ESO 208A: Computational Methods in Engineering Major Quiz 2 Duration: 40 min 02.11.19 Name: Roll No: Section: Instructions: Show all calculations. An answer, without any supporting calculations, will bear zero credit even if it were correct. No credit for solving by any other method than asked. Perform calculations using infinite precision but report your intermediate calculations upto 4 significant digits with rounding. Q1. [9+7] Derive the finite difference approximations for 𝑓 ? ′ and 𝑓 ? ′′ in terms of 𝑓 ? , 𝑓 ?−1 and 𝑓 ?+1 using the method of undetermined coefficients. What are the orders of inaccuracies of these approximations? Sol: This problem is a direct application of the method of undetermined coefficients discussed extensively in class and through a tutorial problem also given. Students were expected to demonstrate that understanding. Any other way of determining the FD approximations such as the use of Lagrange polynomial will bear no credit.