AP微積分課程設(shè)計

1、精選優(yōu)質(zhì)文檔-傾情為你奉上北京中加學校AP微積分課程的實施方案正值北京中加學校建校十五周年之際，為了實現(xiàn)百年名校的偉大目標，無論是在管理，還是在教育教學上都需要不斷健全和完善體制機制。然而，學科課程的建設(shè)和更新勢必首當其沖，迫在眉睫。暑假在大連舉行的北京中加學校數(shù)學課程和教學多元化的探究教學研討會為北京中加學校的學科建設(shè)開了先河，也奠定了思想基礎(chǔ)。借此良機，對于北京中加學校的特色學科之一，AP微積分，我們借鑒過去的教學經(jīng)驗，整合國內(nèi)外教學資源，依據(jù)美國大學理事會AP微積分的課程標準，擬定了關(guān)于AP微積分課程的教學設(shè)想。一、指導思想本課程是北京中加學校為學生開設(shè)的一門國際數(shù)學專業(yè)基礎(chǔ)課。開設(shè)本課

2、程的目的，在于以美國大學理事會規(guī)定的AP 微積分課程標準為指導，按照理論與實踐相結(jié)合的原則，通過對微積分基本原理及規(guī)律的講授，使學生系統(tǒng)掌握極限、連續(xù)、導數(shù)和積分等知識的基本原理、基本內(nèi)容和基本方法，對微積分在經(jīng)濟活動中的應(yīng)用有比較清晰的了解，提高學生專業(yè)詞匯量和閱讀英語原版書籍的能力，拓寬學生國際數(shù)學視野，使學生體驗到數(shù)學的價值和美學認知。課內(nèi)學時144，4學分，從高一第一學期開始開設(shè)，高二第二學期結(jié)束，將近兩個學年授完。二、課程目標AP微積分是在高中學習階段有余力、有能力、成績優(yōu)秀的學生有機會先修的美國大學基礎(chǔ)課程以獲得美國大學學分專業(yè)的必修課。要求學生在學完本課程后，掌握本課程

3、的基本原理、基本內(nèi)容、基本方法及基本知識，并具有對所學的微積分知識進行現(xiàn)實理解和實際應(yīng)用的能力，從而順利通過AP考試。據(jù)此，本課程考核著重于基本知識的掌握、理解和應(yīng)用分析能力兩個方面。在各章的考核要求中，有關(guān)基本概念、基本理論、基本公式、應(yīng)用分析能力的內(nèi)容按“識記、理解、簡單應(yīng)用和綜合應(yīng)用”四個層次要求。三、教學進度北京中加學校AP微積分教學內(nèi)容及其進度計劃學期普通班國際班AP微積分課時分配高一第一學期第一模塊集合（4課時）函數(shù)與基本初等函數(shù)（32課時）解析幾何（9課時）復合函數(shù)、反函數(shù)以及作圖計算器的使用高中課程：6課時/周，共54課時；AP微積分：2課時/周，共18課時；第二模塊直線與圓的

4、方程（9課時）圓錐曲線（8課時）三角函數(shù)（16課時）極限極限的運算法則高中課程：6課時/周，共54課時；AP微積分：2課時/周，共18課時；第二學期第三模塊三角恒等變換反三角函數(shù)導數(shù)導數(shù)的基本公式高中課程：2課時/周，共18課時；AP微積分：6課時/周，共54課時；第四模塊立體幾何導數(shù)的運算法則高中課程：2課時/周，共18課時；AP微積分：6課時/周，共54課時；高二第一學期第五模塊常用邏輯用語平面向量解三角形導數(shù)的應(yīng)用高中課程：2課時/周，共18課時；AP微積分：6課時/周，共54課時；第六模塊數(shù)列不等式積分方程微分方程高中課程：2課時/周，共18課時；AP微積分：6課時/周，共54課時；第

5、二學期第七模塊復數(shù)統(tǒng)計計數(shù)原理AP微積分總復習AP微積分AB考試高中課程：2課時/周，共18課時；AP微積分：6課時/周，共54課時；第八模塊參數(shù)方程極坐標AP微積分BC高中課程：4課時/周，共36課時；AP微積分BC：4課時/周，共36課時；高三第一學期總復習總復習畢業(yè)會考AP微積分BC高中課程：4課時/周，共36課時；AP微積分BC：4課時/周，共36課時；第二學期微積分其它大學預(yù)修課程AP微積分BCAP微積分BC考試高中課程：4課時/周，共36課時；AP微積分BC：4課時/周，共36課時；四、課程內(nèi)容Chapter 2 Limits and Derivatives第二章 極限和導數(shù)Tea

