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Dustinsfl said:Last two inner product questions.
The first one I am little confused on and the second one I don't know what to do.
See worked attached.
Can you elaborate on this a bit more? You haven't said quite enough so that I'm not sure I understand what you're talking about. If you have a given integral on one side, and 1/(s - 1) times the same integral on the other side, add -1/(s - 1) times the integral to both sides, and then combine the two integrals using the rules of plain old fractions. At that point you can solve for the integral algebraically.Dustinsfl said:On the integration by parts comment, I have an unrelated issue. I was doing a Laplace Transform of e^(-st+t)*sin(t) but after doing integration by parts, I had a form of the original with a 1/(s-1) time the integral so I can't subtract across to the other side. What can I do there since if I keep going it will an endless cyclical cycle?
The inner product of two vectors is a mathematical operation that takes two vectors and produces a scalar. It is also known as the dot product and is calculated by multiplying the corresponding components of the two vectors and adding the results together.
The inner product is used in mathematics to determine the angle between two vectors, to project one vector onto another, and to calculate the magnitude (or length) of a vector.
The inner product can be interpreted geometrically as the product of the lengths of two vectors and the cosine of the angle between them. This means that the inner product is positive if the angle between the vectors is acute, negative if the angle is obtuse, and zero if the vectors are perpendicular.
The inner product is a scalar value, while the cross product produces a vector. Additionally, the inner product is commutative (a·b = b·a), while the cross product is anti-commutative (a×b = -b×a). The inner product is also used for calculating the angle between two vectors, while the cross product is used for calculating the area of a parallelogram formed by two vectors.
In physics, the inner product is used to calculate work, energy, and power in a system. It is also used in the study of waves and harmonic motion, as well as in quantum mechanics to calculate probabilities and expectation values.