Math 141B Syllabus Spring 2008 Mathematics for the Biological Sciences Instructor: Dr. M. Fabbri, McAllister 409 Website: www.math.psu.edu\ fabbri Text: Calculus for The Life Sciences Bittinger, Brand and Quintanilla 1st Ed. 2006, Pearson Addison Wes
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MATH 141B Instructor: Dr. M.Fabbri
Midterm#1 Solutions
Date: Feb 19, 2008
1. (This is #15 Ver B) Compute the integral first, evaluate later. Let u = 4x and dv = e2x dx. Then du = 4 dx and 1 v = 2 e2x . Hence, 4xe2x dx = Evaluating, gives
0
u d
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MATH 141B
QUIZ#8 Solutions c-2 dc =
Date: Tues March 25, 2008
1. Separating and integrating gives -20
20 dt, or = t + K, where K is a constant. c c 1 20 = t + 200 and hence = . Since c(0) = 0.1 = 1/10, we get K = 200. Therefore, c 20 t + 200 2
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MATH 141B
QUIZ#1
Due: Tues Jan 22, 2008
Instructor: Dr. Fabbri
Duration: 15 minutes x2 cos x dx and circle the correct answer below.
0
[ 2 ] 1. Compute the definite integral
A) -2,
B) ,
C) -,
D) 2
E) none of the above
1 [ 2 ] 2. If f
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MATH 141B
Quiz#8
Due: Tues March 25, 2008
[ 2 ] 1. At high temperatures nitrogen dioxide NO2 decomposes into NO and O2 . If c(t) denotes the concentration of NO2 , then (at 600 K) c(t) changes according to the separable differential equation dc
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MATH 141B
Quiz#7
Due: Tues March 18, 2008
More interesting and realistic models take some time to set up. However, since I've clearly laid things out, you'll simply be going through the 7-step method to solve a linear differential equation, and
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MATH 141B Instructor: Dr. M.Fabbri
QUIZ#1 Solutions
Due: Tues Jan 22, 2008
Duration: 15 minutes 1. First let's compute the corresponding indefinite integral, and then do the evaluation. If u = x2 and dv = cos x dx then du = 2x dx and v = sin x.
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MATH 141B Print Name: Instructor: Dr. Fabbri
Quiz#2
Version A
Due: Tues Jan 29, 2008
[ 2 ] 1. By analyzing the matrix dimensions, which of the following statements are true? i) Suppose that A is a (5 2)-matrix and C is a (4 3)-matrix. If B i
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Date: Feb 19, 2008 MATH 141B EXAMINATION 1 Print NAME: STUDENT NUMBER:
FORM B
There are 16 multiple choice questions each worth 5 points. The remaining 20 points are long answer questions on the last two pages. For each multiple choice answer, ci
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MATH 141B
Quiz#4
Date: Mon Feb 12, 2008
Instructor: Dr. Fabbri [ 2 ] 1. Consider the matrix A = -3 2 . Which of the following 3 statements are true? 1 -4
i) A has characteristic equation r 2 - 7r + 10 = 0. ii) A has two distinct eigenvalues. i
MATH 141B 1. Integration by Parts The formula is:
Exam 1 Overview
u dv = uv - We first applied this to the two classes of integrals: xn emx dx and
v du
xn sin(mx) dx,
In both cases, n is allowed to be any natural number, and m any real number.
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Date: Feb 19, 2008 MATH 141B EXAMINATION 1 Print NAME: STUDENT NUMBER:
FORM A
There are 16 multiple choice questions each worth 5 points. The remaining 20 points are long answer questions on the last two pages. For each multiple choice answer, ci
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MATH 141B
Quiz#9
Due: Friday March 28, 2008
[ 2 ] 1. Consider the initial value problem y + y - 12y = 0 y(0) = 1, y (0) = -1
The homogeneous differential equation has general solution has the form yh = c1 er1 x + c2 er2 x , where r1 and
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MATH 141B
Quiz#6
Due: Tues March 4, 2008
[ 2 ] 1. Find the maximum value of the function f (x, y) = 9 - 2x + 4y - x2 - 4y 2 .
A) z = 3,
B) z = 5,
C) z = 10,
D) z = 11,
E) none of the above
[ 2 ] 2. For the function f (x, y) = x4 + y 4 - 4
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MATH 141B
QUIZ#7 Solutions
Date: Tues March 18, 2008
1. V = 100 and F = 25, so F/V = 1/4. Since I = c F = (0.1)(25) = 2.5, the differential 1 1 1 1 equation is y - 4 y + 2.5. In standard form, we get y + 4 y = 5 . Now, F (t) = 4 dt = 4 t, 2
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MATH 141B Instructor: Dr. M.Fabbri
QUIZ#3 Solutions
Date: Tues Feb 5, 2008
1. i) False. Adding the first two columns as the 4th and 5th columns we get the matrix: a-1 1 0 a-1 1 1 -2 a + 2 1 -2, 3 0 a 3 0 Now using the method of diagonals to com
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MATH 141B Print Name: Instructor: Dr. Fabbri
Quiz#3
Date: Tues Feb 5, 2008
a-1 1 0 -2 a + 2 , where a is a real number. Which of the following [ 2 ] 1. Consider the matrix 1 3 0 a statements are true? i) det A = 2a2 + 4a + 6. ii) A is an inv
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MATH 141B Instructor: Dr. M.Fabbri
QUIZ#5 Solutions
Date: Fri Feb 15, 2008
1. i) False. V (r, h) = r 2 h, whose graph is not a cylinder. An equation involving r, h and V whose graph in 3-space (with axes r, h and V ) is a cylinder is h2 + r 2 =
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MATH 141B
QUIZ#6 Solutions
Date: Tues March 4, 2008
1. fx = -2 - 2x = 0 when x = -1 and fy = 4 - 8y = 0 when y = 1/2. We need to test the point (-1, 1/2). fxx = -2, fyy = -8 and fxy = 0. Therefore, D = (-2)(-8) - 02 = 16 > 0. Finally, since fxx
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MATH 141B Instructor: Dr. Fabbri
Quiz#5
Due: Fri Feb 15, 2008
[ 2 ] 1. A suitable model for the bacteria bacillus subtilis is a cylinder with radius r and height h. Then the volume, V (h, r), of such a cylinder is a function of two variables. W
MATH 141B 1. Integration by Parts The formula is:
Overview
u dv = uv - We first applied this to the two classes of integrals: xn emx dx and
v du
xn sin(mx) dx,
In both cases, n is allowed to be any natural number, and m any real number. The la