Date: Thu, 17 Oct 102 22:51:07 +0800 (EAT) From: wangwc@math.nthu.edu.tw To: wangwc@math.nthu.edu.tw Subject: homework for chap3 3.6: 22, 26, 34, 38, 44, 58 3.7: 20, 34, 51 3.8: 11, 12, 22(write formula only), 24(read only) Chap3: 90 Date: Wed, 13 Nov 102 04:25:02 +0800 (EAT) From: wangwc@math.nthu.edu.tw To: wangwc@math.nthu.edu.tw Subject: HW Chap 6 Dear class: Here are some guideluines for the midterm: Chap 4: Only 4.2-4.5 Chap 6:The materials on Chap 6 contains 3 parts: (a)The elementary and algrbraic properties of Transcendental functions. (b)Dereivatives of Transcendental functions. (c)Integration of Transcendental functions. Basicly (a) is high school material except perhaps the hyperbolic functions. We will only exam on (b) and those of (a) needed in the derivation of derivatice of Transcendental functions (like cosh^2 x - sinh^2 x = 1) A good practice for Chap 6 is try to write down by yourself the the derivatives of Inverse trigonoetric functions and hyperbolic and inverse hyperbolic functions. Also th best overall practice is to mix all the functions you have learned and try to get derivatives. In other words, if you know how to take derivatives of these functions, you are fine. The following HW's will be reviwed on Friday's extra recitation course, so work hard and ask qustions on Thursdays and Fridays. Good luck. 6.1: 46,48,60,66 6.2: 28(c) 6.3: 78, 85-90. 6.4: Integration, skip. 6.5: Elementary application for exponential functions, will not exam. 6.6: 28, 33, 37-46, 48, 52, 54 6.7: 7, 8, 12, 17(a) (Only need to study on little o and big O and Example 7-9.) 6.9: 14,16,22,70,72 6.10: 10,12,28,29. Date: Thu, 21 Nov 102 17:02:39 +0800 (EAT) From: wangwc@math.nthu.edu.tw To: wangwc@math.nthu.edu.tw Subject: Homeworks Dear class: Here are the HW's for this week. You can skip section 5.1. 4.6: 25, 26, 28, 30 5.2: 34, 36, 46, 48 Additional: Here I use \sum_{k=1}^n to mean n ___ \ / --- k=1 Problems: (1) \sum_{k=1}^n 1 = ? (2) \sum_{k=1}^n n = ? (3) we know from class that \sum_{k=1}^n k^3 = (1/4) n^4 + O(n^3) repeat the procedure in class to calulate the O(n^3) exactly. 5.3: 2, 35, 36, 40, 45 5.4: 6, 12, 14, 20, 56, 66, 70, 74 Optional: It is easy to see that the definite integral of sin(x) from 0 to pi(3.14159...) is cos(0) - cos(pi) = 2 According to the definition on page 287, formula (10) Can you find a \delta with \epsilon = 0.01? (Hint: section 4.6, problem 26) Date: Fri, 29 Nov 102 14:50:37 +0800 (EAT) From: wangwc@math.nthu.edu.tw To: wangwc@math.nthu.edu.tw Subject: Homework 5.5: 8,10,12,14,24,45,50,54 5.6: 53,54,56,58,74 6.4: 10,26,19,48,70,78,79 6.9: 52,54,56,58,64,68,80 We'll skip 5.7. Next Tuesday, we'll continue on 6.10 and then Chap 7. Date: Sun, 29 Dec 102 15:46:36 +0800 (EAT) From: wangwc@math.nthu.edu.tw To: wangwc@math.nthu.edu.tw Subject: hw for chap 8 Dear class: Tuesday is the final class and we will talk about the Improper integrals (8.6). We'll only give very dhort introduction on (8.5). No class on Thursday. As a practice for the techniques of integration (8.2, 8.3 and 8.4), I suggest you practice on the problems on page P554: 129, 131, 133, ... upto 193. These problems are ordered randomly, mixing the techniques in 8.2-8.4 together. Do as many problems as you can. You can find the solutions for these problems at the back of the textbook. Tuesday evening is the final class of problem session, if you still have difficulties on these probelms (or other parts), you can ask the TA then. You don't need to give these homework problems to the TA. Dear class: The homework policy for this semester is as follows: On the homework session, you need to prepare for the homework assignments first. The TA will either ask you to do the problems, and/or, if most people have difficulties, explain those harder problems. Afterwards, everybody has to write up the homeworks and give it to the TA next time. The complete solution will then be posted on the course homepage. Most of the quiz problems will be from the