Calculus for Biology and Medicine MAT 17B (Fall 2012)
MWF 11:00 - 11:50 am, GEIDT 1002

GENERAL INFORMATION

Instructor : Amitabh Basu
Office Hours : Monday 3-4pm, Wednesday 3-4pm, email for appointment. Office Hours will be in my office : Mathematical Sciences Building (MSB) 3111.
Email : abasu [at] math [dot] ucdavis [dot] edu
Teaching Assistant : Sections A01, A02 - Joohee Hong. Her email is : jhong [at] math [dot] ucdavis [dot] edu. Joohee's office hours will on Tuesdays and Thursdays, 2-3pm in MSB 3137.
Section A03 - Rebecca Starr. Her email is : rstarr [at] math [dot] ucdavis [dot] edu. Rebecca's office hours will be on Tuesdays from 10 - 11 am, in MSB 2232.
Text : Calculus for Biology and Medicine, by Claudia Neuhauser, 3rd Edition.
Syllabus and Schedule : We will follow the department syllabus.

ANNOUNCEMENTS

• Practice Midterm I has been put up. Please see below under "Midterms and Final".
• FINAL INFORMATION : Date : Thursday, December 13, 2012. Time : 1:00pm - 3:00pm. Venue: YOUNG 198.

LECTURE NOTES

• Slides from lecture on Friday, November 9, 2012. This covers Section 9.1 from the book.

There will be 2 in-class examinations (Midterm I and Midterm II) and a Final exam. In addition, there will be Quizzes during the Discussion sessions. Homework will be assigned after every lecture, but will not be graded. You will be graded based on the Quizzes, Midterms and Finals based on the weightage listed below under "Grades".

