Engineering mathematics – III
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ENGINEERING MATHEMATICS – III
Module-I Fourier Series: Periodic functions, Fourier Expansions, Half Range Expansions, Complex form of Fourier series, Practical Harmonic Analysis. Fourier Transforms: Infinite Fourier Transforms, Fourier Sine and Cosine Transforms, Properties, Inverse Transforms. 11+ 2 Hrs. Module-II Probability: Additional rule, conditional probability, multiplication rule, Baye’s theorem. 6 + 2 Hrs. Module-III Partial differential equations (P.D.E.): Formation of Partial Differential Equation, Solution of Langrange’s Linear P.D.E. of the type Pp+Qq=R. Method of Separation of Variables. 8 + 3 Hrs. Module-IV Applications of P.D.E.: Classification of PDE, solution of one dimensional heat wave and two dimensional Laplace’s equation by the method of separation of variables. 7 + 3 Hrs. Module-V Calculus of Variation: Variation of a function and a functional, Extremal of a functional, Variational problems, Euler’s equation, Standard Variational problems including geodesics, Minimal surface of revolution, hanging chain and Brochistrochrone problem. 7 + 3 Hrs. TEXT BOOK
REFERENCE BOOKS
ENVIRONMENTAL SCIENCES
Module-I Environment and Human Activities Introduction, component of Environment and their interaction. Ecology-Definition of ecology. Ecosystem-Types, structure and functions of ecosystem. Energy flow and mineral cycling. Food chains and food webs. Ecological pyramids. Bio-geo-chemical cycles. Human activities-Food-world food, world food supply, undernourishment around the world and Indian food production. Shelter-Indian scenario. Economic and social security-economic security, impact of globalization and economic liberalization. Social security. 05 Hrs. Module-II Effect Of Human Activities On Environment Introduction. Agriculture-effect of modern agriculture on soil and water, Ecofriendly farming system. Effects on soil micro life. Housing-effect of housing on land use and effect of building materials. Mining-Minerals in geosphere, Mining and extraction. Environmental effects of mining. Transportation-modes of transport. transport & land use, environmental effects of transport. Environmental impact assessment-steps in EIA process. Environmental impact statement (EIS) presentation and benefits of EIS. Sustainable development concepts. Action strategies for sustainable development. 05 Hrs. Module-III |
