Book for complementing differential equations

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Discussion Overview

The discussion revolves around seeking recommendations for books that complement the study of differential equations, particularly focusing on the geometric aspects necessary for solving related exercises. Participants express the need for resources that cover geometric analysis and coordinate geometry.

Discussion Character

  • Homework-related
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant mentions struggling with a specific exercise that requires understanding the geometry of functions and requests book recommendations.
  • Another participant notes that a solid foundation in algebra, trigonometry, geometry, and calculus is typically necessary before tackling differential equations.
  • Some participants express their own challenges in self-learning geometry and request guidance on suitable texts.
  • One participant suggests "Elements of Coordinate Geometry" by S L Loney as a helpful resource, while another mentions it is quite old and difficult to read, proposing "Elementary Euclidean Geometry" by C G Gibson as a modern alternative.
  • A suggestion is made to explore tutorials from Khan Academy as a potential resource.

Areas of Agreement / Disagreement

Participants generally agree on the need for a solid background in various mathematical subjects before studying differential equations. However, there is no consensus on specific book recommendations, as opinions on the suitability of suggested texts vary.

Contextual Notes

Some participants express uncertainty about their geometric knowledge and its impact on learning differential equations, highlighting a potential gap in their understanding that may affect their studies.

Santilopez10
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Hello! Currently I own Differential Equations by H.B Phillips, a really old book, but difficult and does it´s purpose. I have only 1 problem, certain exercises require certain geometrical functional study I suppose, for example:
"find the equation of the curves so that the part of every tangent between the y-axis and the tangent point P(x,y) is divided in 2 equal parts by the x-axis." (sorry if I translated wrong)
To be honest, I hesitated a bit trying to find such a curve, so I checked the answers, and it was a simple quadratic equation, therefore I realized I need to study a bit geometry of functions, so if someone can recommend a book I would thank him a lot.
 
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The usual understanding is that, before you get to the study of differential equations, you have gone through algebra, trigonometry, geometry, analytical geometry, differential and integral calculus. Without that background, a DE text is likely to be quite difficult.
 
Dr.D said:
The usual understanding is that, before you get to the study of differential equations, you have gone through algebra, trigonometry, geometry, analytical geometry, differential and integral calculus. Without that background, a DE text is likely to be quite difficult.
the only problem is that I am trying to learn it by my self, so I don´t have anyone who can teach me. I´ve already learned plenty of calculus, algebra, and trigonometry, but no geometric analysis, would you mind recommending a book of the subject?
 
I don't have any current recommendations. I studied geometry in high school 60+ years ago. Try Google.
 
Dr.D said:
I don't have any current recommendations. I studied geometry in high school 60+ years ago. Try Google.
alright, thanks.
 
Looks like you need some help with coordinate geometry.
One nice book is Elements of Coordinate Geometry by S L Loney
 
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kaustubhb said:
Looks like you need some help with coordinate geometry.
One nice book is Elements of Coordinate Geometry by S L Loney

That book is ~100 old and is barely readable.
A modern alternative would be Elementary Euclidean Geometry by C G Gibson.
 
A good suggestion would be tutorials from Khan Academy.
 
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