Applications of differential equations with questions answers
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Course
8975
Institution
Ned University Of Engineering And Technology
This document comprises of complete applications of differential equations with solved examples which are easy to understand with complete formulas and their derivation too.
This document also includes some applications of linear algebra.
, LINEAR ALGEBRA
INTRODUCTION:
Linear algebra, a fundamental mathematical discipline, is a crucial
prerequisite for understanding machine learning. While it
encompasses various advanced theories, machine learning
practitioners can focus on its practical aspects, leveraging its
essential tools and notations. The field's development can be
traced back to Hermann Grassmann's work in 1844, followed by
contributions from James Joseph Sylvester and Arthur Cayley, who
laid the foundation for modern linear algebra.
ELECTRICAL CIRCUITS:
In electronics, a circuit is a continuous loop that enables the flow of electricity
from a source, through conductors, and back to the source, typically powering a
device or load. More broadly, the term "circuit" refers to any defined path that
allows the flow of electricity, data, or signals. An electrical circuit specifically
consists of a closed loop of wires and components that allows current to flow
when a voltage is applied across any two points in the circuit.
RELATION BETWEEN LINEAR
ALGEBRA AND ELECTRICAL ALGEBRA
By converting a circuit into a system of linear equations, you can simplify its analysis using matrix
methods, just like solving a system of equations. Take this circuit as an example: by writing equations for
each node and branch, you can create a matrix representation of the circuit, which can be row-reduced
to solve for currents and voltages at each node, making circuit analysis more manageable and efficient.
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