Kumaun University Phd syllabus

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As you want the syllabus of PhD in Physics of Kumaun University for study so here I am providing you the syllabus below
Kumaun University Syllabus
1. Mathematical Methods of Physics: Vector algebra and vector calculus; matrices, Cayley Hamilton theorem, eigenvalue problems; Linear differential equations; Hermite, Bessel, Laguerre and Legendre; Fourier series, Fourier and Laplace transforms; complex analysis: poles, residues and evaluation of integrals


2. Classical Mechanics: Central-force motion; Two-body collisions, Rigid body dynamics, moment of inertia tensor, Variational principle, Lagrangian and Hamiltonian formalisms and equations of motion; Poisson brackets and canonical transformations, Special theory of relativity, Lorentz Transformations, relativistic kinematics and mass–energy equivalence.


3. Electromagnetic Theory: Gauss’ Law and its applications; Biot-Savart law, electromagnetic induction; Maxwell's equations in free and linear isotropicb media; Gauge invariance; Electromagnetic waves in free space, dielectrics, and conductors; Lorentz invariance of Maxwell’s equations


4. Quantum Mechanics: Wave-particle duality; Heisenberg's uncertainty principle; Dirac’s bra and Ket notations, time-dependent and time-independent Schroedinger equation ; Time independent perturbation theory and applications; Time dependent perturbation and Fermi's Golden Rule; Elementary theory of scattering, partial waves and Born Approximation; Identical particles, Pauli's exclusion principle, Klein Gordon and Dirac equations.


5. Thermodynamic and Statistical Physics: Laws of thermodynamics and their consequences; Phase space, Micro canonical, canonical and grand-canonical ensembles; partition functions; Free Energy and connection with thermodynamic quantities; Classical and quantum statistics, ideal Fermi and Bose gases.

6. Electronics: Semiconductor devices: diodes, junctions, transistors, field effect devices; Optoelectronic devices: including solar cells, photodetectors, and LEDs; Operational amplifiers and their applications; Digital techniques and applications (registers, counters, comparators and similar circuits); A/D and D/A converters.

7. Experimental Techniques and data analysis: Data interpretation and analysis; Precision and accuracy, error analysis; chi-square test; Transducers (temperature, pressure/vacuum, magnetic field, vibration, optical, and particle detectors), , impedance matching, amplification (Op-amp based, instrumentation amp, feedback), filtering and noise reduction, shielding and grounding.

8. Atomic & Molecular Physics: Quantum states of an electron in an atom; Electron spin; Stern-Gerlach experiment; Spectrum of Hydrogen, helium and alkali atoms;Relativistic corrections for energy levels of hydrogen; Hyperfine structure; LS & JJ coupling; Zeeman, Paschen Back & Stark effect; X-ray spectroscopy.

9. Condensed Matter Physics: Bravais lattices; Elastic properties, phonons, lattice specific heat; Free electron theory; Drude model of electrical and thermal conductivity; Hall effect; Dia,, Para , and Ferromagnetism; band theory of metals, insulators and Semiconductors; Superconductivity.

10. Nuclear and Particle Physics: Basic nuclear properties: size, shape, charge distribution, spin and parity; Binding energy, Semi-empirical mass formula; Liquid drop model; Fission and fusion; Isospin; Elementary ideas of alpha, beta and gamma decays ; Nuclear reactions, Classification of fundamental forces; Elementary particles (quarks, Baryons, mesons, leptons); isospin, strangeness; Gell-Mann-Nishijima formula; C, P, and T invariance ; parity non-conservation in weak interaction.

10. STATISTICS
1. Statistical Methods: Measures of central tendency, dispersion, skewness, kurtosis,
correlation, regression, interpolation, extrapolation, index numbers, time series and vital
statistics.
2. Sampling Methods: simple random Sampling, stratified sampling, systematic sampling,
ratio and regression methods, cluster sampling, two-stage sampling, double sampling, Nonsampling
errors.
3. Design of Experiments: Block designs, CRD, RBD, LSD, BIBD, PBIPD, Factorial
designs, confounding in block designs.
4. Probability: Compound probability, conditional probability, bayes theorem, expectation,
MGF, characteristic function, Inversion and continuity theorems for C. F., Kolmogorov's
inequality, The weak law of large numbers, The strong law of large numbers, Bernoulli's ,
Kintchine's theorems, Central limit theorem.
5. Testing of Hypothesis: Null hypothesis, alternative hypothesis, simple and compound
hypothesis, errors in testing, Neyman Pearson Lemma and its generalization, UMP Tests,
Unbiased Tests, UMPU Tests, Tests with Neyman structure and UMP similar tests,
Likelihood Ratio tests and their large sample properties along with simple applications.
6. Estimation: Elements of Decision Theory, Admissibility, Properties of good estimators,
Unbiasedness, Efficiency, Sufficiency and completeness, Cramer –Rao inequality and it's
generalization, Bhattacharya's Bounds, Characteristics of distribution admitting sufficient
statistic, Rao-Blackwell Theorem and Lehmann - Scheffe theorem. Method of Estimation,
Method of Maximum Likelihood, Method of Moments, Method of Chi-Square, Properties
of M.L.E.
7. Multivariate Analysis: Singular and Non Singular Multivariate Normal distributions,
Marginal and Conditional distributions, Characteristic Function and Moment Generating

