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Atomic Structure Planck’s quantum theory ‐ wave particle duality ‐ Heisenberg’s principle ‐ Schrodinger wave equation – particle in a box and hydrogen atom ‐ VB and MO theories. Spectroscopy Ro tat i o n a l and vi brat ional s pectra ‐ harmonic anharmonic oscillator and Rigid Rotor ‐ selection rules ‐ fundamentals, overtones [...]
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ENGINEERING MATHEMATICS Linear Algebra Matrix algebra, Systems of linear equations, Eigen values and eigenvectors. Calculus Functions of single variable, Limit, continuity and differentiability, Mean value theorems, Evaluation of definite and improper integrals, Partial derivatives, Total derivative, Maxima and minima, Gradient, Divergence and Curl, Vector identities, Directional derivatives, Line, Surface and Volume integrals, Stokes, Gauss and [...]
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Engineering Mathematics Mathematical Logic: Syntax of First Order Logic, Semantics of First Order Logic, a Sequent Calculus, the Completeness Theorem, the Limitations of First Order Logic. Differential and Integral Calculus : Limit, Continuity, Differentiability, Leibniz theorem, Mean Value Theorems, Taylor’s theorem, Integrals, Improper integrals, Total Differentiation, Partial derivatives ,Maxima and Minima, vector calculus, Linear differential [...]
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Laws of thermodynamics ‐ reversible nad irreversible process ‐ concept of ideal gas and real gas ‐ equations of states ‐ Maxwell relations ‐ adiabatic and isothermal compression ‐ phase equilibrium ‐ Gibbs phase rule ‐ system of variable composition ‐ vant Hoffs equation ‐ applications of Gibbs ‐ Duhem equation. Law of conservation of [...]
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ENGINEERING MATHEMATICS Linear Algebra: Matrix Algebra, Systems of linear equations, Eigen values and eigen vectors. Calculus: Mean value theorems, Theorems of integral calculus, Evaluation of definite and improper integrals, Partial Derivatives, Maxima and minima, Multiple integrals, Fourier series. Vector identities, Directional derivatives, Line, Surface and Volume integrals, Stokes, Gauss and Green’s theorems. Differential equations: First [...]
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ENGINEERING MATHEMATICS Linear Algebra: Matrix Algebra, Systems of linear equations, Eigen values and eigen vectors. Calculus: Mean value theorems, Theorems of integral calculus, Evaluation of definite and improper integrals, Partial Derivatives, Maxima and minima, Multiple integrals, Fourier series. Vector identities, Directional derivatives, Line, Surface and Volume integrals, Stokes, Gauss and Green’s theorems. Differential equations: First [...]
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ENGINEERING MATHEMATICS Linear Algebra: Matrix Algebra, Systems of linear equations, Eigen values and eigen vectors. Calculus: Mean value theorems, Theorems of integral calculus, Evaluation of definite and improper integrals, Partial Derivatives, Maxima and minima, Multiple integrals, Fourier series. Vector identities, Directional derivatives, Line, Surface and Volume integrals, Stokes, Gauss and Green’s theorems. Differential equations: First [...]
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Biophysics Levels of structures in Biological macromolecules. Basic strategies in biophysics. Forces that determine protein and nucleic acid structure, Prediction of proteins structure nucleic acids, Properties of lipid bilayers, Biochemical Kinetics studies, unimolecular reactions, methods of determining macromolecular structures inclusive of the spectroscopic techniques like UV‐vis abs o rp tion, IR absorption, circular dichro ism [...]
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MATHEMATICAL FUNDAMENTALS Engineering Mathematics Geometry Equations of straight line, common normal between straight lines in space; Equations of circles, ellipse, etc.; Parametric representation. Linear Algebra Matrix algebra, Systems of linear equations, Eigen values and eigenvectors. Calculus Functions of single variable, Limit, continuity and differentiability, Mean value theorems, Evaluation of definite and improper integrals, Partial derivatives, [...]
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Quantum Physics: Basis of Quantum Physics, de Broglie’s concept, operators, physical imperfection of wave function, normalised and orthogonal wave function, Heisenberg’s uncertainty Principle. Solid State Physics: Crystal structure, Bravais lattices and its basis, Miller indices, X‐ray diffraction and Bragg’s law, free electron theory of metals. Fermi energy and density of states, origin of energy bands, concept of holes [...]
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