Here's how declension works.
Adjective endings can be annoying, but if you understand how they work, then they are very easy to get right. Take for example:
With the der declensions.
Der berühmte Mann ist alt. // Since the original gender is show aka der. You just use a -e for declension.
Ich sehe den alten Mann. // Since den is not the original gender for the accusative masculine (which would be der), you need to add -en to show the case and gender of the noun being declined.
Ich sehe die neue Blume. // Since the feminine in the accusative is the original gender for Blume. You just add -e.
Ich sehe das neue Buch. // Same thing for the neuter noun.
All of the plurals have -en, since there is no original gender definitive for plural. Same thing for the dative and genitive cases. They also get all -en.
Do the same method for the indefinite articles, too.
Now with no definitive/indefinite articles in front of the noun. It's decline with the ending of the definite article for example.
Guter Rat ist wichtig. // You need to show that the noun »Rat« is in the nominative. So you add the -er from der onto it.
Any adjective before a noun must be declined with the appropriate ending. An adjective placed after a noun is not declined. You need to know three things to decline an adjective: noun gender, case and the type of article being used. In this sentence Buch is a neuter noun in the accusative case and a definite article is being used. In this situation an "e" is added. As the original post suggested there are some patterns. Any use of an article restricts the ending to just "e" or "en". I am sure you will pick out the patterns quickly upon looking at the tables I have linked.
Here is an explanation of some logic behind the endings but be careful to note where the rules don't apply to plurals. https://www.duolingo.com/comment/14943863/The-logic-behind-German-adjective-declension-endings
Seufz. "Etwas eingehend studieren" oder "etwas genau studieren" passt hier prima. Kein Fehler. Studieren wird eben nicht bloß im universitären Kontext verwendet.
"Sie studierte den Fahrplan." Hieße umschrieben: "Sie betrachtete den Fahrplan eingehend."
Dennoch hast Du generell recht, dass "Studieren" vor allem universitären Bezug aufweist.
> Ich sehe den alten Mann. // Since den is not the original gender for the accusative masculine (which would be der), you need to add -en to show the case and gender of the noun being declined.
Youre talking about articles when you say gender. The Article den is not the same as der (or its the same with a different declension, depending on how you view grammar). BUT den and der share the same gender. Both are masculine articles, they do not share the same kasus.