Btech Unit 02 Applications of Partial Differential Equations in MATH 4 AKTU

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.

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Important Questions For Math 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.

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