Functions, Maximum Likelihood Estimation of Mean and Co-Variance matrix,
independence and joint sufficiency for these estimates, Hotelling's T2 statistic as a function
of the Likelihood Ratio criterion, It's distribution and applications, Mahalanobis D2 statistic
and it's distribution, Discriminant function(for two variables), Principal Components and
Canonical Correlations. Path Analysis, Factor Analysis , Discriminant Analysis,
MANOVA.
8. Non-parametric Inference: Tests for randomness, tests for goodness of fit, one sample
and two sample tests, Linear rank statistic and general two way sample problem, Linear
Rank tests for location and scale problems, Rank test for one way and two way classified
data, Multivariate non parametric test for one sample location problems, Asymptotic
relative efficiency, examples of ARE tests.
9. Stochastic Process and Reliability Theory: Definition of Stochastic processes, Markov
Chain, one step and n- step transition probabilities, Chapman-Kolmogorov Equation, first
passage and first return probabilities, classification of states, Markov Chains with
continuous state space, Poisson Processes, Birth and death processes, elements of Markov
Process.
Definition of Reliability , Maintainability and Availability, Life distributions, failure rates
and bath tub failure curve, exponential, Gamma, Weibull and Log Normal models, Linearly
increasing Hazard model, mean time to system failure and mean time between failure
components and system reliability, series and parallel configuration, Active and standby
redundancy and preventive Maintenance.
10. Bayesian Inference and Econometrics: General structure of a Bayesian Decision
problem, role of loss function, Risk function, Prior information, Application of Bayes
theorem in computing posterior distributions, Bayes estimators of the posterior mean under
squared error loss, Bayesian notion of sufficiency, construction of conjugate priors,
improper and diffuse priors.
Construction of economic models, Endogenous and Exogenous Variables, concept of
Multicolinearity, Identification Problems, rank and order condition of Identifiability,
identification under bilinear restrictions, identifiability everywhere in the parametric space,
WALA'S criterion of identification,
11. ZOOLOGY
1. Microbiology, Biotechnology and Instrumentation: Kinds of Microorganisms: Viruses,
Bacteriophages, Rickettsiae, Bacteria, Fungi, Slime moulds etc. Environmental
Microbiology: Microbiology of air, water, soil and Bioremediation. Microbiology of food:
Microbial contamination and spoilage of industrial and domestic food, sources of food
poisoning and food preservation. Antibiotics: History of Penicillin, Classification of
Antibiotics, Non-medical uses of antibiotics. Biotechnology: Scope and importance,
Restriction enzymes in cloning, Techniques used in recombinant DNA technology (agarose
and polyacrylamide gel electrophoresis, PEGE, Southern, Northern and Western Blotting,
dot blots and slot blots); Cloning vectors for recombinant DNA (Plasmids, Phages,
Cosmids, Viruses and Transposons), Transgenic plants and animals.
Instrumentation:Elementary knowledge of the functioning and application of the following
equipments: Microscopy: Light and phase contrast, Interference, Fluorescence and electron

