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COURSE CONTENTS, G M Masters Introduction to Environmental. CS 101 Computer Programming Engineering and Science Second Indian. Utilization 2026 Reprint Prentice Hall of India 2004. Functional organization of computers algo M L Davis and D A Cornwell. rithms basic programming concepts Introduction to Environmental Engineering. FORTRAN language programming Program 2nd Edition McGraw Hill 1998. testing and debugging Modular, programming subroutines Selected examples R T Wright Environmental Science. from Numerical Analysis Game playing Towards a Sustainable Future 9th Edition. sorting searching methods etc Prentice Hall of India 2007. Supplementary Reading Materials Selected, Texts References Book Chapters and Papers. N N Biswas FORTRAN IV Computer, Programming Radiant Books 1979 HS 200 Environmental Studies 3 0 0 3. K D Sharma Programming in Fortran IV Social issues and the environment Public. Affiliated East West 1976 awareness and Human rights Indicators of. sustainability Governance of Natural, Resources Common pool resources issues.

ES 200 Environmental Studies 3 0 0 3 and management. Multidisciplinary nature of environmental Environmental ethics Religion and environ. problems Ecosystems Biodiversity and its ment Wilderness and Developing Trends. conservation Indicators of environmental Environmental movements and Activism. pollution Environment and human health Social Ecology and Bioregionalism. Utilization of natural resources and environ Environmental justice. mental degradation Sustainable develop, ment Environmental policy and law Environmental economics Trade and envi. Environmental impact assessment Pollution ronment Economics of environmental regu. of lakes rivers and groundwater Principles lation Natural resource accounting Green. of water and wastewater treatment Solid and GDP, hazardous waste management Air Pollution. sources and effects Atmospheric transport of Environment and development Resettlement. pollutants Noise pollution Global issues and and rehabilitation of people Impacts of. climate change Global warming Acid rain climate change on economy and society. Ozone layer depletion Vulnerability and adaptation to climate. Texts References Text References, W P Cunningham and M A Cunningham N Agar Life s Intrinsic Value Columbia. Principles of Environmental Science Tata University Press 2001. McGraw Hill Publishing Company 2002, P Dasgupta and G Maler G Eds The. J A Nathanson Basic Environmental Environment and Emerging Development. Technology Water Supply Waste Issues Vol I Oxford University Press 1997. Management and Pollution Control 4th, R Guha Mahatma Gandhi and.

Edition Prentice Hall of India 2002, Environmental Movement in A. Raghuramaraju Ed Debating on Gandhi K Hoffman and R Kunze Linear Algebra. Oxford University Press 2006 Pearson Education India 2003. R Guha and M Gadgil Ecology and Equity S Lang Linear Algebra Undergraduate. The Use and Abuse of Nature in Texts in Mathematics Springer Verlag New. Contemporary India Penguin 1995 York 1989, N Hanley J F Shogren and B White P Lax Linear Algebra John Wiley Sons. Environmental Economics in Theory and 1997, Practice MacMillan 2004. H E Rose Linear Algebra Birkhauser 2002, A Naess and G Sessions Basic Principles of. Deep Ecology Ecophilosophy Vol 6 1984 S Lang Algebra 3rd Edition. Springer India 2004, M Redclift and G Woodgate Eds.

International Handbook of Environmental O Zariski and P Samuel Commutative. Sociology Edward Edgar 1997 Algebra Vol I Springer 1975. MA 401 Linear Algebra 3 1 0 8, MA 403 Real Analysis 3108. Vector spaces over fields subspaces bases, and dimension Review of basic concepts of real numbers. Archimedean property Completeness, Systems of linear equations matrices rank. Gaussian elimination Metric spaces compactness connectedness. with emphasis on Rn, Linear transformations representation of. linear transformations by matrices rank Continuity and uniform continuity. nullity theorem duality and transpose, Monotonic functions Functions of bounded.

