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Muxammad al-xorazmiy nomidagi toshkent axborot texnologiyalari universiteti urganch filiali
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| bet | 5/8 | | Sana | 29.05.2024 | | Hajmi | 136 Kb. | | #256351 |
Bog'liq Ildiz yotgan oraliqni ajratish va Mathcadning standart funksiyalari yordamida chiziqsiz tenglamalarni yechish2. **Diferensial Tenglamalar:**
Mathcad differensial tenglamalarni yechish va ularni tahlil qilish uchun kuchli vositalarga ega. Obyektga yo'naltirilgan yondashuv yordamida oddiy va qiyosiy differensial tenglamalarni yechish mumkin.
```math
\frac{dy}{dx} + y = e^x
```
Bu tenglamani Mathcadda quyidagi usulda yechish mumkin:
```math
odesolve( \frac{dy}{dx} + y = e^x, y(0) = 1, x)
```
3. **Integrallar va Hosilalar:**
Mathcad integrallar va hosilalarni hisoblash imkonini beradi. Analitik va sonli integrallarni osongina hisoblash mumkin.
**Hosila:**
```math
\frac{d}{dx} (x^3) = 3x^2
```
**Integral:**
```math
\int_0^1 x^2 \, dx = \frac{1}{3}
```
4. **Matritsa va Vektorlar:**
Mathcad matritsa va vektorlar bilan ishlashda keng imkoniyatlarga ega. Matritsa algebra, determinant, teskari matritsa va boshqa operatsiyalarni osongina amalga oshirish mumkin.
**Matritsa:**
```math
\mathbf{A} := \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix}
```
**Determinant:**
```math
\det(\mathbf{A}) = -2
```
5. **Sonli Metodlar:**
Mathcad sonli metodlar yordamida murakkab hisob-kitoblarni amalga oshiradi. Masalan, ildizlarni topish, integral va hosilalarni sonli hisoblash, differensial tenglamalarni sonli yechish kabi masalalarni hal qilish mumkin.
**Ildizlarni topish:**
```math
root(f(x), x, [a, b])
```
6. **Optimizatsiya:**
Mathcad optimizatsiya masalalarini ham yechish imkoniyatiga ega. Bu turli xil texnik va ilmiy optimizatsiya muammolarini hal qilish uchun foydali bo'lishi mumkin.
**Minimalizatsiya:**
```math
minimize(f(x), x)
```
### Misollar:
Algebraik Tenglama Yechish:
```math
\text{Tenglama: } x^2 + 3x - 4 = 0
\text{Yechish: solve}(x^2 + 3x - 4, x)
```
Differensial Tenglama Yechish:
```math
\text{Tenglama: } \frac{dy}{dx} + 2y = \sin(x)
\text{Yechish: odesolve}(\frac{dy}{dx} + 2y = \sin(x), y(0) = 0, x)
```
Matritsa Operatsiyalari:
```math
\mathbf{A} := \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix}
\mathbf{B} := \begin{pmatrix} 2 & 0 \\ 1 & 3 \end{pmatrix}
\mathbf{A} + \mathbf{B}
\mathbf{A} \cdot \mathbf{B}
```
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