Zvezdelina Entcheva Stankova

[zvezda]

Visiting Professor

Office:

713 Evans Hall
Department of Mathematics
University of California at Berkeley
Berkeley, CA 94720-3840

Tel: 510-642-3768
Fax: 510-642-8204
Email: stankova@math.berkeley.edu
Office Hours Tuesdays 9:30-11pm in front of 2050 Valley LSB (if all students' questions are answered before 11pm, the instructor heads back to the office: Evans 713); Thursdays, 9:30-10:50am in Evans 713.
Webpage: http://math.berkeley.edu/~stankova

Course Syllabus for MATH 16A, spring 2014:

PDF format (+ other administrative FAQ's)

For enrollment questions:

Do NOT contact the instructor or the GSIs. We have no control over enrollment. Contact instead Thomas Brown, 965 Evans.

Email is ONLY for emergencies (e.g., medical and family emergencies).

Email is NOT for resolving enrollment questions, or asking for letters, or for discussion of midterm results, or for any discussion about how the student is doing in the class or how to improve. I have received lately a number of such emails, to all of which the response is to come see me in person in office hours (bringing all necessary documentation with you). You are also welcome to visit any GSI's office hours to discuss math questions or how to improve in the course; the GSIs are very qualified to discuss any math question. This is clearly written in the syllabus and was discussed in detail during the first lecture.

Office Hours of GSIs and MATH 98 Instructors (Updated 1/30/2014):

1. Martinez, Maria, Mon 9-10:30AM, 1037 Evans.

2. Monson, David, Fri 9-10:30A, 866 Evans.

3. Safdari, Mohammad, Wed 2-3:30PM, 789 Evans.

4. Youcis, Alex, Friday 1-2:30PM, 852 Evans.

5. Zhang, Te, Wed 3:30-5PM, 1041 Evans.

6. Wong, Michael (MATH 98), Mon-Thu 10AM-4PM, 103 Chavez

7. Wiley, Joseph (MATH 98), Mon-Thu 10AM-4PM, 103 Chavez


Final Exam:

Thursday, May 15, 2014, 7-10pm, Hearst Gym, Room 220.

A note on the mortgage problem from class, Tuesday, 4/15:

The mortgage example in class yielded the formula: P(30)-P(0)=-(4.1107/0.03)(e^{0.03x30}-1)= -137 .02333... (e^{0.9}-1)= - 199.99968... As a result, P(30)=P(0)-199.99968=200-199.99968, which rounds to 0, and the balance has been paid off in 30 years.

In general, for those who are interested in how the formula for the money owed in a loan was obtained, set up P'(t)=Ae^{rt}, where r is the yearly interest rate compounded continuously, P(0) is the initial amount of loan, and A is an unknown. Since P(t) is an antiderivative of P'(t), we can calculate it: P(t)=(A/r)e^{rt}+C. To find A and C, note that P(0)=(A/r) +C, so C=P(0)-A/r. Plugging back into the formula for P(t), we have P(t)=(A/r)e^{rt}+P(0)-A/r. Finally, we want P(3)=0 so that the loan is paid off in 30 years; this leads to P(30)=0=(A/r)e^{30r}+P(0)-A/r. Solving for A yields: (A/r) (e^{30r}-1)=-P(0), i.e., A=-rP(0)/(e^{30r}-1).

In our problem, plugging in r=0.03 and P(0)=200, yields A=-0.03 x 200/(e^{0.9}-1)=-4.1107... This is how the constant -4.1107 came up in the formula in this problem, yielding the rate P'(t)=-4.1107 e^{0.03 t}.


Homework Assignments and Notes:

If not specified odd or even exercises, it is assumed only even exercises, e.g., #2-8 means 2,4,6,8. Asterisk * usually means that the problem is hard/tricky.

HW11 Solutions. HW Solutions are posted about a day before the quiz and will be taken off the web in a week. Do NOT ask for solutions to be posted earlier: you must attempt to do your homework without help from posted solutions. If you are late copying them, or you lose them, or some other thing happens: do NOT ask us for the files of the previous solution since we do NOT distribute electronic files of the HW solutions. Instead, ask your classmates for the HW solution files.

HW12B. From 6.3. The Definite Integral and Area under a Graph: (up to Theorem 2 on page 314. Explanation of Theorem 2 is for now optional.) #2,4,6,10,12,18,20,22,24,28,30,32,36,38,42,46. Bonus: #26,48*(you are allowed here to use the formula in #47).

HW12A. From 6.2. The Definite Integral and Net Change of a Function: #2,6,7,10,12,14,16,18,20,22,24,28,30,32,34,36,42. Bonus: #40,44.

HW11B. From 6.1. Antidifferentiation: #2,4,10,12,14,18,20,24,26,30,32,40,42,46,48,50,52,56,60. Bonus: #36 (what is the derivative of ln|x|?), #54, 64. For problems #26-36: first take the derivative of the right-hand side, set it equal to the function on the left-hand side, and solve for k.

HW11A. From 5.2. Compound Interest: #2,4,8,10,18,20,24,25,26,27,28. From 5.3. Applications of the Natural Logarithm Function to Economics (Read Relative Rates of Change; optional: Elasticity of Demand): #2,4,6,8,10,12.