6、ching Content教學內(nèi)容Teaching Requirements and Objectives教學要求和目標Time學時2.1 The Tangent and Velocity Problems2.1切線和速率問題The student will apply the derivative to solve problems, including tangent and normal lines to a curve, curve sketching, velocity, acceleration.2.2 The Limit of a Function2.2 函數(shù)的極限The stu

7、dent will define and apply the properties of limits of functions. This will include limits of a constant, sum, product, quotient, one-sided limits, limits at infinity, infinite limits, and nonexistent limits.2.3 Calculating Limits Using the Limit Laws2.3利用極限法則計算極限2.5 Continuity2.5 連續(xù)性The student wil

8、l state the definition of continuity and determine where a function is continuous or discontinuous. This will include continuity at a point; continuity over a closed interval; and graphical interpretation of continuity and discontinuity.2.6 Limits at Infinity; Horizontal Asymptotes2.6 無窮遠處極限和水平漸近線Th

9、e student will define and apply the properties of elementary functions, including algebraic, trigonometric, exponential, and composite functions and their inverses, and graph these functions using a graphing calculator. Properties of functions will include domains, ranges, combinations, odd, even, p

10、eriodicity, symmetry, asymptotes, zeros, upper and lower bounds, and intervals where the function is increasing or decreasing.The student will also define and apply the properties of limits of functions. This will include limits of a constant, sum, product, quotient, one-sided limits, limits at infi

11、nity, infinite limits, and nonexistent limits.2.7 Tangents, Velocities, and Other Rates of Change2.7切線、速度和其它的變化率2.8 Derivatives2.8導數(shù)The student will find the derivative of an algebraic function by using the definition of a derivative. This will include investigating and describing the relationship b

12、etween differentiability and continuity.2.9 The Derivative as a Function2.9 導函數(shù)Review復習Chapter 3 Differentiation Rules第三章 導數(shù)法則Teaching Content教學內(nèi)容Teaching Requirements and Objectives教學要求和目標Time學時3.1 Derivatives of Polynomials and Exponential Functions3.1多項式函數(shù)和指數(shù)函數(shù)的導數(shù)The student will apply formulas t

13、o find the derivative of algebraic, trigonometric, exponential, and logarithmic functions and their inverses.3.2 The Product and Quotient Rules3.2導數(shù)的乘法和除法運算法則The student will apply formulas to find the derivative of the sum of elementary functions.3.3 Rates of Change in the Natural and Social Scienc

14、es3.3自然科學和社會科學中的變化率Students will be able to understand the mathematical modeling process of derivatives (rates of changes) in the real world3.4Derivatives of Trigonometric Functions3.4三角函數(shù)的導數(shù)Students will be able to use the differentiation rules of trigonometric functions 3.5 The Chain Rule3.5鏈式法則Th

15、e student will apply formulas to find the derivative of the sum, product, quotient, inverse and composite (chain rule) of elementary functions.3.6 Implicit Differentiation3.6隱函數(shù)求導The student will find the derivative of an implicitly defined function.3.7 Higher Derivatives3.7高階導數(shù)The student will find

16、 the higher order derivatives of algebraic, trigonometric, exponential, and logarithmic functions.3.8Derivative of Logarithmic Functions3.8對數(shù)函數(shù)的導數(shù)The student will use logarithmic differentiation as a technique to differentiate non-logarithmic functions.3.9 Hyperbolic Functions3.9 雙曲函數(shù)The student wil

17、l be able to understand the definition of hyperbolic functions, and solve for its derivatives.3.11 Linear Approximations and Differentials3.11 線性逼近和微分The student will apply the derivative to solve problems, including tangent and normal lines to a curve, curve sketching, velocity, acceleration, relat

18、ed rates of change, Newton's method, differentials and linear approximations, and optimization problems.Review復習Chapter 4 Applications of Differentiation第四章 導數(shù)的應(yīng)用Teaching Content教學內(nèi)容Teaching Requirements and Objectives教學要求和目標Time學時4.1 Maximum and Minimum Values4.1 極大值和極小值The student will be able

19、 to understand extreme values of a function, find critical values of a function and find extreme values of a function.4.2 The Mean Value Theorem4.2 中值定理The student will state (without proof) the Mean Value Theorem for derivatives and apply it both algebraically and graphically.4.3 How Derivative Aff

20、ect the Shape of a Graph4.3導數(shù)是如何改變圖像的形狀The student will graph these functions using a graphing calculator, including understanding and using the First Derivative Test and the Second Derivative Test to determine mins and maxs.4.4 Indeterminate Forms and L Hospitals Rules4.4 不定式和洛必達法則The student will

21、use l'Hopital's rule to find the limit of functions whose limits yield the indeterminate forms: 0/0 and infinity/infinity4.7 Optimization Problems4.7最優(yōu)化問題The student will be able to use derivatives to solve optimization problems4.9 Newtons Method4.9牛頓法則The student will be able to use Newtons

