what is the different between 'convince' and 'persuade'?

[Rebecca]

HI!
Could you please tell me what is the different between 'convince' and 'persuade'?
Thanks in advance.

[Mister Micawber]

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From the American Heritage Dictionary:

SYNONYMS: 'persuade, induce, prevail, convince'. These verbs mean to succeed in causing a person to do or consent to something. 'Persuade' means to win someone over, as by reasoning or personal forcefulness: Nothing could persuade her to change her mind. To 'induce' is to lead, as to a course of action, by means of influence or persuasion: “Pray what could induce him to commit so rash an action?” (Oliver Goldsmith). One 'prevails' on somebody who resists: “He had prevailed upon the king to spare them” (Daniel Defoe). To 'convince' is to persuade by the use of argument or evidence: The sales clerk convinced me that the car was worth the price.
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Native English teacher at Mister Micawber's

[Rebecca]

Thank you very much!