Applied and Computational Mathematics

Introduction to applied and computational mathematics:
In this article we learn about applied and computational mathematics problems. In applied mathematics we solve more advanced math problems. Applied mathematics is advanced method of school level mathematics. Computational mathematics is involving research of some important math topics. Computational mathematics involves areas, volume, symbolic methods and numerical methods. Applied and computational mathematics problems are easily solved by using formulas. Now in this article we solve some applied mathematics problems. Having problem with Computational Formula for Standard Deviation keep reading my upcoming posts, i will try to help you.

Example Problems for Applied and Computational Mathematics

Find the first derivative of the given step function f(x) =`{ (9x + 5 if x gt1), (3x^4 + 4x if x lt 1):}`

Solution:

Given step function is f(x) =` { (9x + 5 if x gt1), (3x^4 + 4x if x lt 1):}`

From the given,

f1(x) = 9x + 5 if x > 1

And

f2(x) = 3x4 + 4x if x < 1

Differentiate the given functions f1(x) and f2(x) with respect to x, we get

f1'(x) = 9

And

f2'(x) = 12x3 + 4

Combining the two functions, we get

f'(x) = `{ (9 if x gt1), (12x^3 + 4 if x lt 1):}`

Answer:

The final answer is f'(x) = `{ (9 if x gt1), (12x^3 + 4 if x lt 1):}`

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Applied and Computational Mathematics Example Problem 2:

Find the double integral value of the given function   `int_0^3int_0^(14)`y dy dx

Solution:

Given function is  `int_0^3int_0^(14)`y dy dx

Here range of x is 3 to 0 and y range is 14 to 0

Integrate the function with respect to 'y'. So, we get

= `int_0^3int_0^(14)`y dy dx

Integrate the coordinates separately, we get

`int_0^(14)`y dy `int_0^3` dx =   `[y^2/2]` 0(14) *  `int_0^3` dx

= `((14^2/2) - 0) xx (x)_0^3`

Substitute the limits in the above equations, in this first substitute the upper limits and then substitute lower limits.

= `(98 - 0)` * `((3) - 0)`

After subtracting, we get

= 98 * 3

After simplifying the above step, we get

= 294

Answer:

The final answer is 294