Elliptical Coordinates (Double Integrals)
Krystian Karczyński
3 July 2024
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There are times in life when the region of integration in a double integral is an ellipse…. What do we do then?
Helpful tricks in complex numbers
Krystian Karczyński
2 July 2024
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Complex numbers as a whole are not a complicated and difficult topic. However, things can get “heated” in less typical and less schematic situations. The key then, as always, is to understand the topic and keep a “cool head,” meaning being clear-headed and confident.
The (Almost) Trigonometric Form of a Complex Number
Krystian Karczyński
2 July 2024
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When solving problems with complex numbers, it’s important to keep in mind that a complex number in trigonometric form has its typical form. And only that form. No more, no less. Therefore, you need to pay attention to when a complex number is in trigonometric form and when it is not.
Indefinite Rational Integrals – Third-Degree Polynomial in the Denominator
Krystian Karczyński
28 June 2024
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In indefinite rational integrals, as we know, it is often necessary to factorize the denominator of the integrand and further decompose it into simple fractions. However, factorization itself can often be tricky.
Why can’t a function graph have two oblique asymptotes as x approaches positive infinity?
Krystian Karczyński
28 June 2024
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To answer the question posed in the title, we don’t need to go back to the definition of an oblique asymptote, we just need to know what a function is.
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