In my textbook 「日本語総まとめN２」, they list the two vocabulary words 「余計に」 and 「余分に」. I am almost unable to differentiate between their appropriate usage.
Here are the example sentences from the book:
他人より余計に勉強する - "study more than others"
いつもより余分に食事を作る - "cook more than usual"
I asked a friend who is a native whether the first example sentence could be replaced with 「余分」instead of「余計」. She mentioned that it could, but she was not able to tell me the reason. She also was unsure of the difference between them.
When should either of these words be used and what are the differences between them?