![]() ![]() ![]() The reason you see a lot of, say, algebra in calculus, is because many of the definitions in the subject are based on the algebraic structure of the real line. Some calculus courses focus most on the computational aspects, some more on the theoretical aspects, and others tend to focus on both. Elementary calculus is also largely concerned with such questions as how does one compute the derivative of a differentiable function? How does one compute the integral of an integrable function? Here there are many techniques to be mastered, e.g., the product rule, the chain rule, integration by parts, change of variable in an integral. One should regard these theorems as descriptions of the various classes.Īnd then there is, of course, the computational aspect. If one knows that a function ƒ is continuous, what else can you say about ƒ? The intermediate value theorem, the extreme value theorem, and so on, are examples of theorems describing further properties enjoyed by continuous functions. ![]() For instance, an integrable function may be less smooth (in some appropriate sense) than a continuous function, which may be less smooth than a differentiable function, which may be less smooth than a twice differentiable function, and so on. Some insight will reveal that this process of grouping functions into classes is an attempt to categorize functions with respect to how "smooth" or "well-behaved" they are. Examples of such classes are the continuous functions, the differentiable functions, the integrable functions, etc. One divides these functions into different classes depending on their properties. Elementary calculus may be described as a study of real-valued functions on the real line. ![]()
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For updates, please see CUNY COVID-19 Guidance on Academic Continuity.Īs is the case with many colleges and universities that have chosen online and distance learning modalities as a result of the COVID-19 pandemic, faculty utilizing Zoom, Blackboard Collaborate and other digital technology to deliver course curriculum/material must be sensitive to issues of privacy. The following text is quoted from CUNY’s Guidance on Academic Continuity to campuses. ![]() ![]() ![]() Wright, sensing her grudge towards him, told her that winning would not bring her father back. She was even willing to break established evidence law so as to show an incriminating picture that strengthened her case to the judge. Eventually, when she was revealed to have manipulated the witness testimony, Wright quickly condemned her for being no different from her ruthless father.įranziska proved to be quite a formidable opponent for Wright, even having researched the Kurain Channeling Technique to strengthen her case. She began the trial by mocking Wright that he would change his plea from "not guilty" to "justified self-defense" in ten minutes, but Wright persisted with the plea of "not guilty". Franziska whipped anyone who she felt was out of line, including the presiding judge himself. Like her father and Edgeworth, she would go to great lengths to get a guilty verdict, resorting to her father's tactics in her efforts to match his fame.Įncounters with Phoenix Wright Main article: Phoenix Wright: Ace Attorney - Justice for Allįranziska first faced Wright in the trial of Maya Fey, who had been accused of the murder of Turner Grey during a spirit channeling at Kurain Village. Compounded with her perfect record up to her arrival in America, she earned a reputation as "the Prodigy". However, Yew shot at them and escaped from the courthouse, with Detective Badd vowing to catch her.įranziska started her prosecuting career shortly after this incident. Franziska then followed Edgeworth as he questioned the various individuals tied with the trial until Edgeworth confronted Calisto Yew as the killer and the Yatagarasu. Upon investigating the crime scene, Franziska and Edgeworth argued about the order of events, with Edgeworth arguing that the evidence didn't make sense with the assumption that the victims had killed each other. Franziska told Edgeworth that they would compete to find the killer first, and Edgeworth played along. Manfred put the two of them in charge of the subsequent investigation, much to the dismay of detective Tyrell Badd, who was supposed to have been a witness in the trial as an expert on the notorious Great Thief Yatagarasu. The corpses of Byrne Faraday & Mack Rell. She took a vacation to the United States, during which she went to the District Court to watch Edgeworth prosecute his first case, but the trial was canceled when Mack Rell and Byrne Faraday, the defendant and prosecutor, respectively, were found dead in a defendant lobby. During her years at elementary school, Franziska would always wind up going to her previous year's classroom on the first day.įeeling overwhelming pressure from her father's reputation as a "perfect" prosecutor, Franziska started her legal studies in Germany at a very young age, and by the age of 13, she was set to pass the bar exam. However, Edgeworth would leave " alone and on ahead without ", causing Franziska to resent him. ![]() Her father began mentoring an orphaned Miles Edgeworth, whom she came to view as a rival and "little brother" (despite being younger than him). Franziska von Karma was born to the infamous undefeated prosecutor Manfred von Karma. ![]() |
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