Determinants Laplace expansions cofactors variation Absolutely continuous functions. adjoint Cramer s Rule Derivatives of functions and Taylor s. Eigenvalues and eigenvectors characteristic, polynomials minimal polynomials Cayley Riemann integral and its properties. Hamilton Theorem triangulation diagonal characterization of Riemann integrable. lization rational canonical form Jordan functions Improper integrals Gamma. canonical form functions, Inner product spaces Gram Schmidt ortho Sequences and series of functions uniform. normalization orthogonal projections linear convergence and its relation to continuity. functionals and adjoints Hermitian self differentiation and integration Fourier series. adjoint unitary and normal operators pointwise convergence Fejer s theorem. Spectral Theorem for normal operators Weierstrass approximation theorem. Bilinear forms symmetric and skew Texts References. symmetric bilinear forms real quadratic T Apostol Mathematical Analysis 2nd. forms Sylvester s law of inertia positive Edition Narosa 2002. definiteness, Texts References, M Artin Algebra Prentice Hall of India. K Ross Elementary Analysis The Theory K D Joshi Introduction to General. of Calculus Springer Int Edition 2004 Topology New Age International 2000. K D Joshi Introduction to General, W Rudin Principles of Mathematical Topology New Age International 2000. Analysis 3rd Edition McGraw Hill 1983, J L Kelley General Topology Van.

Nostrand 1955, MA 406 General Topology 3 1 0 8, J R Munkres Topology 2nd Edition. Prerequisites MA 403 Real Analysis Pearson Education India 2001. Topological Spaces open sets closed sets G F Simmons Introduction to Topology. neighbourhoods bases sub bases limit and Modern Analysis McGraw Hill 1963. points closures interiors continuous, functions homeomorphisms MA 408 Measure Theory 3 1 0 8. Examples of topological spaces subspace Prerequisites MA 403 Real Analysis. topology product topology metric topology, order topology Semi algebra Algebra Monotone class. Sigma algebra Monotone class theorem, Quotient Topology Construction of cylinder Measure spaces. cone Moebius band torus etc, Outline of extension of measures from.

Connectedness and Compactness Connected algebras to the generated sigma algebras. spaces Connected subspaces of the real line Measurable sets Lebesgue Measure and its. Components and local connectedness properties, Compact spaces Heine Borel Theorem. Local compactness Measurable functions and their properties. Integration and Convergence theorems, Separation Axioms Hausdorff spaces. Regularity Complete Regularity Normality Introduction to Lp spaces Riesz Fischer. Urysohn Lemma Tychonoff embedding and theorem Riesz Representation theorem for L2. Urysohn Metrization Theorem Tietze spaces Absolute continuity of measures. Extension Theorem Tychnoff Theorem, Radon Nikodym theorem Dual of Lp spaces. One point Compactification, Product measure spaces Fubini s theorem. Complete metric spaces and function spaces, Characterization of compact metric spaces Fundamental Theorem of Calculus for.

equicontinuity Ascoli Arzela Theorem Lebesgue Integrals an outline. Baire Category Theorem Applications space, filling curve nowhere differentiable Texts References. continuous function, P R Halmos Measure Theory Graduate Text. Optional Topics Topological Groups and, in Mathematics Springer Verlag 1979. orbit spaces Paracompactness and partition, of unity Stone Cech Compactification Nets Inder K Rana An Introduction to Measure. and filters and Integration 2nd Edition Narosa, Publishing House New Delhi 2004.

Texts References H L Royden Real Analysis 3rd Edition. Macmillan 1988, M A Armstrong Basic Topology Springer. India 2004, MA 410 Multivariable Calculus 2106 Cauchy Riemann conditions Mappings by. elementary functions Riemann surfaces, Prerequisites MA 403 Real Analysis Conformal mappings. MA 401 Linear Algebra, Functions on Euclidean spaces continuity Contour integrals Cauchy Goursat Theorem. differentiability partial and directional, derivatives Chain Rule Inverse Function Uniform convergence of sequences and.

Theorem Implicit Function Theorem series Taylor and Laurent series Isolated. singularities and residues Evaluation of real, Riemann Integral of real valued functions on integrals. Euclidean spaces measure zero sets Fubini s, Theorem Zeroes and poles Maximum Modulus. Principle Argument Principle Rouche s, Partition of unity change of variables theorem. Integration on chains tensors differential Texts References. forms Poincar Lemma singular chains, integration on chains Stokes Theorem for J B Conway Functions of One Complex. integrals of differential forms on chains Variable 2nd Edition Narosa New. general version Fundamental theorem of Delhi 1978, T W Gamelin Complex Analysis Springer.

