Cálculo Numerico em Python

❈♦♠♣✉t❛çã♦
❈✐❡♥tí✜❝❛
❝♦♠ P②t❤♦♥

❈♦♠♣✉t❛çã♦
❈✐❡♥tí✜❝❛
❝♦♠ P②t❤♦♥

❯♠❛ ✐♥tr♦❞✉çã♦ à ♣r♦❣r❛♠❛çã♦
♣❛r❛ ❝✐❡♥t✐st❛s
❋❧á✈✐♦ ❈♦❞❡ç♦ ❈♦❡❧❤♦

P❡tró♣♦❧✐s ✕ ❘❏

❊❞✐çã♦ ❞♦ ❆✉t♦r
✷✵✵✼

❝ ✷✵✵✼ ❋❧á✈✐♦ ❈♦❞❡ç♦ ❈♦❡❧❤♦
❚♦❞♦s ♦s ❞✐r❡✐t♦s r❡s❡r✈❛❞♦s✳
■❙❇◆✿ ✾✼✽✲✽✺✲✾✵✼✸✹✻✲✵✲✹
❈❛♣❛✿ ▼♦s❛✐❝♦ ❝♦♥str✉í❞♦ ❝♦♠ ❛s ✜❣✉r❛s ❞❡st❡ ❧✐✈r♦ ✐♠✐t❛♥❞♦ ♦ ❧♦❣♦t✐♣♦ ❞❛
❧✐♥❣✉❛❣❡♠ P②t❤♦♥✳ ❈♦♥❝❡❜✐❞♦ ❡ r❡❛❧✐③❛❞♦ ♣❡❧♦ ❛✉t♦r✱ ❝♦♠ ♦ ❛✉①í❧✐♦ ❞♦ s♦❢t✇❛r❡
❧✐✈r❡ ▼❡t❛♣✐①❡❧✳
❘❡✈✐sã♦ ♦rt♦❣rá✜❝❛✿ P❛✉❧♦ ❋✳ ❈♦❡❧❤♦ ❡ ▲✉❝✐❡♥❡ ❈✳ ❈♦❡❧❤♦✳
❊❞✐çã♦ ❞♦ ❛✉t♦r✳ P❡tró♣♦❧✐s ✲ ❘❏ ✲ ❇r❛s✐❧

Pr✐♠❡✐r❛ ❊❞✐çã♦✿

❏✉❧❤♦ ✷✵✵✼

❊st❡ ❧✐✈r♦ é ❞❡❞✐❝❛❞♦ à ♠✐♥❤❛ ❡s♣♦s❛ ❡ ♠❡✉ ✜❧❤♦✱ s❡♠
♦s q✉❛✐s ♥❛❞❛ ❞✐ss♦ ✈❛❧❡r✐❛ ❛ ♣❡♥❛✳

❆❣r❛❞❡❝✐♠❡♥t♦s
▼✉✐t❛s ♣❡ss♦❛s ❢♦r❛♠ ✐♥❞✐s♣❡♥sá✈❡✐s ♣❛r❛ q✉❡ ❡st❡ ❧✐✈r♦ s❡ t♦r♥❛ss❡
✉♠❛ r❡❛❧✐❞❛❞❡✳

