Self-studying Multivariable Calc

Student Lounge College Life
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<p>Does anyone know of any good resources to self-study multivariable calculus? Textbooks, comprehensive study guides, and internet resources are kind of what I'm looking for.</p>

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<p>I sing the praises of MIT OpenCourseWare. Just Google it.</p>

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<p>^ Thanks, I’ll check it out. I’ve heard good things.</p>

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<p>I used this book in my calculus III class: [Amazon.com:</a> Vector Calculus (9780471725695): Miroslav Lovric: Books](<a href=“http://www.amazon.com/Vector-Calculus-Miroslav-Lovric/dp/0471725692]Amazon.com:”>http://www.amazon.com/Vector-Calculus-Miroslav-Lovric/dp/0471725692) . Being a freshman in college, I actually did the readings, and found that I could understand the book. It’s not a big, heavy book, so that is a plus. </p>

<p>It’s a mostly standard calculus book, although at the end of the book, there is a hurried treatment of a fancy math formalism that lets you do calculus with more than just functions from R^3 to R^3. He writes down an equation where he moves the partial sign from the integrand to the volume of integration and makes a big deal about it.</p>

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<p>I self-studied Multivariable Calculus this summer and used the following:</p>

<p>Youtube
MIT OCW - Multivariable Calculus Lecture Playlist
UCBerkeley - Multivariable Calculus Lecture Playlist
PatrickJMT - Specialized topics in Multivariable Calculus</p>

<p>Textbooks
<a href=“http://www.mecmath.net/calc3book.pdf[/url]”>http://www.mecmath.net/calc3book.pdf&lt;/a&gt;&lt;/p&gt;

<p>Websites
<a href=“http://www.examswithsolutions.com/Subjects/math_exams.html[/url]”>http://www.examswithsolutions.com/Subjects/math_exams.html&lt;/a&gt; <– Exams to test yourself and see if you truly grasp the concepts.</p>

<p>The combination of these sources were REALLY helpful. I learned interesting things and the online lectures and textbook complemented each other well. I would take notes from the lecture, add notes that weren’t in the lecture from the textbook and then do practice problems at the end of each section in the textbook.</p>

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<p>

Stokes’ Theorem? That theorem is a big deal because the two partial signs mean completely different things. Think of it in one dimension: it says that the value of a path integral, for some functions<a href=“and%20I%20can%20tell%20you%20exactly%20which!”>/u</a>, is independent of the path you take and only depends on the endpoints. The Fundamental Theorem of Calculus is a special case of Stokes’ Theorem too!!!</p>

<p>Stokes’ Theorem connects analysis to topology and is the core of a field called “geometric analysis.” I didn’t understand the fuss either when I first encountered it as a freshman, but several years and a couple of graduate courses later I see the big deal.</p>

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<p>I knew that a math guy would freak out when I said that. Mission accomplished.</p>

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<p>Are there sequences and series in calc 3? I’ve kinda skipped sequences and series in calc 2, so I’m wondering if it was necessary or important to learn / know before jumping into calc 3.</p>

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<p>Not quite. You freaked out a math girl! ;)</p>

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<p>

Wow, thanks. This will definitely be useful</p>

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<p>You shouldn’t see sequences in Calc 3…unless, of course, your school didn’t teach them in Calc 2 and saves them for Calc 3 (rare, but possible).</p>

<p>You never know though. Taylor Series are pretty easy after you study them for a bit. </p>

<p>Series and Sequences WILL come up again (multiple times, most likely) if you take any upper division math classes. It seems to never go away in Numerical Analysis.</p>