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Advanced Mathematics

Author： Date：18-11-2007 Hits：

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**Objectives and Requirements:**

Advanced Mathematics is the most important basis subject for the majors of science and technology at university. The subject is concentrated on the basic concepts, basic theories and basic methods by the limiting method. By the study of the subject, the student must master the following contents: be skilled in the function, be skilled in finding limits, be skilled in judging the continuity of a function, be skilled in finding derivatives and finding derivatives of implicit functions, understand the relation between the monotone and the first derivative of a function, understand the relation between the convexity and the second derivative of a function, be able to sketch the graph of a function, be able to do approximate calculation, be able to distinguish the difference and connection between definite integral and indefinite integral, be able to evaluate integral, be able to evaluate the area bounded by curves. The ability of students to analyze problem, to solve problem will be enhanced. Advance mathematics is necessary for the following courses.

**Contents:**

Advanced mathematics is consist of the following contents:Functions, the definition of the limit, finding limits, limiting method, finding the asymptote of a function, the continuity of a function, the derivative of an explicit and implicit function and its computation, the differential and its evaluation, the monotone of a function, the convexity of a function, sketching the graph of a function, the indefinite and definite integral of a function and its evaluation by substation and by part, the application of the indefinite integral and the define integral, the basic theorem of calculus.

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