**Table Of Contents**

Students will investigate numerous applications of partial differential equations in Unit 02 of Math 4 AKTU. This section discusses the heat equation, wave equation, and Laplace equation, as well as its applications in physics, engineering, and other disciplines. Students will have a strong knowledge of how partial differential equations are used to describe real-world occurrences by the end of this course.

Dudes 🤔.. You want more useful details regarding this subject. Please keep in mind this as well.Important Questions ForMath 4 (Mathematics 4):*Unit-01 *Unit-02 *Unit-03 *Unit-04 *Unit-05 *Short-Q/Ans *Question-Paper with solution 21-22

**Q1. Solve by separation of variables: **

**Ans.**

**Q2. Solve by method of separation of variable for PDE **

**Ans.**

**Q3. Find the displacement of a finite string of length L that is fixed at both ends and is released from rest with an initial displacement f(x). **

**Ans.**

**Q4. Find the temperature distribution in a rod of length ‘a’** **which is perfectly insulated including the ends and the initial** **temperature distribution is x(a-x),0 <x<a. **

**Ans.**

**Q5. Solve by the method of separation of variables **

**Ans.**

**Q6. A square plate is bounded by lines x =0,y= 0; x = 20,y = 20.** **Its faces are insulated. The temperature along the upper horizontal** **edge is given by u (x, 20) = x (20-z) when 0 <x < 20 while the upper** **three edges are kept at 0 °C. Find the steady state temperature. **

**Ans.**

**Q7. Solve this eq1 object to the conditions u(x,0) =0, **

**Ans.**

**Q8. Solve the Laplace equation**

** in a rectangle in the xy-plane, 0 <= x <= a and 0 <= y <= b satisfying the following boundary conditions u(x, 0) =0, u(x, b) =0 and u (0, y) = 0, u(a,y) =f(y). **

**Ans.**

**Important Question with solutions | AKTU Quantums | Syllabus | Short Questions**

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