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Introduction to differentiation
Published in John Bird, Engineering Mathematics, 2017
There are many practical situations engineers have to analyse which involve quantities that are varying. Typical examples include the stress in a loaded beam, the temperature of an industrial chemical, the rate at which the speed of a vehicle is increasing or decreasing, the current in an electrical circuit or the torque on a turbine blade. Differential calculus, or differentiation, is a mathematical technique for analysing the way in which functions change. There are many methods and rules of differentiation which are individually covered in the following chapters. A good knowledge of algebra, in particular, laws of indices, is essential. This chapter explains how to differentiate the five most common functions, providing an important base for future chapters.
Introduction to differentiation
Published in John Bird, Bird's Basic Engineering Mathematics, 2021
There are many practical situations engineers have to analyse which involve quantities that are varying. Typical examples include the stress in a loaded beam, the temperature of an industrial chemical, the rate at which the speed of a vehicle is increasing or decreasing, the current in an electrical circuit or the torque on a turbine blade. Differential calculus, or differentiation, is a mathematical technique for analysing the way in which functions change. A good knowledge of algebra, in particular, laws of indices, is essential. This chapter explains how to differentiate the five most common functions, providing an important base for future studies.
Introduction to differentiation
Published in John Bird, Basic Engineering Mathematics, 2017
There are many practical situations engineers have to analyse which involve quantities that are varying. Typical examples include the stress in a loaded beam, the temperature of an industrial chemical, the rate at which the speed of a vehicle is increasing or decreasing, the current in an electrical circuit or the torque on a turbine blade. Differential calculus, or differentiation, is a mathematical technique for analysing the way in which functions change. A good knowledge of algebra, in particular, laws of indices, is essential. This chapter explains how to differentiate the five most common functions, providing an important base for future studies.
Implications of causality for quantum biology – I: topology change
Published in Molecular Physics, 2018
To describe a tangent space over a causally evolving underlying manifold Tx(Φ), it requires the use of the Poincare group [2–5]. In general, one must also use the exterior calculus for the cotangent space of the underlying manifold T*x(Φ) as many topological properties are most effectively formulated for the cotangent space [17–20]. In terms of vector spaces, the Tx(Φ) are spanned by (QM) and the T*x(Φ) are spanned by dxi (geometry and topology). The cotangent space and the tangent space are related by the fact that the value of a cotangent space element dxi at a tangent space element ∂j maps to a real number according to dxi(∂j) = δij. In Table 1, the cotangent space has an intrinsic algebraic structure defined by the antisymmetric wedge product dxi∧dxj = −dxj∧dxi. Linear combinations such as are termed 1-forms. The 2-forms are defined as . A differential calculus based on the exterior derivative denoted d is defined using the rule as described in [17–20]. The wave operator is defined by ☐ = ∂2t − ∇2.
Characterization of Test Sets for Multiple Faults in Combinational Network
Published in IETE Journal of Education, 2021
It would be worth mentioning here that the notation “” has been introduced in [6] to denote the Boolean expression , and hence “” should never be thought of in ordinary sense as “Derivative” of a function used in the topic “Differential calculus” of Mathematics. In a similar manner, each of the notations for higher order Boolean differences introduced in [5] also corresponds to a Boolean expression involving Exclusive-OR operators, and it has no co-relation with the term “Derivative” of a function used in the topic “Differential calculus” of Mathematics.
Fractional gravitational search-radial basis neural network for bone marrow white blood cell classification
Published in The Imaging Science Journal, 2018
Namdev Devidas Pergad, Satish T. Hamde
The positions of the agents at the next iteration are computed with the adaptation of the fractional calculus theory [19] in the gravitational search algorithm. The fractional calculus is the extension of the integral and differential calculus of the conventional mathematics. The incorporation of the fractional calculus increases the search space of the optimization algorithm. This is because of the natural and inherent memory property of the fractional calculus [19]. The updated position of the agents is computed as follows: