GATE

The unit covers following points - Introduction to vectors and their significance in mathematics and physics - Explanation of linear integral, involving the integration of vector fields along curves or paths - Discussion on surface integrals, focusing on the integration of vector fields over surfaces - Overview of volume integrals, used to calculate properties within three-dimensional regions - Introduction to Stokes' theorem, relating line integrals of vector fields to surface integrals ...

The unit covers following points - Introduction to vectors and their role in mathematics and physics - Explanation of curl as a measure of rotational behavior in vector fields - Discussion on directional derivatives, indicating how a function changes along a given direction - Overview of gradients, representing the rate of change of a scalar function in space - Application of vectors in solving numerical problems involving normal surfaces and vector fields - Illustrative examples and exer...

The unit covers following points - Introduction to linear differential equations and their importance in various fields of mathematics and physics - Explanation of Cauchy's equations, fundamental in understanding the behavior of linear differential equations - Overview of legendary equations and their significance in solving specific types of linear differential equations - Application of linear differential equations to practical problems in engineering, physics, and other disciplines - I...

The unit covers following points - Introduction to linear differential equations and their significance in mathematics and engineering - Explanation of basic concepts such as order, linearity, and homogeneity - Overview of methods for solving first-order linear differential equations, including separation of variables and integrating factors - Discussion on solving higher-order linear differential equations using techniques like the method of undetermined coefficients and variation of param...

The unit covers following points - Introduction to canal design principles in irrigation engineering - Explanation of Blinks' theory for designing irrigation canals based on optimal velocity distribution - Overview of other theories in canal design such as Lacey's theory and Kennedy's theories - Discussion on the importance of proper canal design for efficient water distribution in agriculture - Considerations for designing canals with various shapes and sizes to meet specific irrigatio...

The unit covers following points - Introduction to canal design principles in irrigation engineering - Explanation of Lacey's theory for estimating flow velocity and discharge in canals - Overview of Kennedy's theories on canal design and efficiency - Definition of canals and their role in water distribution for agriculture - Types of canals: main canals, branch canals, distributaries, etc. - Design considerations for canals with different shapes: trapezoidal, triangular, rectangular, e...

The unit covers following points - Introduction to gravity dams and their importance in irrigation engineering - Overview of analysis techniques for gravity dams - Discussion on design considerations and factors influencing dam stability - Calculation methods for determining dam dimensions and structural integrity - Illustrative diagrams and equations demonstrating key concepts - Emphasis on safety and reliability in dam design and construction.

The unit covers following points - Crop water requirements overview - Explanation of evapotranspiration (ET) - Factors affecting water needs: climate, soil type, crop type, etc. - Methods for calculating irrigation scheduling - Diagrams and equations illustrating concepts - Importance of efficient water management in agriculture

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