Homeworks
• HW1 (Friday, September 28, 2012) :
Problems on page 272 (Section 5.8) from textbook : Problems 3, 9, 11, 15, 19, 20, 21, 23, 27, 29, 31, 32, (The next set of problems is asking for the particular antiderivative - "initial value problem" is a fancy way to say "particular antiderivative") 61, 63, 69, 71.
HW 1 Solutions. Missing pages for Problems 63 and 69.
• HW2 (Monday, October 1, 2012) :
Problems on page 291 (Section 6.1) from textbook : Problems 1, 5, 6, 7, 13, 20, 21, 34, 35, 36.
HW 2 Solutions.
There is a typo in HW 2 Solutions on Problem 20. k should start from 0 and not 1.
• HW3 (Wednesday, October 3, 2012) :
Problems on page 305 (Section 6.2) : Problems 41, 43, 45, 47, 51, 55, 56, 62, 65, 67, 70 (Hint : Use trig identities : sin^2 + cos^2 = 1, cos/sin = cot, 1/sin = csc), 73, 75, 76, 82, 95, 102, 103, 110, 111, 119.
HW 3 Solutions.
• HW4 (Friday, October 5, 2012) :
Problems on page 321 (Section 6.3) : Problems 1, 3, 4, 5, 6, 7, 8, 9, 11 (Careful with this one - the order of the functions changes at x = 1), 12.
HW 4 Solutions. Missing page after Solution to Problem 5.
• HW5 (Monday, October 8, 2012) :
Problems on page 322 (section 6.3.3): Problems 25, 26, 27 b), 32 b), 32 c).
Probems on page 322 (section 6.3.4): Problems 36, 37, 38, 39, 40, 43.
Also find the volumes of the solids of revolution formed by rotating the regions in Problems 6, 7, 10 on page 321.
HW 5 Solutions.
There is a typo in the solution to #36. (sqrt(2x))^2 = 2x, and not 2x^2 like in the solutions. The final antiderivative should be simply "\pi x^2". So the final answer should be "\pi 2^2 - \pi 0^2 = 4\pi".
• HW6 (Monday, October 10, 2012) :
Problems on page 333 (Section 7.1): Problems 2, 3, 6, 7, 9, 11, 12, 13, 14, 15, 18, 21, 25, 27, 28, 29, 30, 32, 33, 35, 47, 48, 52, 56, 59.
HW 6 Solutions. HW 6 Solution to Problem 52 on page 334.
There is a typo in the solutions for HW 6. On Problem 27, the final answer is "-cot(ln(x)) + C" and not "-cos(ln(x))+C".
Another typo on HW 6 : On Problem 15, the final answer should be 3(x+4) - 12ln|x+4| + C. I forgot to distribute the 3 completely.
• HW7 (Friday, October 12, 2012) :
Problems on page 342 (Section 7.2) : Problems 2, 7, 10, 12, 13, 16, 22, 23.
Problems on page 343 (Section 7.2) : Problems 40, 41, 42, 44, 47, 70.
HW 7 Solutions - I. HW 7 Solutions - II.
There are three typos in these solutions. In Problem #2, there should be a 3 in front of the answer : so the correct answer is 3xsinx + 3cosx + C. The second error is in Problem 22. The second term (2/9) is erroneously computed as (4^(3/2)) = 8/9, whereas (4^(3/2)) = 16/9. So the final answer should be : ((16ln2)/3) - (14/9). The third error is in the solution to Problem 41. There should be a 2 in front of the second term in the final answer : The right answer is -x^2e^{-x^2/2} - 2e^{-x^2/2} + C.
• HW8 (Monday, October 15, 2012) :
Problems on page 350-351 (Section 7.3) : 5, 6, 9, 10, 11, 13, 15, 16, 29, 31. Also do Problems 1, 2, 4, 17, 18, 33, 35, 36, 38, 50 (in this last one, the denominator factorizes into linear terms - it is not a problem with irreducible quadratic terms).
HW 8 Solutions. There is a typo in Problem 2. I forgot to take the (-) sign in the beginning. The final answer should be 3 - x + (4/(x-1)); this is the negative of the answer I put up.
• HW9 (Monday, October 22, 2012) :
Problems on page 351 (Section 7.3) : Problems 19, 20, 23, 25, 26, 32, 34, 39, 52.
HW 9 Solutions
• HW10 (Wednesday, October 24, 2012) :
Problems on page 362 (Section 7.4) : Problems 2, 4, 9, 10, 11, 12, 13, 14, 16, 17, 19, 22, 25, 26, 29, 31.
HW 10 Solutions.
• HW11 (Friday, October 26, 2012) :
Problems on page 370 (Section 7.5) : Problems 1, 3, 4, 6, 9, 11, 12, 15.
Problems on page 381 (Section 7.6) : Problems 6, 7, 9, 10, 13, 14, 16, 19, 21, 22.
Solutions to Section 7.5, Solutions to Section 7.6.
There is a typo in the solution to Problem 9 on page 370. In the final answer, the first term in the paranthesis should be 1/2 instead of 1.
There is a typo in the solution to Problem 14 on page 381. The final term should have 24 in the denominator, and not 120.
There is a mistake in the solution to Problem 13 on page 382. You should use x=1 to evaluate the polynomial, instead of x=0.1 as done in the solutions.
• HW12 (Monday, October 29, 2012) :
Problems on page 404 (Section 8.1) : Problems 9, 10, 11, 12, 16, 20, 21 (Part b. is canceled - only do Part a. of Problem 21), 22 (No need to sketch the graph in Part b.), 27, 29, 30, 36, 39 a), 42 (Part b is canceled - only do Part a.of Problem 42), 45, 47, 48, 49.
HW 12 Solutions.
There is an error in the solution of Problem 30. Please see the new solution here.
• HW13 (Wednesday, October 31, 2012) :
Problems on page 417 (Section 8.2) : Compute the equilibrium points and discuss their stability for Problems 1, 2, 3, 4, 6, 10. Ignore the different parts in the problems - only compute the equilibrium points and discuss their stability.
HW 13 Solutions.
There is an error in the solution of Problem 10 with the calculation of the stability of the equilibrium points. the correct solution is here.
• HW14 (Friday, November 2, 2012) :
Problems from the notes on FOLDE : Problems 2, 4, 6, 10, 12, 18, 27, 31, 32, 34.
HW 14 Solutions.
There is an error in the solution to Problem 34. I took the function Q(x) = 1/x^2. But it should be 10/x^2. Consequently, the general solution should be y = 10/3x + C/x^4. Using y=10, x = 1, we should then get C = 20/3. So the final solution would be (10x^3+20)/3x^4.
There is another error in Problem 34. P(x) should be taken as -4/x. This completely changes the final answer. The final answer should be y = 2/x + 12x^4.
• HW15 (Monday, November 5, 2012) :
Problems from these problems : Problems 28, 29, 31.
Solutions. There is an error in the solution to Problem 31. The correct solution is here. There is also an error in Problem 29. The integral in Step 3 of applying the FOLDE technique should be 50e^{t/20}. Consequently, the final answer for A(t) = 50 - 50e^{-t/20} and at t=30, the answer should be 50 - 50e^{-30/20}.

