![]() ![]() See also the Wikipedia article on differential forms. In response to questions about similarities between Stokes’ theorem and Divergence theorem, I have made some BONUS and OPTIONAL notes on differential forms and generalized Stokes’ theorem: Optional Bonus notes on differential forms. Solutions to some review problems for a multivariable calculus exam dealing with vectors, lines, planes, and introduction to 3-dimensional space. Green’s theorem (cont), divergence, and curl More triple integrals, comparisons, and vector fields Triple integrals in cylindrical and spherical coordinates Here is a set of practice problems to accompany the Functions of Several Variables section of the 3-Dimensional Space chapter of the notes for Paul Dawkins Calculus II course at Lamar University. Note, I made a few mistakes in lecture, but notes are corrected.ĭouble integrals on general regions continued & polar regions Gain a profound understanding of multivariable calculus with this excellent and clear. Lecture had a substitute teacher provided notes differ from lecture. Understanding Multivariable Calculus: Problems, Solutions, and Tips. Tangent plane, linear approximation, and chain ruleĬhain rule, directional derivative, and gradient Gateway Exam practice is available on WebHWĮquations of planes, cylinders, and quadric surfaces Note, recordings will be available for 7 10 days after the lecture, and will then be unpublished. For more challenging problems, look at old exams.For practice problems, look at examples and exercises in the corresponding textbook sections answers to odd numbered questions are in the back of the book. For problems 3 7 using only Properties 1 9 from the Limit Properties section, one-sided limit properties (if needed) and the definition of continuity determine if the given function is continuous or discontinuous at the indicated points.Prelab assignments due the day of your lab meeting.You may also attend any instructor’s office hours (see Canvas syllabus) or go to the Math Lab when they are open.Let’s now return to the problem that we started before the previous theorem. Friday’s 9a–10a ( Math Atrium in East Hall) The same thing is true for multivariable calculus, but this time we have to deal with more than one form of the chain rule.Monday’s 9a–10a ( Math Atrium in East Hall). ![]()
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