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Multivariable Calculus Tutoring
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How we help you master: Multivariable Calculus
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Recent Tutoring Session Reviews
We just spent all our time doing several different types of integrals using various techniques including stake's theorem, green's theorem, divergence theorem, clever geometry, volumes of revolution, and various coordinate transforms.
We primarily worked through the concept of partial derivatives. We went over how to take them, what they look like on a surface, and the relationships of the second partials. We also discussed the concept of continuity in multivariable functions.
We covered homework on partial derivatives including: tangent planes and linear approximations, the chain rule, directional derivatives and gradient vectors. The student answered all of the questions and had some assistance and clarifications from me when necessary.
This was our first session. We worked on solving gradient problems, especially rates of change from a point in a direction. It was easy to explain and the student picked up on the solution method readily. He seemed to understand the process by the end of the session.
The student and I reviewed the midterm exam that she took several weeks ago. The student and I went over finding each answer that she had missed. The student and I focused on finding gradients and unit vectors. We went over differentiation that she did not understand including product rule and chain rule. We worked through an example in a book and then the student would repeat that type of problem and explain to me how to solve. I felt that this method was effective for the student to understand the topics.
We worked a problem involving a double integral today. I showed the student how the intermediate integrals can be thought of as marginal densities, or "line segment densities" rather than the point density that the original integrand provides. We computed 2 triple integrals; The emphasis being on drawing the domain being integrated over, so as to figure out appropriate bounds of integration. We computed a couple line integrals. We did a both scalar function line integrals, and we integrated a path through a vector field. I gave her a short list of problems to work prior to our session next week.
The student and I worked on several subjects for his midterm Tuesday: differentials, double integrals, optimization, and vectors. He seems to have a good handle on the material and is mostly self-sufficient.
Presented an outline of the class in order to give perspective and direction to the student. Talked about vectors and some vector operations, volume and surface integrals, parametric surfaces and curves, higher-dimensional analogues of the fundamental theorem of calculus, and geometric/visual interpretations of the above.
For our first session, we went over the syllabus and the structure of the class. Otherwise, we primarily focused on multivariable calculus -- specifically, partial derivatives with two or three variables of interest. She has a strong grasp of derivatives and was quickly able to apply standard derivative rules (product rule, chain rule, etc.) to more complicated functions with multiple variables. We also went over some homework problems contextualizing partial derivatives more conceptually.
We covered multivariable calculus and pre-calculus topics: limits, continuity, higher dimensions, partial derivatives, implicit differentiation, chain rule, and such. The student was struggling most with vectors and planes, basically geometry topics. He struggles visualizing, especially abstract topics. Which is why I think in the future I may desire to focus on visualization aids and to increase visualization of problems for the students test taking. I left him with the rest of the problems we did not cover on the exercises.
We worked on surface integrals of vector fields, solved several practice problems relating to integral of vector fields over surfaces (flux), and problems related to divergence of vector fields. Overall the session was productive. The student is very skilled and has a good grasp of the basics of the subject. I recommended an additional textbook to the student as a reference for further study.
The topics covered: analytical and geometric definition of vectors and unit vectors, addition and subtraction of vectors, scalar multiplication of a scalar and vector, and the dot product of two vectors. We covered a decent amount of material.
How can a Multivariable Calculus tutor from Varsity Tutors help you master Multivariable Calculus?
Multivariable calculus is a challenging branch of mathematics that is based in deriving and integrating functions that involve more than one variable. It can be a tremendously useful problem-solving tool in a wide variety of subjects ranging from theoretical physics to real-world engineering problems; even so, many students find this course to be a difficult step to take in their mathematics education. Many encounter problems that arise from an incomplete or incorrect understanding of concepts taught in previous calculus and algebra courses, while others may be stopped in their tracks by the various complex theorems one must master in order to apply the fundamental theorem of calculus to situations involving multiple variables. If you’re apprehensive about your multivariable calculus class, would like expert help in mastering course content, or need some guidance about what to focus on as you prepare for a midterm or final exam, you may find that your study aid options are scarce. You may also find that the options you do encounter don’t suit your needs—class-based review can skim over the material you find confusing to focus on topics you already understand, and written resources are completely impersonal. Varsity Tutors’ multivariable calculus tutoring avoids these pitfalls to bring custom-tailored instruction to students all across the country.
Varsity Tutors’ multivariable calculus tutoring is distinguished by its level of customization. We understand that every student is a unique learner with different strengths, weaknesses, and academic concerns. We provide tutoring that is equally individualized in order to make it as efficient as possible, allowing your instructor to help you learn the content and bolster the skills you most need to work on. We begin to customize your tutoring from the moment you contact one of our educational directors. While all of our multivariable calculus tutors are content experts and superb instructors, our directors can take your specific academic situation into account when selecting the tutor whose skill set best prepares them to help you. Your tutor can then help you to identify gaps or weak spots in your understanding of multivariable calculus, and can design a learning plan to work on just these concepts in order to shore up your knowledge and skills. All of our tutoring is one-on-one, so you and your instructor can spend as much time on a concept as it takes for you to fully master it. Completely understand partial derivatives, but have a hard time with multiple integration? No problem! Your lesson plans can be adjusted on the fly to allow you and your tutor to focus attention on the concepts that most concern you, and when preparing for an exam, your tutor can help you review and pinpoint exactly where focusing your studies can do you the most good.
Multivariable calculus is a crucial skill for students in quantitative fields and can unlock new realms of possibility in research and in future classes. Don’t settle for getting anything less than complete understanding out of your multivariable calculus class—contact Varsity Tutors’ educational directors today for more information about the multivariable calculus tutoring options available near you or to start working with one of our superb personal instructors!