Mrs. Dubose is a prime example of this "quiet courage" Atticus tries to teach Scout and Jem. She does her best to break herself of the morphine habit before she dies. This takes great mental strength to focus on Jem reading to her rather than succumbing to the physical dependence on morphine. When she died, she was completely free of morphine.
Atticus is another example of this. When Scout comes home from her first day of school, she doesn't want to go back because Miss Caroline yelled at her and made her look like a fool in front of the whole class. Rather than forcing Scout to go back to school or telling her she has to go because he is the parent and says so, Atticus reasons with Scout, teaches her what a compromise is, and allows her to make the decision whether or not to go back to school. By dealing with his children this way, Atticus doesn't have to physically punish them--Jem says, when he goes back for his pants at the Radley place that Atticus hasn't even whipped him and he isn't going to start now.
Atticus shoots a rabbid dog with one shot and the people in Macomb tell the children that Atticus is the best shot in the county. The tell them that Atticus knows how to use a gun, he just chooses not to. A second example of using the mind over muscle is when Scout faces Cecil Jacobs in the school yard the next day: "You gonna take that back boy?" "You gotta make me first!" he yelled. Scout remembered what Atticus had told her about not fighting and trying to ignore insults and then, "dropped my fists and walked away." Yet another example of using your head instead of muscle is when Jem had torn up Mrs. Dubose's flowers. When Atticus got home he was angry at Jem, but instead of whipping him or hitting him Atticus sent Jem over to Mrs. Dubose house to appologize and to clean up the mess. When Mrs. Dubose told Jem she wanted him to read to her Atticus made Jem do the reading every afternoon for a month. Mrs. Dubose is an example of mind over matter. She refuses to take pain medication because she is a heroin addict and quietly suffers until she dies, rather than use heroin again.