homeworks. The homework grade will consist of 2 parts. (A) How many problems you have written. (B) The TA will randomly choose some problems to check if you have done it correctly. (Since obviously, the TA cannot grade every problem for everyone) There is a also a schedule change this week. I have to travel on Thursday so I will lecture on Tuesday morning 10-12 AM AND 6-7 PM. We will have homework session at Tuesday 7-8 PM (by me) AND Thursday 10-11 AM (by TA). The homeworks for 9.1-9.3 are 9.1: 8, 36, 57, 59, 60, 66 71(bcde), 72(be) 9.2: 14,20,34,62,63 9.3: 23,24,28,40,41,48,61,62(a,b) Please first prepare section 9.1-2 for Tuesday 7-8 PM. The TA will continue on Thursday and you can give them (9.1-9.3) to TA next Tuesday 6 PM. 9.4: 2, 6, 14, 24, 28, 30, 39, 40, 41, 44(+ Does it converge? Why?) 9.5: 4, 24, 25, 33, 46, 48. 9.6: 12, 16, 21, 27, 28, 35, 36, 38, 41, 43, 44, 45, 46, 47 Additional: Does problem 36 contradicts Theroem 11? Why? 46: d) find a power series that converges on [-1,1) and diverges elsewhere. e) same for (-1,1] 9.7: 1,3,7,25,29,33,50,54,57,58 9.8: 10,14,28,29,31,32,33,34(a) Chap 9: 27,28,2930,32,34,49-54. Dear class: I have further simplified the plan for Chap 10. The key issue here is the calculus of parametrized curves (10.4) and integration in polar coordinates (10.8) and the calculus of slopes for curves expressed as r=f(theta) (part of 10.6). The homework assignment will be on these sections and topics. To be more specific, for example, you DO NOT need to know that r = 1/(2+cos(theta)) is an ellipse (10.7) But you NEED to know how to caluclate (or write the formula) for the arclength (10.4) and area enclosed by this curve (10.8). For the quiz on 9.1-9.6: it will be helpful to review the homework assignments and then list all the convergence tests you have learned (how many?) and write down a few examples for each of them. We will skip most sections in Chap 11, only introduce the cylndrical and spherical coordinates (11.7). Here is the homewok assignment for Chap 10. 10.4: 10,14,17,23,24,28,29 10.6: 16,18 10.8: 22,31,32,35,37 11.7:2-9 12.1: 9, 24, 30(Hint: use fundamental Theorem of Calculus to find dr/dt first, you will need dr/dt(0), then find r(t) similarly) 32, 34, 43 12.3: 7, 13, 16(for the parameter t in part(a), call it ta, etc. what is the relation between ta and tb, tb and tc?) 12.4: 9, 12, 13, 15, 17, 18, 26, 27, 35, 36 additional:(1) find the curvature and torsion for the helix (a cost, a sint, b t ) using 2 different methods.^X (2) find the curvature for r=f(theta) (3) derive formula(20) at page 784 (Hint will be given in class) We will teach 13.2-13.8 on Chap 13. The midterm will cover upto either 12.3 or 12.4. I have put old midterm exams on the course homepage. The old exams contain problems up to all of Chap 13, but did not contain Chap 12 (I did not teach Chap 12 then). In the old midterm exam, the problems in Chap 9 are particularly useful. I will put another sample/guideline for midterm on the course homepage shortly. The midterm is going to be more demanding than the quiz, so prepare early. The homework problems are must. 13.2: 28,30,32,34,35,36 13.3: 28,41,42,44 13.4: 5,6,8,11,13,20,21,24,29,30,35,36 13.5: 11, 21, 23, 30, 40, 44. Extra: (1) Find the Taylor expression of f(x,y) up to quadratic terms (x^2, xy, y^2) and give an expression of the error term (2) Find the Taylor expression of f(x,y,z) upto linear terms and give an expression of the error term. (3) Suppose F(x,y,z)=0 can define either x=f(y,z), y=g(z,x) or z=h(x,y) implicitly. (For example 2x+3y-4z-1=0). Show that the following identity hold: f_y * g_z * h_x = -1. (Sometimes, this identity is written as x_y * y_z * z_x = -1, which might be a little hard to understand) 13.6: 16,21,24,26,28,29,38,40,48,50,53,54 13.7: 18,35,36,42,45 13.8: 7,8,25,27,31 14.1: 2,4,6,9,11,14,20,24,26,28,32,34,36,38,40,46 Please read page 884 on how to get the limits of integration. This is the most important topic in this Chapter. 14.3: 8,10,13,14,24