【正文】 7. Comprehend the Fourier series and system of triangular functions, and hand Fourier series expansion to functions.19 / 20。s series expansion to functions。s series。 4. Govern the convergence and convergent interval of a power series, and the properties of power series in their convergent intervals。 Use flexibly the Termwise Comparison Test, Limit Test, Ratio Test and Root Test for convergence of series of positive number terms。 be acquainted with judging the convergence and divergence of infinite series。 5. Apply practically the formula of solution of a linear differential equation。 3. Be acquaint with solving homogeneous differential equations and other methods for solving differential equations。7. Apply multiple integral, line integral and surface integral to geometric and physical problems. Part Seven: Ordinary differential equation1. Learn well terminologies and notions on differential equations, such as ordinary differential Equation, the order and degree of a differential equation, special (particular) solutions, general (plete) Solution and the initialvalue problem。6. Know the vector fields, divergence, rotation and some particular fields。 4. Control the spirit of the Green’s formula, understand the putation of a line integral is independent of line and its physical meaning。2. Be able to pute double integrals and trip1e integrals in rectangle coordinate system, tripolar coordinate system, cylindrical coordinates and spherical coordinates。 7. Be acquainted with tangent lines and normal planes, and tangent planes and normal lines of a surface。5. Work well on the concepts of directional derivative and gradient with putation。 3. Demonstrate understanding of partial derivative and total differentiation, and the condition of existence of a total differentiation。7. Know the classification of quadric surfaces.Part Five: Differentiation of multiple real variables1. Learn well functions of multiple real variables, especially, those of two real variables。5. Be familiar with general and parameter equations of space curves。 3. Be able to determine equations of a plane or a line in space, by means of connection between planes and lines of space to overe mathematical problems。6. Comprehend two types of improper integrals as the limit values of a definite integral of active upper limit.Part Four: Vector algebra and Analytic Geometry of Space1. Understand the rectangular coordinates system of space, the concept of a vector and express a vector by coordinates, some particular vectors (unite vectors, direction cosine of a vector)。3. Use an integral of active upper limit to define a function,4. Applying the core theorem of the NewtonLeibnizs’ formula to pute an definite integral is very important,。12. Know well the concepts of curvature and curvature radius, and be able to estimate them。 determine vertical asymptotes and horizontal asymptotes。 be familiar with deciding monotone and determining extremum by derivative。9. Feeling the thought a polynomial approximating to a function, that is the Talory’s formula。8. Using L’Hopital’s rule in putation of indeterminate limits is a significant technique。6. Show understanding of the concept of highrank derivatives, and pute proficiently highrank derivatives on explicit and implicit functions。4. Demonstrate understanding of the major aspects of differentiation, such as geometric significance, the idea of local linearity, and so on。2. Recognize the connection between derivative and continuity。9. Be aware of each elementary function is continuous on its domain, emphasize the knowledge of continuous functions defined on closed intervals, the importance is to apply the theory of limits and continuity to solve problems。 8. Realize the difference of being continuous at a point and in an interval about a function。6. Know well how to use two important limits (the circular limit, elimit) in practical problems。4. Understand the “ε－N” definition and the “ε－δ” definition, and apply them to deal with simple problems。 2. Know the concept of a pound function, and the inverse function of a function。 understand and apply the core theorems and methods, generating examples as needed, and asking the next natural question. be able to translate suitable problems to calculus problems, formulate a method of solution for them, and analyze the efficiency of the solution. acquaint him/herself with limit as a tool for solving problems, both of theoretical and practical nature. Series.Capability. This course aims primarily to improve students39。 Advanced Mathematics of functions of multiple real variables。 Advanced Mathematics of functions of one real variable。2. 網(wǎng)站正在籌劃建設中。然而，在大學不同的專業(yè)里有不同的名字，也常稱為《微積分》（國外的許多大學里用這個名稱），在數(shù)學專業(yè)里把它叫做《數(shù)學分析》（至少學三至四個學期）。其中，對授課教師的課時和課程教學工作量給予政策性傾斜；重視雙語教學師資隊伍建設，尤其是注重對中青年教師的培養(yǎng)；學院加大軟硬件投入；在課程建設相關教材方面，鼓勵教師使用優(yōu)秀英文教材；教學質(zhì)量常抓不懈。聘請國外專家來校授課，進行教學方法學術交流，提高教師的雙語教學水平。42雙語師資建設及授課計劃（含外聘人員）現(xiàn)有教學隊伍主要成員都有豐富的教學經(jīng)驗。課程英文網(wǎng)站建設規(guī)劃：本科程的教學網(wǎng)絡平臺建設目前還處于起步階段。 2009－2012 對本課程的教師進行培訓，加強青年教師的培養(yǎng)，開拓視野，掌握課程發(fā)展的前沿最新信息。 2010－2011利用國內(nèi)外優(yōu)秀教材，結合本校實際，針對一、二個專業(yè)的需求，初步編寫本課程基礎教材以及相應的輔導教材。結合實際教學中的反饋信息，更新教學內(nèi)容，探索基礎教材的建設。3. 教學錄像（正在進行）4．課程建設規(guī)劃41 本課程三年內(nèi)的建設規(guī)劃（含課程網(wǎng)站建設規(guī)劃）課程階段建設規(guī)劃：（1）國內(nèi)網(wǎng)站主要包括：中國數(shù)學資源網(wǎng)：