What are some tips for succeeding in Calculus II?

In summary, the speaker is taking calculus 2 in the summer and is studying by themselves without a syllabus. They have covered several techniques but are unsure of what else they should focus on. Some suggestions include integration by substitution, the fundamental theorem of calculus, Newton method, Euler method, L'Hopital's rule, and integration and differentiation of polar and parametric functions. The speaker is also advised to focus on problem solving and achieving beautiful, clear notation in their work. It is also suggested to try different approaches when stuck on a problem.
  • #1
Dan350
44
0
Hello users!

Im taking calculus 2 for summer(staring in 3 weeks), and it's the first time I take the course.

Im studyng by my self, but I don't have a syllabus or something to follow.

I already Covered this parts:

Integration by Parts
Trig Sub
Trigonometric Integrals
Improper Integrals
Partial Fractions

Whats left? And what should I focus more on?
Thank You!
 
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  • #2
Dan350 said:
Hello users!

Im taking calculus 2 for summer(staring in 3 weeks), and it's the first time I take the course.

Im studyng by my self, but I don't have a syllabus or something to follow.

I already Covered this parts:

Integration by Parts
Trig Sub
Trigonometric Integrals
Improper Integrals
Partial Fractions

Whats left? And what should I focus more on?
Thank You!

This looks like a good start, but without knowing exactly what the syllabus is for the course you're taking, I can't say more. One technique that you omitted is integration by substitution, which is probably simpler than any of the techniques you listed.

When you say you "covered" the techniques above, what does that mean? Did you just read the section or did you work a bunch of problems in these sections?
 
  • #3
Do you know the fundamental theorem of calculus?
 
  • #4
If you haven't covered these in Calc 1, here you go.
Newton Method
Euler Method
L'Hopital's rule
Shell and Disk method for revolution of solids
Integration/differentiation of polar and parametric functions
Integration to find distance traveled in parametric and cartesian

These may be beyond Calc 2, but I didn't think so. These are arguably more important than those above
Infinite series
Taylor series/polynomials
 
  • #5
Dan350 said:
And what should I focus more on?
Thank You!

Problem solving. Are you working or attempting to work every single problem at the end of the sections? Also, beauty. That's a shock isn't it? Is your math pretty? Strive for perfect, beautiful notation when you do math so there is no ambiguity about the notation. Also, when you encounter a problem you can't solve, tear it apart and work on a simple, similar-looking problem, and keep making it simple until you can solve it, and then start building it back up again. Sometimes that works, sometimes not but try. What else? Oh yeah, the try thing. When you're absolutely stuck, just try things even if they're a long shot because you'll find often, just the slightest perturbation in thinking can lead to a drastically different direction which then leads to the solution.

Sometimes the road to the right answer is cluttered with the wrong answers. :)
 

What is Calculus II?

Calculus II is the second course in a series of college-level mathematics courses focused on the study of derivatives, integrals, and their applications. It builds upon the foundations established in Calculus I and introduces new concepts such as integration techniques, sequences and series, and multivariable calculus.

Why is Calculus II important?

Calculus II is important because it provides a deeper understanding of mathematical concepts and their real-world applications. It is a fundamental tool in fields such as physics, engineering, economics, and many others. Additionally, it serves as a prerequisite for advanced math courses and is often required for majors in STEM fields.

What are some tips for succeeding in Calculus II?

To succeed in Calculus II, it is important to have a strong foundation in Calculus I. It is also helpful to stay organized and keep up with the material on a regular basis. Practice is key, so make sure to work through plenty of problems and seek help from your instructor or classmates if needed. Don't be afraid to ask questions and actively participate in class.

What are some common challenges in Calculus II?

Some common challenges in Calculus II include understanding and applying integration techniques, manipulating and solving complex equations, and visualizing and working with multivariable functions. Many students also struggle with the pace of the course, as it covers a lot of material in a short amount of time.

How can I prepare for Calculus II?

To prepare for Calculus II, make sure to review and solidify your understanding of Calculus I concepts. You can also practice your algebra and trigonometry skills, as these are important tools in Calculus II. Familiarizing yourself with the course material and seeking out additional resources, such as textbooks or online tutorials, can also help you feel more prepared for the course.

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