❙❡r✐❛ ✐♠♣♦ssí✈❡❧ ❧✐st❛r t♦❞❛s ❡❧❛s✳

▼❛s ❛❧❣✉♠❛s

✜❣✉r❛s ❢✉♥❞❛♠❡♥t❛✐s ♠❡r❡❝❡♠ ✉♠❛ ♠❡♥çã♦ ❡s♣❡❝✐❛❧✳

❘✐❝❤❛r❞ ▼✳ ❙t❛❧❧♠❛♥✳

❙❡♠ ♦ ❙♦❢t✇❛r❡ ▲✐✈r❡ t✉❞♦ ♦ q✉❡ ❡✉ s❡✐

s♦❜r❡ ♣r♦❣r❛♠❛çã♦✱ ♣r♦✈❛✈❡❧♠❡♥t❡ s❡ r❡❞✉③✐r✐❛ ❛ ❛❧❣✉♥s ❝♦✲
♠❛♥❞♦s ❞❡ ❉❖❙✳

▲✐♥✉s ❚♦r✈❛❧❞s✳

❙❡♠ ♦ ▲✐♥✉①✱ ♥✉♥❝❛ t❡r✐❛ ♠❡ ❛♣r♦①✐♠❛❞♦ ♦ s✉✲

✜❝✐❡♥t❡ ❞❛ ♣r♦❣r❛♠❛çã♦ ♣❛r❛ ❝♦♥❤❡❝❡r ❛ ❧✐♥❣✉❛❣❡♠ P②t❤♦♥✳

●✉✐❞♦ ✈❛♥ ❘♦ss✉♠✳

▼✉✐t♦ ♦❜r✐❣❛❞♦ ♣♦r ❡st❛ ❜❡❧❛ ❧✐♥❣✉❛❣❡♠✱ ❡

♣♦r ❛❝r❡❞✐t❛r q✉❡ ❡❧❡❣â♥❝✐❛ ❡ ❝❧❛r❡③❛ sã♦ ❛tr✐❜✉t♦s ✐♠♣♦rt❛♥✲ t❡s ❞❡ ✉♠❛ ❧✐♥❣✉❛❣❡♠ ❞❡ ♣r♦❣r❛♠❛çã♦✳

❈♦♠✉♥✐❞❛❞❡ P②t❤♦♥✳

❖❜r✐❣❛❞♦ ♣♦r t♦❞❛s ❡st❛ ❡①t❡♥sõ❡s ♠❛✲

r❛✈✐❧❤♦s❛s ❛♦ P②t❤♦♥✳ ➚ ❝♦♠✉♥✐❞❛❞❡ ❞❡ ❞❡s❡♥✈♦❧✈❡❞♦r❡s ❞♦
◆✉♠♣② ❡ ❙❝✐♣② s❡❣✉❡ ✉♠ ❛❣r❛❞❡❝✐♠❡♥t♦ ❡s♣❡❝✐❛❧ ♣♦r ❢❛❝✐❧✐t❛r
❛ ❛❞♦çã♦ ❞♦ P②t❤♦♥ ♣♦r ❝✐❡♥t✐st❛s✳
❆❧❡♠ ❞❡st❛s ♣❡ss♦❛s ❣♦st❛r✐❛ ❛✐♥❞❛ ❞❡ ❛❣r❛❞❡❝❡r ❛♦ ❋❡r♥❛♥❞♦ P❡✲ r❡③ ✭❝r✐❛❞♦r ❡ ♠❛♥t❡♥❡❞♦r ❞♦ ■♣②t❤♦♥✮ ♣♦r ❡st❡ ✐♥❝r✐✈❡❧♠❡♥t❡ út✐❧ s♦❢t✇❛r❡ ❡ ♣♦r ♣❡r♠✐t✐r q✉❡ ❡✉ ✉t✐❧✐③❛ss❡ ❛❧❣✉♥s ❞♦s ❡①❡♠♣❧♦s ❞❛ s✉❛ ❞♦❝✉♠❡♥t❛çã♦ ♥❡st❡ ❧✐✈r♦✳

❙✉♠ár✐♦
❙✉♠ár✐♦

✐

▲✐st❛ ❞❡ ❋✐❣✉r❛s

✈✐✐

▲✐st❛ ❞❡ ❚❛❜❡❧❛s

①

▲✐st❛❣❡♥s

①✐

Pr❡❢á❝✐♦✿ ❈♦♠♣✉t❛çã♦ ❈✐❡♥tí✜❝❛

❉❛ ❈♦♠♣✉t❛çã♦ ❈✐❡♥tí✜❝❛ ❡ s✉❛ ❞❡✜♥✐çã♦ ♣r❛❣♠át✐❝❛✳
❉♦ ♣♦rq✉ê ❡st❛ s❡ ❞✐❢❡r❡♥❝✐❛✱ ❡♠