22、 method to approximate roots of an equation.4.10Antiderivatives4.10 原函數(shù)（反導數(shù)）The student will be able to understand the concept of an antiderivative, the geometry of the antiderivative and that of slope fields and also work rectilinear motion problems with antiderivativesReview復習Chapter 5 Integrals第五

23、章 積分Teaching Content教學內(nèi)容Teaching Requirements and Objectives教學要求和目標Time學時5.1 Areas and Distances5.1 面積和距離The student will identify the properties of the definite integral. This will include the Fundamental Theorem of Calculus and the definite integral as an area and as a limit of a sum as well as th

24、e fundamental theorem.5.2 The Definite Integral5.2不定積分The student will compute an approximate value for a definite integral. This will include numerical calculations using Riemann Sums and the Trapezoidal Rule.5.3 The Fundamental Theorem of Calculus5.3微積分基本定理The student will identify the properties

25、of the definite integral. This will include the Fundamental Theorem of Calculus and the definite integral as an area and as a limit of a sum as well as the fundamental theorem. The integral from a to x of f(t)d(t) dt/dx = f(x)5.4 Indefinite Integrals and the Net Change Theorem5.4 不定積分和原函數(shù)定理The stude

26、nt will find the indefinite integral of algebraic, exponential, logarithmic, and trigonometric functions. 5.5 The Substitution Rule5.5 換元積分法The student will find the indefinite integral of algebraic, exponential, logarithmic, and trigonometric functions. The special integration techniques of substit

27、ution (change of variables) and integration by parts will be included.Review復習Chapter 6 Applications of Integration 第六章 積分的應(yīng)用Teaching Content教學內(nèi)容Teaching Requirements and Objectives教學要求和目標Time學時6.1 Areas Between Curves6.1 曲邊面積The student will apply the definite integral to solve problems. These prob

28、lems will include finding distance traveled on a line and velocity from acceleration with initial conditions, growth and decay problems, solutions of separable differential equations, the average value of a function, area between curves, volumes of solids of revolution about the axes or lines parall

29、el to the axes using disc/washer and shell methods, and volumes of solids with known cross-sectional areas.6.2 Volumes6.2 體積The student will apply the definite integral to solve problems. These problems will include area between curves, volumes of solids of revolution about the axes or lines paralle

30、l to the axes using disc/washer and shell methods, and volumes of solids with known cross-sectional areas.6.3 Volumes by Cylindrical Shells6.3 圓柱體體積The student will apply the definite integral to solve problems. These problems will include area between curves, volumes of solids of revolution about t

31、he axes or lines parallel to the axes using disc/washer and shell methods, and volumes of solids with known cross-sectional areas.6.4 Work6.4 物體功The student will apply the definite integral to solve problems. These problems will include finding distance traveled on a line and velocity from accelerat

32、ion with initial conditions, growth and decay problems, work done.6.5 Average Value of a Function6.5 實函數(shù)均值The student will apply the definite integral to solve problems. These problems will include the average value of a function.6.6 Density Function6.6 密度函數(shù)The student will apply the definite integr

33、al to solve problems. These problems will include finding distance traveled on a line and velocity from acceleration with initial conditions, growth and decay problems.Review復習Chapter 7 Techniques of Integration第七章 積分技巧Teaching Content教學內(nèi)容Teaching Requirements and Objectives教學要求和目標Time學時7.1 Integrat

34、ion by Parts7.1 分部積分法The student will find the definite and indefinite integral of algebraic, exponential, logarithmic, and trigonometric functions. The special integration techniques of substitution (change of variables) and integration by parts will be included.7.2 Trigonometric Integrals7.2 三角函數(shù)積

35、分7.3 Trigonometric Substitution7.3 三角函數(shù)替換7.4 Integration of Rational Functions by Partial Fractions7.4 有理函數(shù)的分部積分Review復習五、考核方式為了彰顯我?！岸嘁话殉咦樱嘁晃蝗瞬拧钡慕逃虒W理念，本課程采用形成性考核與終結(jié)性考核相結(jié)合的方式。（一）形成性考核內(nèi)容 本課程的形成性考核具體內(nèi)容分為學習內(nèi)容考核和學習過程考核。學習內(nèi)容考核：1 平時作業(yè)：任課教師課堂上集中布置的隨堂作業(yè)和課后作業(yè)。同時，不同年級的教師在布置作業(yè)時也可根據(jù)各班的實際情況適當加以細化、加入一些限制性條件或進一步的

