IntroductionThis manual is for calculus students who are using the textbook by Swokowski 6th edition. This text has many problems with incorrect facts, wrong application of rules, and misapplication of formulas. The errors range from small to major problems that end up costing the student points on their homework or exams. We hope that this manual will convince you to buy a new copy of this text if someone is giving it away for free because they know it's riddled with incorrect facts and misapplication of formulas. This manual contains many suggestions on how to approach problems, including examples and videos which demonstrate more than just one solution. These suggestions might be useful to students who are studying partial differential equations as well, because these students will not be using a different text.Analytical GeometryIn Lecture 1 after the instructor says the phrase "the x-axis" he should have said "the positive x-axis". He says this at 0:47. In Lecture 2 at 2:05 the instructor should have said to look at Figure 1 which is a graph of y=x².
Note: The numbers used in the examples below are for fictitious purposes only, so they will work in linear algebra, but they will not lead you to any real world problems. Skip them if you want. At 0:28 in Lecture 1, the instructor should have said that the "homogeneous equation" of y=x² is y=ax+b. He says it at 0:28. At 0:36 he says that the "differential equation of y=x² is y'=-b²+cx-dx." He says this twice at 0:36 and 0:40. The statement of the differential equation was correct because I had not said b²+cx-dx; I had said y'=-b+cx-dx. But I should have said b+cx-dx. See the difference. At 1:08 he speaks to the "unknown" and says that "the equation" is y'=-b²+cx-dx. He said this twice at 1:08 and 1:11. See the difference. At 4:20 in Lecture 2, he says that "y=f(x)" (the function is f(x)=24) and then at 5:15 he says that we will use an integrator for this integrand. At 8:56 he says to take a look at Figure 7 which is a graph of x=y-(k²y+m²x). He says this at 8:56. At 11:24 he says that the graph of y=x² is the graph of y'=-b²+cx-dx. He said this twice at 11:24 and 11:25. The statement of the differential equation was correct because I had not said b²+cx-dx; I had said y'=-b+cx-dx. See the difference. At 12:09 he speaks to the "unknown" and says that you need to find "the solution" of f(x)=24, which is x=(-2/3)b/3(c+1). He said this twice at 12:09 and 12:10. See the difference.
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