Syllabus of Advanced Mathematics高等数学英文大纲（国外高校免学分亲测可用）.docx

XXXX UniversitySyllabus of Advanced MathematicsCode:Advanced Mathematics: XXXXXXXXCredits:4Credit Hours:72 Prerequisites:Elementary MathematicsSuitable For:Architecture and Civil Engineering Category Textbooks:Advanced Mathematics(I) ISBN: 978-7-04020-549-7Tongji University, Department of Mathematics, the sixth edition, 2007Assignment:Available in spring for Advanced Mathematics (I)Assessment:Written ExaminationOffered ByFaculty of School of Science and TechnologyCourse Content1 Functions, Limits, Continuous1. Understand the concept of functions and functions characteristics: monotone, periodicity and parity; 2. Understand the concept of a composite functions and inverse functions;3. Familiar with the characteristics of basic functions and its graphics;4. Be able to establish a simple function related to practical problems;5. Understand the concept of limits and four algorithms and Substitution rule;6. Understand two limits exist Standards (Squeeze Rule and monotone bounded Guidelines);7. Understand infinitesimal, infinite and infinitesimal concept of order.8. Understand the type of function that continuously and in a continuous range of concepts and conceptual point of discontinuity, and be able to determine the point of interruption.9. Understand the nature of elementary functions (intermediate value theorem and the maximum and minimum theorem) the continuity and continuous function of closed interval.2, Derivative1. Understand the concept of derivative and differential, and understand the relationship between the derivative of geometric meaning and the function that may be between conductivity and continuity.2. Derivation, master the basic elementary functions and elementary functions derivative formulas derivative master four algorithms and complex derivative of the function for the law.3. To understand the concept of higher order derivative.4. Be able to seek implicit function, derivative of a function of the parameters determined by the formula and inverse function.5. Understand Rolle theorem, Lagrange Theorem, Cauchy theorem and Taylor theorem.6.Know how to use the Hospital law.7. Be able to use derivative monotonic function and demand function of the extreme value. Be able to solve the problem of relatively simple application of the maximum and minimum values.8. Be able to use the derivative of the function graph of irregularities, be able to seek inflection point, know how to depict graphics functions (including horizontal and vertical asymptote).9. Understanding the concept of curvature and radius of curvature and calculates curvature and radius of curvature.10. Learn demand equation approximate solution of dichotomy and tangent method.3, Functions of one Variable Calculus1. Understand the concept and nature of the original function and indefinite integral. Master the basic formula: indefinite integral, substitution and integration by law.2. Understand the concept and nature of definite integrals.3. Understand the change as a function of the upper limit of integration and derivation theorem by Newton-Leibniz formulas.4. Master definite integral transducer element method and integration by parts.5. Understand the concept of generalized integral.6. Understand the definite integral of approximate calculation method (rectangle method, trapezoidal method and parabola method).7. Be able to be used to express some definite integral geometry and physical (such as area, volume, arc length, power, water pressure, etc.).Textbooks and ReferencesTextbook: Advanced Mathematics I Tongji University, Department of Applied Mathematics References: 1. Advanced M