Föreläsning 10

Lärare: Lars Bergqvist

Innehåll: Integraler, fortsättning

Litteratur: Adams 7.1, 7.3, 7.7 samt 7.9

Nyckelbegrepp

Volymsintegraler: kurva som roterar runt x-axeln

https://www.khanacademy.org/math/integral-calculus/solid_revolution_topic/disc-method/v/disk-method-around-x-axis

Volymsintegraler: kurva som roterar runt y-axeln

https://www.khanacademy.org/math/integral-calculus/solid_revolution_topic/disc-method/v/calculating-integral-disc-method-around-vertical-line

"Skivor" respektive "cylindriska skal"

Kurvlängd (arc length)

http://ocw.mit.edu/courses/mathematics/18-01sc-single-variable-calculus-fall-2010/unit-4-techniques-of-integration/part-b-partial-fractions-integration-by-parts-arc-length-and-surface-area/session-78-computing-the-length-of-a-curve/

Ytintegral: kurva som roterar runt x- eller y-axeln

http://ocw.mit.edu/courses/mathematics/18-01sc-single-variable-calculus-fall-2010/unit-4-techniques-of-integration/part-b-partial-fractions-integration-by-parts-arc-length-and-surface-area/session-79-surface-area/

Tillämpningar inom ekonomi, finans, ekologi

Första ordningens differentialekvationer

https://www.khanacademy.org/math/differential-equations/first-order-differential-equations

Separabel differentialekvation

https://www.khanacademy.org/math/differential-equations/first-order-differential-equations/separable-equations/v/separable-differential-equations

Första ordningens linjär differentialekvation