Problem 1 (50%)
ENEG4210 Optimization of Energy Systems
Homework 1 Due March 7th 2022
a) Use the complex-step method to compute the 2nd derivative of a function 𝑓(𝑥);
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b) Use central finite differences to compute the second derivative;
c) Construct a convergence plot as in Fig. 2.4 at page 26 of the textbook.
[Hint: use the function 𝑓(𝑥) = sin 𝑥 at 𝑥 = 1 for the computations] 2
Problem 2 (50%)
Consider a function 𝑓(𝑥, 𝑦) = sin (𝑥 + 𝑦2). Use Complex-Step Method to compute the gradient, Hessian; then compute the convergence plots for the function. [hint: use x=1; y=1]
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