36、要求。2階段性測驗：是根據(jù)課程教學安排布置的階段性綜合測驗。階段性測驗主要考查學生在一個單元內(nèi)的學習狀態(tài)，其測查內(nèi)容屬于教學中的重點，涉及到講過的大部分基本概念、基本原則和基本方法。3課堂討論：在課程教學過程中，在指定時間，圍繞一定的主題，對課程的重點、難點內(nèi)容，集中進行若干次課堂討論。課堂討論的題目提前一周告知學生，讓學生以學習小組為單位進行討論前的準備，每學習小組推選一人做代表性發(fā)言并提供以小組名義提交的討論提綱。指導教師根據(jù)各小組學生參與程度、發(fā)言情況及討論提綱給予評價并以小組形式給予評定成績。學習過程考核：1建立學習小組：參與試點的班級應(yīng)該以5-6名學生組成學習小組，指定學習組長并報班

37、主任及指導教師。根據(jù)學校和任課老師的要求，有計劃有目的地開展學習活動，完成并按時上交形成性考核中要求以小組為單位進行的作業(yè)。小組學習應(yīng)該有盡可能詳細的學習過程記錄，反映學生在學習小組活動中的內(nèi)容、體會及存在問題，期末交到指導教師處，作為指導教師對學生形成性考核成績評定的依據(jù)之一。2. 課堂出勤：學生是否按時上課，在很大程度反映了該學生對待學習的態(tài)度；學生在課堂上是否聽從教師的指令也都應(yīng)該考慮在考勤的范圍內(nèi)。（二）終結(jié)性考試終結(jié)性考試主要考核學生對AP微積分的基本理論、基本知識、基本概念的理解與把握，總分100分。終結(jié)性考試的題型嚴格參照AP考試的題型和設(shè)置。 （三）成績評定形成性考核成績占總成

38、績的60%。形成性考核成績由任課教師根據(jù)學生實際表現(xiàn)情況評定，由教學處責任教師評審，最終確定學生的課程形成性考核成績。北京中加學校對形成性考核進行抽樣檢查。終結(jié)性考核占課程總成績的40%，見表2，然后通過計算機在線登分并匯總。表2 北京中加學校學生學業(yè)成績評定分配表項目形成性考核內(nèi)容終結(jié)性考核內(nèi)容作業(yè)測驗討論小組出勤比例15%15%10%10%10%40%學期成績?yōu)槠谥谐煽兒推谀┏煽兏髡?0%。根據(jù)北京中加學校的規(guī)定，本課程實行形成性考核成績和終結(jié)性考試成績的總綜合成績達到60分及以上（及格），即可獲得本課程相應(yīng)學分。女人，應(yīng)該活出自己的自信和精彩，不能把賴以生存的東西寄托在他人身上，不管他多

39、么愛你，終有一天會厭倦你的依賴和無所事事。越有能力的女人，越自信；越有能力的女人，越可愛；越有能力的女人，越值得擁有和疼惜。愛情，充滿了熱烈和激情，在熱情戀愛中的男女，都會忽略掉對方的缺點，看到的都是優(yōu)點，甚至失去理智和冷靜。倘若戀愛時候，太過于理智和冷靜，可能就不叫愛情。再熱烈的愛，都有冷卻的時候，冷卻后的我們，始終是要考慮現(xiàn)實生活里的柴米油鹽醬醋茶的。最好的愛情，是能夠經(jīng)歷時間的考驗，在激情過后，依然愿意陪你在俗世煙火里，看細水長流。都說陪伴是最長情的愛，但是最好的陪伴，就是簡單的柴米油鹽。人生充滿世味，需要醉人的浪漫，更離不開俗世煙火，然而不是每一個人都會因為愛情，而走進一生無悔的圓滿婚

40、姻里。再浪漫的婚姻，都離不開柴米油鹽醬醋茶的瓢碗碰撞。好的愛情和婚姻，是兩個人同視著一個方向，攜手并進。在婚姻里，女人的獨立并不是為了證明什么？而是讓自己活的更精彩，讓生活更幸福。優(yōu)秀的女人，也會讓你更具有魅力。真正愛你的人，不光讓你有豐衣足食的生活，更會讓你越來越優(yōu)秀。一個聰明的女人，她不會因為安逸的生活去愛上一個男人，她會因為這個男人的優(yōu)秀而義無反顧的愛上他。一般來說，男人和女人，是一樣的，都希望另一半是可以在生活里獨立行走的人，是可以給自己成長和進步的人，能夠讓自己有安全感，絕不是在患得患失里生活。真正愛你的人，沒有配不配，也許對方不是最好條件的一個，但一定是那個可以讓你進步，也最讓你悸動心靈的人。沒有誰愿意看到自己的另一半，每一天都在渾渾噩噩不思進取的活著。愛你的人，相處中會讓你越活越漂亮，越活越精彩。在愛情的路上，兩個真心相愛的人，會彼此相互成長，相互快樂的進步。你也許不優(yōu)秀，但是因為愛，優(yōu)秀可以影響你，這就叫，近