The Bus Pants Utilization

The Bus Pants Utilization is the 12th episode of the fourth season of the CBS sitcom The Big Bang Theory. It aired on January 6th, 2011.

Plot Summary
Leonard has an idea to make a smartphone app to solve differential equations. Sheldon quickly puts himself in charge of the team to build the app, but Leonard is able to recover his place as the leader. After some time, Sheldon becomes dissatisfied with Leonard's leadership (or most likely becomes indignant that he's not in control instead) and calls for a vote of no confidence and an immediate change in leadership, which results in Sheldon removed from any connection to the project.

Expanded Plot
Sheldon, Howard and Raj are eating together in the Cafeteria when Leonard approaches them with an idea for a smartphone app that helps users solve Differential Equations. Leonard quickly recruits Howard and Raj, with Sheldon volunteering himself. Leonard mentions they may make a little money off the app, leading Howard to imagine building a place over the garage to escape his mother with the money, and Raj dreams of taking pretty girls on "Submarine Rides".

When they get back home, Leonard announces that nobody else is currently making an app like theirs, in the presence of Penny, Sheldon is afraid Penny will steal Leonard's idea, he points out an "Unlikely but very plausible scenario" that Penny befriends the gang to steal a marketable idea from them, Penny points out that she hangs out with them partly because she receives free food. After Penny leaves, Sheldon quickly designates himself as the Leader of the group, when he lists himself as Chief Executive Officer, Chief Financial Officer, Chief Operating Officer, Chief Science Officer, Chairman Of the Board and Head of the Secret Santa Committee, meanwhile Leonard is only listed as Founder. After a brief argument, Leonard is able to regain his post as the Leader. Over time, Sheldon continues to mock Leonard's leadership, and makes further attempts to glorify himself by suggesting that the project be named after him, despite the fact that it was Leonard's idea, but is told to shut up. When Sheldon abruptly proposes a vote to change the Leadership, he is promptly kicked off the team for his obnoxious behavior.

Although Sheldon is off the team, Leonard is still fine with driving him to work, but that changes after Sheldon critcizes Leonard's height and saying he has a "Big Napoleon Complex." Sheldon has to put on his Bus Pants and use the bus to go to work (presumably this is the origin of the title) as a result of this. Sheldon tries to persuade Howard and Raj to join his rivaling team and abandon Leonard with gifts. Failing that, Sheldon tries to hinder the team's progress by playing his noisy Theremin in front of them, which results in him getting kicked out the apartment.

Penny finds Sheldon playing it at the hallway and tells him about her idea for an app that help user find places on the internet to buy shoes which Sheldon turns down. Feeling sympathy for him she invites him for Hot Cocoa, and he accepts with the remark "A disappointing drink for a disappointing day", a decision which she soon regrets. Leonard agrees that he will let Sheldon back on the team and into the apartment if Penny is able to make Sheldon apologize, thinking it was impossible. Penny manages to do it by telling Sheldon to perform his apology with sarcasm (while also lying to him by claiming that the others desperately need his help). After a brief period back in the team, Sheldon is kicked off again and is seen in the last scene making an the algorithm for Penny's shoe finder app.

Quotes
Raj: (After playing a farting noise on his phone) Was that the best 99 cents I've ever spent or what!

Sheldon: (to Leonard) Oh dear lord, shush! You have so few ideas, leonard, and now you're just gonna spill the beans to an outsider? (points to Penny)

Raj: Last night I had a dream, we got so rich from the app, we bought matching side by side mansions! But, there was a secret tunnel connecting your front yard to my back yard. What do you think that means?

Howard: It means after we've played handball I'm showering at home.

Sheldon: (singing) Nobody knows the trouble I've seen... Nobody know my sorrows... Nobody knows the troubles I've seen... Glory, hallelujah!

Sheldon: Well, I suppose it's appropriate.

Penny: What does that mean?

Sheldon: A disappointing drink for a disappointing day.

Trivia

 * Engineers solve differential equations. Sheldon is flippant when he states, "Howard doesn’t. He’s only an engineer.". However, he could be refering only to the Shrödinger equation, which is not used by engineers.
 * When Leonard starts to talk about his app idea in front of Penny, Sheldon tries to drown out their voice by singing "Deep In The Heart Of Texas "
 * Sheldon proposes the name for the app to be, "the Surprisingly Helpful Equation Link Differential Optimized Numerator", which abbreviated spells SHELDON; when the others reject that idea, he proposes a secret name for the project, "Project Nodlehs", which is "Sheldon" spelled backwards.
 * Sheldon says "Windows 95 was the Chicago project, the atomic bomb the Manhattan Project" and thus he proposes "Project Nodlehs" which is "Sheldon" spelled backwards.
 * Sheldon says, "A customer service representative with an Indian accent will create the impression we’re a vast enterprise that uses overseas call centers." Raj's cousin, Sanjay Koothrappali, works at a call center, as stated in The Pirate Solution.
 * According to Sheldon, bus pants are pants that someone wears over regular pants on a bus where other people sat before him.
 * This is not the first time that Sheldon gets voted off the team for being too obnoxious.