Learning Math with Limited Visual Tools When Calculus is Required

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Discussion Overview

The discussion revolves around the challenges of learning differential calculus of several variables, particularly in the absence of visual aids and effective teaching methods. Participants share their experiences and seek advice on how to improve their understanding and engagement with the subject, including the use of visual tools and alternative resources.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested
  • Homework-related

Main Points Raised

  • One participant expresses frustration with their instructor's inability to provide visual representations of 3D graphs, which hinders their understanding of the material.
  • Another participant suggests that drawing graphs is essential for mastering the concepts in multivariable calculus, emphasizing the importance of developing skills in this area.
  • A different participant notes that while they can draw graphs, they struggle with visualizing derivatives in 3D due to a lack of explanation from the instructor.
  • Some participants recommend using different textbooks or resources, indicating that the current textbook may not be sufficient for their learning needs.
  • Several suggestions are made regarding software tools, such as graphing calculators and programs like Maple, to aid in visualizing mathematical concepts.
  • One participant reflects on their mixed feelings about math, noting that they enjoy math-related subjects but struggle with the math itself, particularly when it is not connected to practical applications.
  • Another participant agrees that studying mathematics can be more challenging than applying it as a tool, suggesting that this experience is not uncommon.

Areas of Agreement / Disagreement

Participants generally express a lack of consensus on the best methods for learning calculus without visual aids. While some agree on the importance of drawing and using tools, others emphasize the need for better instructional methods and resources.

Contextual Notes

Participants mention limitations in their current textbooks and teaching methods, as well as varying levels of comfort with visualizing mathematical concepts. There is also an acknowledgment of the subjective nature of learning preferences and experiences.

Who May Find This Useful

This discussion may be useful for students struggling with calculus, particularly those who find it difficult to visualize concepts without adequate instructional support or resources.

bubbles
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I'm currently taking calculus ("differential calculus of several variables") and I really dislike math (even though I used to like math), but it's required for my major (comp sci). My teacher can't draw and does not show us graphics of 3-D graphs and functions, so I have a hard time 'seeing' the math. The textbook I'm using isn't really good (not as helpful as the textbook I used for single variable calculus). Do you have suggestions to help me learn math and make it more interesting? Are there any helpful visual tools online? Thanks in advance for any suggestions.
 
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Bubbles,
If your teacher can not draw, you still must learn to draw fittingly for your Calculus course. Drawing for 3D several variables (three of them) is a necessary part of your course. Your course may or may not be interesting, but it will have some components which you need for your major field - you don't know which you need until later in whatever jobs you do. At least, you need to develop skills in Calculus as a tool. Your book should have a few applied problems to help make the course more interesting; otherwise, you probably have a poor book.

You might be able to find a graphing calculator with some 3D capabilities, but you should not need this kind of technology. None of the rest of us ever needed such technology when we studied multivariable Calculus; WE LEARNED TO DRAW. ...but in case you find some good 3D program, I hope you use it well and enjoy it.

Could you ASK your teacher to draw some 3D representations for clarity of presentation? Seriously, when I was a student, 3D cartesian graph drawing was both part of instruction ON A CHALK BOARD, and part of study & practice exercises (on paper).
 
I don't have a problem drawing the graphs, but I have problems visualizing derivatives in 3-D since my instructor doesn't draw them; he just has us memorize equations and solve problems. I guess the textbook I'm using (stewart, 5e) isn't that bad since it seems to be pretty popular, but it doesn't explain things as clearly and as detailed as the textbook I used for single variable calculus (larson, 8e), and I actually liked my previous calculus course. I think what I need is some studying materials (in addition to the book). Do you think that it's easier to memorize formulas by just reading them over and over or should I do practice problems? Unlike in other classes, I just don't see why or how the formulas make sense since the instructor doesn't explain why we use those formulas, so memorizing them is a bit difficult.
 
use a different book.
 
Id get maple, derive or a cheap graphing calculator, maybe this will help you see the math better.
 
Ya. I personally use maple 11 when I need REAL detail, but I also have a really cool graphing calculator with more functions than I can name in a day. 3D graphing is one of them. A TI Voyage 200 is a great calculator for 3D graphing mainly because it has numerous uptions for the graph, and it also has a bigger screen.
 
Thanks for the advice. I am going to do more practice problems (both inside and outside the textbook). I still can't visualize partial derivatives and interpret them though I know how to take the derivatives, but I just learned them, so that might take some time to understand. I will probably have to do some outside reading (recommendations?) to get a better grasp of the material since I don't really like the textbook.

It's strange that I like math-related subjects but not the math itself. I've always been able to do math but I never really liked it until I see it being applied in physics. Is it possible to do well in math-related subjects if I don't like math (but also don't dislike it)?
 
bubbles said:
...clipped out...
It's strange that I like math-related subjects but not the math itself. I've always been able to do math but I never really liked it until I see it being applied in physics. Is it possible to do well in math-related subjects if I don't like math (but also don't dislike it)?

That is not strange. STUDYING the Mathematics can be more difficult than learning to use Mathematics as a tool.
 

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