0
What else can I help you with?
How do you find general solutions to difference equations in time series give written example please?
The answer will depend on the nature of the differential equation.
Second order differential equation for RLC series circuit?
In an RLC series circuit, which comprises a resistor (R), inductor (L), and capacitor (C) connected in series, the second-order differential equation can be derived from Kirchhoff's voltage law. It is expressed as ( L \frac{d^2i(t)}{dt^2} + R \frac{di(t)}{dt} + \frac{1}{C} i(t) = 0 ), where ( i(t) ) is the current through the circuit. This equation models the dynamics of the circuit's response to applied voltage, capturing both transient and steady-state behavior. The solution to this equation can reveal underdamped, critically damped, or overdamped responses depending on the values of R, L, and C.
How is pi 3.14 found?
The numerical value of pi is often found using a Taylor or Maclaurin series (Taylor series centered at 0).
What is Taylor series method?
f(x)=lnx
How are Taylor series used in the real world?
Taylor series are widely used in various fields of science and engineering to approximate complex functions with polynomial expressions, making calculations simpler and more efficient. For example, they are essential in numerical methods for solving differential equations, optimizing algorithms in computer science, and modeling physical systems in physics and engineering. Additionally, Taylor series enable the analysis of functions near specific points, which is valuable in fields like economics for forecasting and in machine learning for optimization techniques. Overall, their ability to provide accurate approximations facilitates problem-solving across numerous applications.
What has the author Arne Broman written?
Arne Broman has written: 'Introduction to partial differential equations' -- subject(s): Partial Differential equations 'On two classes of trigonometrical series'
How do you find general solutions to difference equations in time series give written example please?
The answer will depend on the nature of the differential equation.
Main points of Legendre differential equation?
The Legendre differential equation is the second-order ordinary differential equation(1)which can be rewritten(2)The above form is a special case of the so-called "associated Legendre differential equation" corresponding to the case . The Legendre differential equation has regular singular points at , 1, and .If the variable is replaced by , then the Legendre differential equation becomes(3)derived below for the associated () case.Since the Legendre differential equation is a second-order ordinary differential equation, it has two linearly independent solutions. A solution which is regular at finite points is called a Legendre function of the first kind, while a solution which is singular at is called a Legendre function of the second kind. If is an integer, the function of the first kind reduces to a polynomial known as theLegendre polynomial.The Legendre differential equation can be solved using the Frobenius method by making a series expansion with ,(4)(5)(6)Plugging in,(7)(8)(9)(10)(11)(12)(13)(14)so each term must vanish and(15)(16)(17)Therefore,(18)(19)(20)(21)(22)so the even solution is(23)Similarly, the odd solution is(24)If is an even integer, the series reduces to a polynomial of degree with only even powers of and the series diverges. If is an odd integer, the series reduces to a polynomial of degree with only odd powers of and the series diverges. The general solution for an integer is then given by the Legendre polynomials(25)(26)where is chosen so as to yield the normalization and is ahypergeometric function.The associated Legendre differential equation is(27)which can be written(28)(Abramowitz and Stegun 1972; Zwillinger 1997, p. 124). The solutions to this equation are called the associated Legendre polynomials (if is an integer), or associated Legendre functions of the first kind (if is not an integer). The complete solution is(29)where is a Legendre function of the second kind.The associated Legendre differential equation is often written in a form obtained by setting . Plugging the identities(30)(31)(32)(33)into (◇) then gives(34)(35)
What is Taylor series?
give the expansion of Taylor series
Second order differential equation for RLC series circuit?
In an RLC series circuit, which comprises a resistor (R), inductor (L), and capacitor (C) connected in series, the second-order differential equation can be derived from Kirchhoff's voltage law. It is expressed as ( L \frac{d^2i(t)}{dt^2} + R \frac{di(t)}{dt} + \frac{1}{C} i(t) = 0 ), where ( i(t) ) is the current through the circuit. This equation models the dynamics of the circuit's response to applied voltage, capturing both transient and steady-state behavior. The solution to this equation can reveal underdamped, critically damped, or overdamped responses depending on the values of R, L, and C.
Why is it that if a equals 0 the Taylor's series becomes the maclaurin's series?
Simply because the Maclaurin series is defined to be a Taylor series where a = 0.
Derive recursion formula for sin by using Taylor's Series?
the Taylor series of sinx
What is Taylor machines?
Taylor machines are a type of mathematical construct used in the field of automated reasoning and artificial intelligence. They are based on the concept of representing functions and their approximations through the use of Taylor series, enabling efficient computation and analysis of complex functions. In particular, Taylor machines can be utilized for tasks like symbolic computation, numerical analysis, and solving differential equations, leveraging the power of Taylor expansions to derive solutions.
Is Taylor Swift in a twilight series?
No but Taylor Lautner is. Taylor Lautner is dating Taylor Swift.
What is the predicate adjective to this sentence It is an introduction to The Lord of the Rings a series of books about hobbits?
I believe that in the sentence It is an introduction to The Lord of the Rings, a series of books about hobbits, the word "introduction" would be the predicate adjective.
Who change the role of Taylor lautner in the eclipse series?
Taylor is still in Eclipse.
What has the author Richard Haberman written?
Richard Haberman has written: 'Applied Partial Differential Equations' 'Elementary applied partial differential equations' -- subject(s): Boundary value problems, Differential equations, Partial, Fourier series, Partial Differential equations
