کلاسیک‌های حساب دیفرانسیل و انتگرال بارونز (بارونز: پیشتاز در آمادگی برای آزمون)

Overview: Both Calculus AB and Calculus BC are covered in this comprehensive AP test preparation manual. Prospective test takers will find four practice exams in Calculus AB and four more in Calculus BC, with all questions answered and solutions explained. The manual also provides a detailed 10-chapter review covering topics for both exams. The authors also offer an overview of the AP Calculus exams, which includes advice to students on making best use of their graphing calculators. Introduction Courses Topics that may be tested on the calculus AB exam Topics that may be tested on the calculus BC exam Examinations Graphing calculator: using your graphing calculator on the AP exam Grading the examinations CLEP calculus examination This review book Diagnostic Tests Calculus AB Calculus BC Topical Review And Practice Functions Definitions Special functions Polynomial and other rational functions Trigonometric functions Exponential and logarithmic functions Parametrically defined functions Practice exercises Limits And Continuity Definitions and examples Asymptotes Theorems on limits Limit of a quotient of polynomials Other basic limits Continuity Practice exercises Differentiation Definition of derivative Formulas Chain rule; the derivative of a composite function Differentiability and continuity Estimating a derivative Numerically Graphically Derivatives of parametrically Defined functions Implicit differentiation Derivative of the inverse of a function Mean value theorem Indeterminate forms and L'Hopitals' rule Recognizing a given limit as a derivative Practice exercises Applications of differential calculus Slope; critical points Tangents and normals Increasing and decreasing functions Case 1: Functions with continuous derivatives Case 2: Functions whose derivatives have discontinuities Maximum, minimum, and inflection points: definitions Maximum, minimum, and inflection points: curve sketching Case 1: Functions that are everywhere differentiable Case 2: Functions whose derivatives may not exist everywhere Global maximum or minimum Case 1: Differentiable functions Case 2: Functions that are not everywhere differentiable Further aids in sketching Optimization: problems involving maxima and minima Relating a function and its derivatives graphically Motion along a line Motion along a curve: velocity and acceleration vectors Tangent-line approximations Related rates Slope of a polar curve Practice exercises Antidifferentiation Antiderivatives Basic formulas Integration by partial fractions Integration by parts Applications of antiderivates; differential equations Practice exercises Definite Integrals Fundamental theorem of calculus (FTC); definition of definite integral Properties of definite integrals Integrals involving parametrically defined functions Definition of definite integral as the limit of a sum: the fundamental theorem again Approximations of the definite integral: Riemann sums Using rectangles Using trapezoids Comparing approximating sums Graphing a function from its derivative; another look Interpreting 1n x as area Average value Practice exercises Applications Of Integration To Geometry Area Area between curves Using symmetry Volume Solids with known cross sections Solids of revolution Arc length Improper integrals Practice exercises Further Applications Of Integration Motion along a straight line Motion along a plane curve Other applications of Riemann sums FTC: definite integral of a rate is net change Practice exercises Differential Equations Basic definitions Slope fields Euler's method Solving first-order differential Equations analytically Exponential growth and decay Case 1: Exponential growth: dy_dt=ky Case 2: Restricted growth: dy_dt=k(A-y) Case 3: Logistic growth: dy_dt=ky(A-y) Practice exercises Sequences And Series Sequences of real numbers Infinite series Definitions Theorems about convergence or divergence of infinite series Test for convergence of infinite series Tests for convergence of nonnegative series Alternating series and absolute convergence Power series Definition; convergence Functions defined by power series Finding a power series for a function: Taylor and Maclaurin series Approximating functions with Taylor and Maclaurin polynomials Taylor's formula with remainder; Lagrange error bound Computations with power series Power series over complex numbers Practice exercises Miscellaneous Multiple-Choice Practice Questions Miscellaneous Free-Response Practice Exercises AB Practice Examinations AB one AB two AB three BC Practice Examinations BC one BC two BC three Appendix: Formulas and theorems for reference Index. 7_4324_APCalc_0FM_012.pdf 1 7_4324_APCalc_013_040.pdf 19 7_4324_APCalc_041_064.pdf 47 7_4324_APCalc_065_086.pdf 71 7_4324_APCalc_087_110.pdf 93 7_4324_APCalc_111_132.pdf 117 7_4324_APCalc_133_158.pdf 139 7_4324_APCalc_159_191.pdf 165 7_4324_APCalc_192_214.pdf 198 7_4324_APCalc_215_228.pdf 221 7_4324_APCalc_229_248.pdf 235 7_4324_APCalc_249_276.pdf 255 7_4324_APCalc_277_290.pdf 283 7_4324_APCalc_291_316.pdf 297 7_4324_APCalc_317_344.pdf 323 7_4324_APCalc_345_355.pdf 351 7_4324_APCalc_356_366.pdf 362 7_4324_APCalc_367_390.pdf 373 7_4324_APCalc_391_406.pdf 397 7_4324_APCalc_407_437.pdf 413 7_4324_APCalc_438_452.pdf 444 7_4324_APCalc_453_488.pdf 459 7_4324_APCalc_489_508.pdf 495 7_4324_APCalc_509_536.pdf 515 7_4324_APCalc_537_564.pdf 543 7_4324_APCalc_565_594.pdf 571 7_4324_APCalc_595_618.pdf 601 7_4324_APCalc_619_642.pdf 625 7_4324_APCalc_643_666.pdf 649 7_4324_APCalc_667_676.pdf 673 7_4324_APCalc_677_682.pdf 683 Both Calculus AB and Calculus BC are covered in this comprehensive AP test preparation manual, which presents four practice exams in Calculus AB and four more in Calculus BC, with all questions answered and solutions explained. A detailed 10-chapter review covers topics for both exams. Students who purchase the book with the optional CD-ROM will get two additional practice tests, one in Calculus AB, and the other in Calculus BC. Tests on the CD-ROM come with solutions explained and automatic scoring of the multiple-choice questions. The authors also offer an overview of the AP Calculus exams, which includes advice to students on making best use of their graphing calculators.
Both Calculus AB and Calculus BC are covered in this comprehensive AP test preparation manual. Prospective test takers will find four practice exams in Calculus AB and four more in Calculus BC, with all questions answered and solutions explained. The manual also provides a detailed 10-chapter review covering topics for both exams. The authors also offer an overview of the AP Calculus exams, which includes advice to students on making best use of their graphing calculators. A study guide for the advanced placement exam in Calculus. Includes review sections on all test topics and eight full-length practice tests with answers and explanations