Precalc topics that are essential in calculus 3

In summary, the conversation discusses the essential topics in Pre-Calculus that are needed for Calculus 3 and the best methods to review them in preparation for the course. The conversation mentions that the notion of a vector and trigonometry are important, as well as concepts covered in a basic linear algebra course. Additionally, reviewing dot products, cross products, determinants, matrix algebra, and parametric equations is recommended. It is also noted that everything from Calculus 1 and 2 will be needed and a good Pre-Calculus course will cover an introduction to limits. There is also a discussion on whether it is more effective to prepare for Calculus 3 by reviewing Pre-Calculus or by reviewing Calculus.
  • #1
annoyinggirl
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Hello,
I will be taking calc3 a semester from now. I will take linear algebra this upcoming semester, so i have a bit of time to prepare for calc.

what are Precal topics that are essential in calculus 3? reading the class description, it seems more geometric than calc 1 and 2.

Also, what are the best methods to learn/review these precal topics in preparation for calc 3?
 
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  • #2
The notion of a vector is probably the most important non-calculus based idea you will need. Trig is also extremely important. If you are taking linear algebra, the vector info will be taken care of. You should review dot products, cross products, determinants, and matrix algebra, but like I said, all these ideas are covered in a basic linear algebra course. You should also review the notion of parametric equations. That is pretty much the working non-calculus ideas you will need. Of course, EVERYTHING from cal 1 and cal 2 will also be needed. Depending on the rigor of the course, you may or may not need taylor series.
 
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Likes annoyinggirl and symbolipoint
  • #3
Everything you study in Pre-Calculus will be needed in the Calculus sequence of courses. A good Pre-Calculus course will also include an introduction to Limits.
 
  • #4
Why would you prepare for calc 3 by studying precalc? Isn't it more logical to review calculus and to make sure you know it cold? Anyway, to answer your question, it's probably trigonometry that you should focus on, since a lot of calc 3 questions will be made a lot easier by trigonometry.
 

1. What is the difference between a limit and a derivative?

A limit is the value that a function approaches as the input approaches a certain value. A derivative, on the other hand, is the instantaneous rate of change of a function at a specific point. In other words, a derivative is the slope of the tangent line at a point on a graph, while a limit is the value that the function is approaching at that point.

2. How are trigonometric functions used in calculus 3?

Trigonometric functions, such as sine, cosine, and tangent, are used to model and analyze periodic phenomena in calculus 3. They are also used in finding the derivatives and integrals of trigonometric expressions.

3. What is the importance of vectors in calculus 3?

Vectors are essential in calculus 3 as they are used to represent and manipulate quantities that have both magnitude and direction. They are used in topics such as vector-valued functions, vector calculus, and multivariable calculus.

4. How does the concept of optimization relate to precalculus topics?

The concept of optimization, which involves finding the maximum or minimum value of a function, is closely related to precalculus topics such as graphing and finding the zeros of a function. These skills are necessary for solving optimization problems in calculus 3.

5. What are the key concepts in precalculus that are necessary for success in calculus 3?

Some key concepts in precalculus that are essential for success in calculus 3 include functions, limits, derivatives, and trigonometry. It is also helpful to have a strong understanding of algebra and graphing techniques.

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