HW10. From 5.1. Exponential Growth and Decay: #2,4,6,10,14,16,20,22,28,31.

HW9B. From 4.4. The Natural Logarithmic Function: #4,6,10,22,26,32,34,40. Bonus: #46,48. From 4.5. The Derivative of ln(x): #6,8,18,20,24,26,30,34. Bonus: #35,36. From 4.6. Properties of the Natural Logarithmic Function (Example 5 on Logarithmic Differentiation is optional): #2,4,6,8,10,12,14,18,22,32. Bonus: #52,54.

HW9A. From 4.1. Exponential Functions: #4,8,14,16,24,30,36. From 4.2. The Exponential Function e^x: #2*,4,6,8,14,17,24,26,32,36,42. From 4.3. Differentiation of the Exponential Functions: #4,10,14,16,18,20,24,26,32 (graph the function in #32 too, investigate with a table what is happening with f'(x) and f"(x) in order to understand what the graph of f(x) looks like), #34,36. Bonus: #40*.

HW8B. From 3.3. Implicit Differentiation and Related Rates: #2,4,8,12,14,16,18,22,24,26,28,30,36,38,42,46. Bonus: #47*,48*.

HW8A. From 3.2. The Chain Rule and the General Power Rule: #2,4,8,16,20,24,30,36,40,41,46,50. Bonus: #56,58.

HW7B. From 3.1. The Product and Quotient Rules: #2,4,6,8,10,12,14,18,22,26,28,30,32,34,38,42,44,46,48,60,62,64. Bonus: #36,65,66.

HW7A. From 2.6. Further Optimization Problems: #2,4,6,10,12,14,16,18,20,22,26,27,28. From 2.7. Applications of Derivatives to Business and Economics: #2,4,6,10,12,14,18. Bonus: #19,20,21.

HW6B. From 2.4. Curve Sketching (Conclusion): #7,8,16,20,24,26,28,30,32,34. Bonus: #34,36. From 2.5. Optimization Problems: #2,4,6,8*,10,13,16,20,24,26. Bonus: #30,31.

HW6A. From 2.2. The First- and Second-Derivative Rules: #2,4,6,12,18,20,24,40,42,44. From 2.3. The First- and Second-Derivative Rules and Curve Sketching: #6,10,16,24,26,30,32,34,36,42. Bonus: #44,46.

HW5. From 2.1. Describing Graphs of Functions: #2,4,6,8,10,12,14,16,18,22,24,26,28,32,34,35,37,39. Bonus: #31,40.

HW4B. From 1.7. More About Derivatives (starting from "The Derivative as a Rate of Change"): #39,40,41,42,44,45,46,48. Bonus: #49,50. From 1.8. The Derivative as a Rate of Change: #4,6,8,10,12,14,16,18,20,26,28. Bonus: #30,32.

HW4A. From 1.6. Some Rules for Differentiation: #14,16,20,24,26,30,32,34,38,44,48,52,54. Bonus: #46,56. From 1.7. More About Derivatives (Read up to "The Derivative as a Rate of Change", p. 106): #8,10,16,20,22,24,28,30,32. Bonus: #34,36.

HW3B. From 1.4. Limits and the Derivative: #62,64,66 (in these problems, it is good to start by plugging in very large, or negatively large, numbers for x to see what is going on; in #66 specifically, divide everything by x^2 and then plug in some very large numbers for x to see what happens), bonus: #56,58,60. From 1.5. Differentibility and Continuity: #1-12 (both odd and even),#16,18,20,22*,24,26*,34; bonus: #31,32.

HW3A. From 1.3. The Derivatives and Limits: #8,14,16,18,24,26,30,38,42,44,46,56, bonus: #48,60*. From 1.4. Limits and the Derivative: #10,12,14,18,20(factor!),34,40,44,46,50, bonus: #48*, 54*.

HW2B. From 1.1. The Slope of a Straight Line: #6,8,10,14,16,18,20,24,26*,32,40,52 bonus: #46,58. (In #24: two lines with perpendicular slopes have negative reciprocal slopes, e.g., 2 and -1/2). From 1.2. The Slope of a Curve at a Point #8,12,14,16,18,20,22,24,37, bonus: #32,38. (In #32, read carefully and use the given information right before Exercise 29.)

HW2A. From 0.5. Exponents and Power Functions: #30,48,50,66,68,70,72,86,94,104, bonus: #106, 108*. From 0.6. Functions and Graphs in Applications: #10,16,18,22,24,37,38,39,40, bonus: #45,46,47,48,49,50.

HW1B. From 0.3. The Algebra of Functions: #20,24,28,32,34,36,38,40 (do NOT use a graphing calculator for #38 and #40), bonus: #37,42 (again, try this without a graphing calculator). From 0.4. Zeros of Functions -- The Quadratic Formula and Factoring: #8,10,20,28,34,40,42, bonus: #44,46.

HW1A. From 0.1. Functions and Their Graphs: #10,18,20,23,24,32,56; bonus: #52,58. From 0.2. Some Important Functions: #8,12,16,32,36; bonus: #22,24.


Berkeley Math Circle

http://mathcircle.berkeley.edu