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1. FUNÇÕES DE VÁRIAS VARIÁVEIS1. FUNÇÕES DE VÁRIAS VARIÁVEIS
2. LIMITES PARA FUNÇÕES DE DUAS 2. LIMITES PARA FUNÇÕES DE DUAS
VARIÁVEISVARIÁVEIS
3. DIFERENCIAÇÃO PARCIAL3. DIFERENCIAÇÃO PARCIAL
4. GRADIENTE E DERIVADA DIRECIONAL4. GRADIENTE E DERIVADA DIRECIONAL
P1
P2
P1 – 08/04 AG – 20/05 P2 – 03/06 PS – 10/06
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1. Atividade em Grupo (AG) - 10% média
2. Prova integrada (PI) – 20% da média
3. Provas individuais – 70% da média
P1 – 09/04 AG – 07/05 P2 – 04/06
Cálculo da média semestralCálculo da média semestral
MS = AG + PI + MP onde MP = (P1 + P2 )/2
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M 6 – APROVADO
3 M< 6 – EXAME
M < 3 - REPROVADO
DATA DO EXAME – 24/06
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FUNÇÃO REAL DE UMA FUNÇÃO REAL DE UMA VARIÁVEL REALVARIÁVEL REAL
LIMITESLIMITES
DERIVADDERIVADASAS
y = y = f(x)f(x)
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y = x2
y = f(x)
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x
y A = x.yA = x.y
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x
y A = f(x, y)A = f(x, y)
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x
y f(x, y) = x.y
f(2,3) = 6f(2,4) = 8
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z = x.y
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y = x2
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y = y = xx22
y’= 2xdy/dx = 2xdy/dx = 2x
z = x.yz = x.y
PARA QUE PARA QUE
SERVE ESSA SERVE ESSA
TAL DE TAL DE
DERIVADA?DERIVADA?
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INTERAÇÃO ENTRE DOIS CORPOS
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TÚNEL DE VENTO NO CTA
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TÚNEL DE VENTO NO CTA
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COMO FUNCIONA O AVIÃO ?
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COMO FUNCIONA O AVIÃO ?V
P
V
P
TEOREMA DE BERNOULLI
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PARA COMPREENDER TODOS OS
FENÔMENOS DE TURBULÊNCIA
TERÍAMOS QUE RESOLVER A
SEGUINTE EQUAÇÃO DIFERENCIAL:
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vpvvt
v).().(
DERIVADA DIRECIONAL
GRADIENTE
PRODUTO ESCALAR
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PESADELO MATEMÁTICO . . .