microscopy. Microtomy: Routine paraffin microtomy, Spectrophotometry. Chromatography
and Electrophoresis. Centrifugation
2. Animal Diversity I: General classification, characters, habits and habitats of non-chordate
phyla. Protozoa: Locomotion and reproduction in protozoa. Porifera: Canal system.
Coelenterata: Polymorphism in Coelenterata, coral reefs. Helminthes: Life cycle of
Wuchereria and Schistosoma. Annelida: Segmental organs, Adaptive radiation in
Polychaeta. Arthropoda: Crustacea (Larval forms); Onychophora (General characters and
affinities); Insecta (social life in honey bee and termites). Echinodermata: Water vascular
system.
3. Animal Diversity II: Classification upto orders, characters, habits and habitats of
chordates. Origin and evolution of chordates, General organisation, classification and
affinities of Protochordata and cyclostomata, Ratitae: Distribution and affinities, Dentition
in mammals, General characters, distribution and affinities of Prototheria and Metatheria.
4. Biological Chemistry and Physiology (With emphasis on Vertebrates): Carbohydrates,
Proteins and Lipids: Chemical structure, classification and sources of biochemically
significant and metabolism. Enzymes: Nomenclature and classification, mechanism of
enzyme action, factors influencing enzyme activity. Vitamins: Chemical structure, source
and deficiency state of fat soluble and water soluble vitamins. Nutrition: Digestion,
absorption and assimilation of various food stuffs. Respiration: Respiratory surfaces in
different groups and gaseous exchange , Respiratory pigments, Transport of oxygen and
Carbon dioxide. Circulation: Haemopoiesis, Heart beat and its regulation and cardiac out
put, Blood flow through arteries, veins and capillaries (pulse and blood pressure) including
regulation, coronary circulation and coronary occlusion. Excretion and osmoregulation:
Functions of kidney, Types of nitrogenous wastes in different animal groups and their
excretion, Renal excretion in vertebrates (urine formation in a mammal in particular).
Nervous Co-ordination : Structure of neuron , nature , origin and propagation of nerve
impulse , Synaptic transmission, Chemistry and functions of neurotransmitters. Muscle
physiology: Structure, kinds and characteristics of muscles.
5. Cytogenetics: Chemistry of gene: Structure of nucleic acids (A, B, C and Z-DNAs, RLmodel
of Sasisekharan; supercoiling; genetic and non-genetic RNAs), DNA –replication
(evidence for semi conservative replication); DNA repair (excision repair, mismatch repair
and SOS repair), DNA repair and genetic disease in humans, Genetic Code: Properties of
genetic code, Mutation and genetic code, Wobble hypothesis, New genetic codes in
mitochondria and ciliate protozoa. Gene Function (Regulation of gene expression): Fine
structure of gene; Benzer’s analysis of r-II locus by deletion and complementation mapping;
Operons in bacteria (lac and trp operons in E. coli); General introduction to complexities of
gene regulation in eukaryotes, organisation of typical eukaryotic gene.
6. Genetics; Chromosome mapping: Chromosome mapping in Drosophila (single and
double crossing over), human chromosomes (Somatic cell genetics). Sex determination:
Chromosome theory of sex determination , Balance theory of sex determination (X/A ratio
in Drosophila), Hormonal and environmental control of sex, Doses compensation in
Drosophila and man. Sexuality and recombination in Bacteria and Viruses: Three modes of
transfer of genetic material (Transformation, transduction and conjugation), Sexual
conjugation in bacteria (F+ , F- and HFR strain), F and sex sexduction. Multiple Alleles :
Multiple alleles and isoalleles (Skin colour in rodents, eye colour in Drosophila , blood
group in humans).

7. Ecology: Basic concepts, Rationale and approach. Habitats: Freshwater (Lakes) and Marine
(Estuary). Environmental factors: Laws of limiting factors , namely temperature. Eutrophication of
freshwater ecosystems: Causes, consequences and control measures. Functioning of ecosystems:
Energy flow, productivity, trophic structure and ecological efficiencies. Ecology of communities:
Namely dominance, various types of diversity indices, Ecotone and niche concept.
8. Evolutionary Biology, Taxonomy and Animal Behaviour: Evolutionary Biology: Synthetic
theory f evolution., Micro, macro and mega evolution., Isolation and Variation. Species and
speciation. Genetic drift (Sewell –Wright effect). Hardy-Weinberg law. Taxonomy, Introduction to
systematics and taxonomy and its significance in Zoology. Modern approaches in taxonomy.
Concept of zoological classification. Species concept.Rules of zoological nomenclature. Collection,
preservation and identification of insects and other specimens. Animal Behaviour Innate Behaviour
and Learned Behaviour Communication: Chemical communication, Visual and Auditory
communication. Migratory Behaviour: Mechanisms of navigation and homing in fish and birds.
Social Behaviour: Types of social acts, Parental care. Biological Rhythms: Kinds of biological
rhythms, Biological clock, Circadian rhythms and their control.
9. Mammalian Endocrinology: Classification and chemical nature of hormones, Complete
knowledge of the generalized mechanisms of action (at molecular level) of protein and
steroid hormones. Molecular structure, origin, release and transport of sex hormone.
Microanatomical and histological structure of mammalian Pituitary, hypothalamohypophysial
system, Pineal, Thyroid, Parathyroid, Endocrine Pancreas and Adrenal glands,
and the molecular structure , synthesis , storage, control of release, transport, denaturation
and physiological actions of their hormones.
10. Developmental Biology: Fertilization: Mechanism of fertilization , early and late changes
in egg organisation caused by fertilization . Cleavage and Blastulation: Patterns of cleavage,
determinate and indeterminate cleavage, influence of yolk on cleavage, metabolic changes
during cleavage, morulation and blastulation in frog , chick and rabbit. Gastrulation: Fate
maps, morphogenetic movements in frog , chick and rabbit. Development and functions of
the foetal membranes in mammals. Organogenesis: Development of brain, eye and heart in
chick. Metamorphosis: Kinds of metamorphosis, Physiological and biochemical changes
during metamorphosis, hormonal control of metamorphosis.
Contact Details:

Kumaun University
Sleepy Hallow, Nainital, Uttarakhand 263001
Phone: 05942 235 563

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