FM5002-HW1-1.25.12

FM5002-HW1-1.25.12 - Fin an cial Math em atics 5002 Hom...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Financial Mathem atics 5002 : Hom ework 1 (0037) Due on 25 January 2012 Scot Adams Solutions 0037 M 1 .Let f L x, y R E e 2 x M y sin L x P y R . a.Compute p p x l f L x, y Rr . b.Compute ± p p x l f L x, y Rr² x S 4, y S 4 . c.Compute p p y l f L x, y . d.Compute ± p p y l f L x, y Rr² x S 4, y S 4 . e. Compute the gradient of f (x, y) with respect to (x, y). f. Evaluate the gradient of f (x, y) with respect to (x, y) at the point (x, y) = ( Π / 4, Π / 4). g. Find the 1 - jet of f (x, y) with respect to (x, y) at the point (x, y) = ( Π / 4, Π / 4). h. Find the 1 st order Maclaurin approximation of f (x + Π / 4, y + Π / 4). i.Compute p 2 p x 2 l f L x, y . j.Compute ± p 2 p x 2 l f L x, y Rr² x S 4, y S 4 . k.Compute p 2 p x p y l f L x, y . l.Compute ± p 2 p x p y l f L x, y Rr² x S 4, y S 4 . m.Compute p 2 p y 2 l f L x, y . n.Compute ± p 2 p y 2 l f L x, y Rr² x S 4, y S 4 . o. Compute the 2 x2 Hessian of f (x, y) with respect to (x, y).
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
p. Evaluate the 2 x2 Hessian of f (x, y) with respect to (x, y) at the point (x, y) = ( Π / 4, Π / 4). q. Find the 2 - jet of f (x, y) with respect to (x, y) at the point (x, y) = ( Π / 4, Π / 4). (Use lexicographic ordering.) r. Find the 2 nd order Maclaurin approximation of f (x + Π / 4, y + Π / 4). a. P P x L f l x, y Rr E e 2 x M y Cos L x p y r p 2 e 2 x M y Sin L x p y r . b. ± P P x L f l x, y Rr² x S 4, y S 4 E 2 e Π S 4 . c. P P y L f l x, y E e 2 x M y Cos L x p y r M e 2 x M y L x p y r . d. ± P P y L f l x, y Rr² x S 4, y S 4 E Me Π S 4 . e. D f l x, y R E ³ e 2 x M y Cos L x p y r p 2 e 2 x M y L x p y r , e 2 x M y Cos L x p y r M e 2 x M y L x p y . f. D f l Π S 4, Π S 4 R E ³ 2 e Π S 4 , Me Π S 4 ´ .
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 5

FM5002-HW1-1.25.12 - Fin an cial Math em atics 5002 Hom...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online