistical Mechanics , World Scientific Transitions under the action of a perturbation acting for a finite time, Transitions under the action of a periodic perturbation. Review of Hydrogen atom, Fine structure, Hyperfine structure as an application of perturbation theory to real systems. Zeeman effect, Stark effect. The semi-classical approach, WKB approaximation. Penetration through a potential barrier. The variational principle, applications.
Scattering theory: Scattering cross-section, partial waves, Yukawa and Coulomb potentials, scattering by square well potential, reaction rates, mean free path, retarded potentials, Born approximation. Relativistic quantum mechanics: Klein-Gordon equation, negative probabilities. Dirac equation, relativistic free particle solutions, negative energy solutions, anti-particles. Recommended Reading B. Bransden and C. Atkins and J. Rajam, Atomic Physics , S. Calculus of residues, Dispersion relations, method of steepest descent.
Gamma and Beta functions: Gamma function, definition and properties, Stirlings series, Beta function, Incomplete Gamma function. Differential equations: Partial differential equations, First order differential equations, separation of variables, singular points, series solutions with Frobenius method, a second solution, nonhomogenneous equations, Greens function, Heat flow and diffusion equations.