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Tutor profile: John L.

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John L.
Naval Academy graduate experienced instructor and tutor
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Questions

Subject: Microsoft Access

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Question:

What are the basic objects and tools used in the design of a database?

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John L.
Answer:

MS Access, like many database applications, incorporates several foundational objects including tables, queries, forms, reports and macros. But the application goes well beyond these foundational objects. For example, the query-writing interface is actually a graphical tool used to construct and edit SQL code. Similarly, the Macro editor can be thought of as a graphical tool to construct Visual Basic code. These advanced features of the program allow users to create robust applications that perform advanced functions on the backend, yet enable end-users to enjoy simple and easy to understand interfaces. Once a designed understands these concepts, the program can be used to construct useful business applications that help to organize and streamline operations.

Subject: Pre-Calculus

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Question:

Why is Pre-Calculus a modern day subject in todays normal curriculum?

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John L.
Answer:

If one examines the history of mathematical education, 40 years ago the subject of Pre-Calculus did not even exist. What colleges were finding, however, is that students entering the course of Calculus were very weak in Algebra and Trigonometry - both foundational courses when studying Calculus. For example, it is difficult to understand why the Cosine is the derivative of the Sine without first understanding what both of those ideas actually represent. Pre-Calculus was thereby invented to revisit many of the foundational concepts assumed to be understood as a student begins the study of Calculus. Specifically the course addresses areas including: Transformations of functions, graphing, factoring, trigonometric concepts, word-problem analysis, and solving systems of linear equations.

Subject: Calculus

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Question:

Explain the meaning and significance of the Fundamental Theorem of Calculus

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John L.
Answer:

As the mathematics of Calculus was developing two branches developed which were thought to be independent of each other: Differential Calculus and Integral Calculus. Differential Calculus focused rates of change whereas Integral Calculus focused on determining areas under curves. Though these two branches appeared very different and unrelated, the Fundamental Theorem of Calculus linked the two branches into one subject by describing the exact nature connecting the two - that is, integration and differentiation are inverse processes of one another. The Fundamental Theorem of Calculus also greatly simplified methods of integration (which were mainly numerical based on Reimann's methods) in favor of Lebniz's method stating that if a function could be determined that was the anti-derivative of the function being observed, then the value of the definite integral is simply the difference of the anti-derivative at the end points. This discovery completely unified the two branches into today's modern study of Calculus.

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