Differentiable manifolds as subspaces of International Edition 2001. Euclidean spaces differentiable functions on, manifolds tangent spaces vector fields R Remmert Theory of Complex Functions. differential forms on manifolds orientations Springer Verlag 1991. integration on manifolds Stokes Theorem on, manifolds A R Shastri An Introduction to. Complex Analysis Macmilan India New, Texts References. Delhi 1999, V Guillemin and A Pollack Differential MA 414 Algebra I 3108. Topology Prentice Hall Inc Englewood, Cliffe New Jersey 1974 Prerequisite MA 401 Linear Algebra.

MA 419 Basic Algebra, W Fleming Functions of Several Variables. 2nd Edition Springer Verlag 1977 Fields Characteristic and prime subfields. Field extensions Finite algebraic and, J R Munkres Analysis on Manifolds. finitely generated field extensions Classical, Addison Wesley 1991 ruler and compass constructions Splitting. fields and normal extensions algebraic, W Rudin Principles of Mathematical. closures Finite fields Cyclotomic fields, Analysis 3rd Edition McGraw Hill 1984 Separable and inseparable extensions.

M Spivak Calculus on Manifolds A, Galois groups Fundamental Theorem of. Modern Approach to Classical Theorems of, Galois Theory Composite extensions. Advanced Calculus W A Benjamin Inc, Examples including cyclotomic extensions. and extensions of finite fields, Norm trace and discriminant Solvability by. MA 412 Complex Analysis 3 1 0 8 radicals Galois Theorem on solvability. Cyclic extensions Abelian extensions, Complex numbers and the point at infinity Polynomials with Galois groups Sn.

Transcendental extensions, Analytic functions, Texts References M Hirsch S Smale and R Deveney. Differential Equations Dynamical Systems, M Artin Algebra Prentice Hall of and Introduction to Chaos Academic Press. India 1994 2004, M Hirsch S Smale and R Deveney, D S Dummit and R M Foote Abstract Differential Equations Dynamical Systems. Algebra 2nd Edition John Wiley 2002 and Introduction to Chaos Academic Press. J A Gallian Contemporary Abstract, Algebra 4th Edition Narosa 1999 L Perko Differential Equations and. Dynamical Systems Texts in Applied, N Jacobson Basic Algebra I 2nd Edition Mathematics Vol 7 2nd Edition Springer.

Hindustan Publishing Co 1984 W H Verlag New York 1998. Freeman 1985, M Rama Mohana Rao Ordinary Differential. MA 417 Ordinary Differential Equations Theory and Applications. Equations 3 1 0 8 Affiliated East West Press Pvt Ltd New. Delhi 1980, Review of solution methods for first order as. well as second order equations Power Series D A Sanchez Ordinary Differential. methods with properties of Bessel functions Equations and Stability Theory An. and Legendr polynomials Introduction Dover Publ Inc New York. Existence and Uniqueness of Initial Value, Problems Picard s and Peano s Theorems MA 419 Basic Algebra 3108. Gronwall s inequality continuation of, solutions and maximal interval of existence Review of basics Equivalence relations and. continuous dependence partitions Division algorithm for integers. primes unique factorization congruences, Higher Order Linear Equations and linear Chinese Remainder Theorem Euler.

Systems fundamental solutions Wronskian function, variation of constants matrix exponential. solution behaviour of solutions Permutations sign of a permutation. inversions cycles and transpositions, Two Dimensional Autonomous Systems and Rudiments of rings and fields elementary. Phase Space Analysis critical points proper properties polynomials in one and several. and improper nodes spiral points and saddle variables divisibility irreducible. points polynomials Division algorithm Remainder, Asymptotic Behavior stability linearized Theorem Factor Theorem Rational Zeros. stability and Lyapunov methods Theorem Relation between the roots and. coefficients Newton s Theorem on, Boundary Value Problems for Second Order symmetric functions Newton s identities. Equations Green s function Sturm Fundamental Theorem of Algebra. comparison theorems and oscillations, eigenvalue problems Rational functions partial fraction.

decomposition unique factorization of, Texts References polynomials in several variables Resultants. and discriminants, Groups subgroups and factor groups. Lagrange s Theorem homomorphisms normal, subgroups Quotients of groups Basic. examples of groups symmetric groups matrix, groups group of rigid motions of the plane and. K Ross Elementary Analysis The Theory of Calculus Springer Int Edition 2004 W Rudin Principles of Mathematical Analysis 3 rd Edition McGraw Hill 1983 MA 406 General Topology 3 1 0 8