Also do all problems from this worksheet. Ignore the parts 1a), 3c) and 4c). DISCLAIMER : These problems have been borrowed from Prof. Duane Kouba in the math department at UC Davis.
Solutions to the worksheet.

• HW16 (Friday, November 9, 2012) :
Problems on page 443 : Problems 9, 10, 13, 16, 17, 20, 21, 23, 25, 26, 28.
HW 16 Solutions. There is an error in the solution to Problem 20. I made a mistake while eliminating 'x' from the 3rd equation. I should have obtained the last equation as "-5y+z = -7", instead of "-5y - z = -7". The correct final solution is "x = 1, y = 2, z = 3".
There is an error in Problem 28 also. The final value of y is computed incorrectly. The correct solution is x = 0, y = 2, z = -1.
• HW17 (Friday, November 16, 2012) :
Problems on page 465 : Problems 7, 9, 10, 14, 15, 21, 23, 24, 25, 27, 28, 29, 31, 34.
HW 17 Solutions.
There is an error in the solution to Problem 9. The entry in the first column and first row should be 19, and not 21.
There is an error in the solution to Problem 31 b). The entry in row 2, column 2 should be 4. Thanks to an anonymous feedback for pointing it out !
• HW18 (Monday, November 19, 2012) :
Problems on page 466: 45, 46, 49, 50 (we have not done the formula for inverses of 3x3 matrices. But for Problem 50, guess what the inverse should be from what we have learnt and show that your guess is indeed correct.), 53-56, 59-62.
HW 18 Solutions.
• HW19 (Wednesday, November 21, 2012) :
Problems on page 466 : Problems 39, 40, 41, 42, 43, 44.
HW 19 Solutions.
There is an error in Problem 40. In the first matrix, the entry in (row 2, column 3) should be switched with (row 2, column 2). Thanks to an anonymous feedback for pointing this out !
• HW20 (Monday, November 26, 2012) :
Problems on page 486 : Problems 3, 8, 9, 17, 22, 24, 28, 32, 33, 34.
HW 20 Solutions.
• HW21 (Wednesday, November 28, 2012) :
Problems on page 487 : Problems 41, 42, 45, 46.
HW 21 Solutions.
• HW22 (Friday, November 30, 2012) :
Problems on page 487 : Problems 52-55 (for Problems 52-55 you do not have find the equations of lines in the direction of the eigenvectors), 57-60.
HW 22 Solutions. Problem 54, the last line should read " .. is an eigenvector with eigenvalue 2", instead of -3. Thanks to an anonymous feedback for pointing this out.
• HW23 (Monday, December 3, 2012) :
Problems on page 500 : Problems 7-10, 15-26.
Solutions.
Problems on page 500 : Problems 31b), 32b), 33, 34.
Solutions. Second page to Problem 31b).
• HW24 (Wedneday, December 5, 2012) :
Problems on page 500 : Problems 35-42.
HW 24 Solutions.
• Homework will be assigned after every lecture. These will not be graded. However, it is highly recommended that you work through your homework problems and clarfiy any doubts related to them during Discussion session or Office Hours. Homeworks develop your problem solving skills and this will be crucial to your success in this course.
• You are allowed to consult your fellow classmates on the Homeworks.
• Calculators may be used for your Homeworks. They are NOT allowed in any of the Midterms or the Final.
Quizzes
• Solutions to Quizzes : Quiz 1, Quiz 2, Quiz 3, Quiz 4, Quiz 5, Quiz 6, Quiz 7, Quiz 8.
• A quiz will be administered on most Discussion sessions. If there is no quiz on a particular Discussion session, this will be announced sufficiently ahead of time.
• Your lowest Quiz grade will be dropped when computing the contribution from Quizzes to the final grade.
• All quizzes will be closed book. Calculators are not allowed.
Midterms and Final