Laplace Transform. Solve the following differential equation completely. y"+y=1+2t³ et Incorporate the following theorems and techniques at least once in your solution: Linearity of Laplace transforms First shifting theorem Laplace transforms of derivatives. Derivatives of Laplace transforms Convolution theorem ●

Laplace Transform. Solve the following differential equation completely. y"+y=1+2t³ et Incorporate the following theorems and techniques at least once in your solution: Linearity of Laplace transforms First shifting theorem Laplace transforms of derivatives. Derivatives of Laplace transforms Convolution theorem ●

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter9: Multivariable Calculus

Section9.4: Total Differentials And Approximations

Problem 22E: Multivariable Calculus Total Differentials and Approximations LIFE SCIENCE APPLICATIONS Horn Volume...

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Plant Growth Researchers have found that the probability P that a plant will grow to radius R can be described by the differential equation dPdR=4DRP2 where D is the density of the plants in an area. Source: Ecology. Given the initial condition P(0)=1, find a formula for P in term of R.
Multivariable Calculus Total Differentials and Approximations LIFE SCIENCE APPLICATIONS Heat Loss In Exercise 50 of Section 2 of this chapter, we found that the rate of heat loss in watts in harbor seal pups could be approximated by H(m,T,A)=15.2m0.67(TA)10.23lnm10.74 Where m is the body mass of the pup in kg, and T and A are the body core temperature and ambient water temperature, respectively in C. Suppose m is 25kg, T is 36.0, and A is 12.0, Approximate the change in H if m changes to 26kg,T to 36.5 and A to 10.0.
Find the general solution for each differential equation. Verify that each solution satisfies the original differential equation. dydx=tanxcos2y
Multivariable Calculus Total Differentials and Approximations LIFE SCIENCE APPLICATIONS Blood Volume In Exercise 52 of Section 2 in this chapter, we found that the number of liters of blood pumped through the lungs in one minute is given by C=bav Suppose a=160,b=200 and v=125. Estimate the change in C if a becomes 145,b becomes 190, and v changes to 130.
Van der Waals Equation In Exercise 18 at the end of Section 2.3, we discussed the ideal gas law, which shows the relationship among volume V, pressure p, and temperature T for a fixed amount 1 mole of a gas. But chemists believe that in many situations, the van der Waals equation gives more accurate results. If we measure temperature T in kelvins, volume V in liters, and pressure p in atmosphere 1 atm is the pressure exerted by the atmosphere at sea level, then the relationship for carbon dioxide is given by p=0.082TV0.0433.592V2atm What volume does this equation predict for 1 mole of carbon dioxide at 500 kelvins and 100 atm?Suggestion: Consider volumes ranging from 0.1 to 1 liter.
Multivariable Calculus Total Differentials and Approximations LIFE SCIENCE APPLICATIONS Horn Volume The volume of the horns from bighorn sheep was estimated by researchers using the equation V=h3(r21+r1r2+r22) where h is the length of a horn segment in centimeters and r1 and r2 are the radii of the two ends of the horn segment in centimeters. Source: Conservation Biology. a. Determine the volume of the segment of horn that is 40cm long with radii of 5cm and 3cm, respectively. b. Use the total differential to estimate the volume of the segment of horn if the horn segment from part a was actually 42cm long with radii of 5.1cm and 2.9cm, respectively. Compare this with the actual volume.