1. Construct the weak form of the following linear equation. Identify the primary and secondary variables.
![723_Construct the linear equation.png](https://secure.tutorsglobe.com/CMSImages/723_Construct%20the%20linear%20equation.png)
2. Construct the weak form of the following linear equation. Are the boundary conditions "essential" or "natural"?
![166_Construct the linear equation1.png](https://secure.tutorsglobe.com/CMSImages/166_Construct%20the%20linear%20equation1.png)
3. Construct the weak form of the following nonlinear equation. Identify the BC's as either "essential" or "natural."
![944_Construct the linear equation2.png](https://secure.tutorsglobe.com/CMSImages/944_Construct%20the%20linear%20equation2.png)
4. Construct the weak forms of the following nonlinear equations representing the Euler-Bernoulli-von Karman nonlinear theory of beams:
![1737_Construct the linear equation3.png](https://secure.tutorsglobe.com/CMSImages/1737_Construct%20the%20linear%20equation3.png)
Hint: Look at example 2.4.3 (pg. 502) in the text to see how to find the weak forms for a system of equations.
5. Using a 2-parameter (N = 2) approximation and algebraic polynomials for the basis functions, compute the Ritz coefficients for the approximate solution to
![1548_Construct the linear equation4.png](https://secure.tutorsglobe.com/CMSImages/1548_Construct%20the%20linear%20equation4.png)