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AP® Calculus BC Students enrolled in Calculus BC have already successfully completed a year of Calculus in our Calculus AB course. Course Overview We cover everything in the Calculus BC topic outline as it appears in the AP® Calculus Course Descriptions. The primary textbook is Calculus, Larson, Hostetler, et al., 8th ed.. We study four major ideas: limits, derivatives, indefinite integrals, and definite integrals. As we develop the concepts, we explain how the mechanics go along with the topics, and stress application. Since concepts are so vital to AP® Calculus, there is an attempt to balance understanding, skills, and use of technology. The course provides students with the opportunity to work with functions represented graphically, numerically, analytically, and verbally—and emphasizes the connections among these representations. Chapter 7 - Applications of Integration 7.4 Arc Length and Surfaces of Revolution Objectives: (1) Find the arc length of a smooth curve; (2) Find the area of a surface of revolution. Day 1: p. 483 # 3, 6, 15 - 23 odd Day 2: p. 483 # 41 & 43 Chapter 8 - Integration Techniques, L'Hôpital's Rule, and Improper Integrals 8.1 Basic Integration Rules Objective: Review procedures for fitting and integrand to the basic integration rules. Day 1: p. 522 # 15 - 33 odd Day 2: p. 522 # 35 - 49 odd Day 3: p. 522 # 57, 58, 61 - 67 odd Test 8.1 (7.4, 8.1) 8.2 Integration by Parts Objective: Find an antiderivative using integration by parts. Day 1: p. 531 # 17 - 35 odd. Day 2: p. 531 # finish day 1 assignment. Day 3: p. 531 # 47 – 63 odd. 8.3 Trigonometric Integrals Objectives: (1) Solve trigonometric integrals involving powers of sine and cosine; (2) Solve trigonometric integrals involving powers of secant and tangent. Day 1: p. 540 # 1 - 18 ALL Day 2: p. 540 # 25 – 41 Odd 8.5 Partial Fractions Objectives: (1) Understand the concept of partial fraction decomposition; (2) Use partial fraction decomposition with non-repeating linear factors to integrate rational functions. Day 1: p. 559 # 1 - 16 ALL Test 8.235 (8.2, 8.3, 8.5) 8.7 Indeterminate Forms and L'Hôpital's Rule Objectives: (1) Recognize limits that produce indeterminate forms; (2) Apply L'Hôpital's Rule to evaluate a limit. Day 1: p. 574 # 5 - 53 odd Day 2: p. 574 # 75 - 78 all 8.8 Improper Integrals Objectives: (1) Evaluate an improper integral that has an infinite limit of integration; (2) Evaluate an improper integral that has an infinite discontinuity. Day 1: p. 585 # 5 - 10 ALL. [Use symbolic integration utility to evaluate integrals. Find limits by analytic methods.] Chapter 8 Test Chapter 9 - Infinite Series 9.1 Sequences Objectives: (1) List terms of a sequence; (2) Determine whether a sequence converges or diverges; (3) Write a formula for the nth term of a sequence; (4) Use properties of monotonic sequences and bounded sequences. Day 1: p. 602 # 1 - 41 odd Day 2: p. 603 # 57 - 67 odd 9.2 Series and Convergence Objectives: (1) Understand the definition of a convergent infinite series; (2) Use properties of infinite geometric series; (3) Use the nth-Term Test for Divergence of an infinite series. Day 1: p. 612 # 1 - 21 odd Day 2: p. 612 # 23 - 28 all Day 3: p. 613 # 57 - 69 odd 9.3 The Integral Test and p-Series Objectives: (1) Use the Integral Test to determine whether an infinite series converges or diverges; (2) Use properties of p-series and harmonic series. Day 1: p. 620 # 1 - 17 odd Day 2: p. 573 # 29 - 36 all 9.4 Comparisons of Series Objectives: (1) Use the Direct Comparison Test to determine whether a series converges or diverges; (2) Use the Limit Comparison Test to determine whether a series converges or diverges. Day 1: p. 628 # 3 - 14 ALL Day 2: p. 628 # 15 - 28 ALL, 29, 36 9.5 Alternating Series Objectives: (1) Use the Alternating Series Test to determine whether an infinite series converges; (2) Use the Alternating Series Remainder to approximate the sum of an alternating series; (3) Classify a convergent series as absolutely or conditionally convergent; (4) Rearrange an infinite series to obtain a different sum. Day 1: p. 636 # 11 - 27 odd Day 2: p. 636 # 47 – 59 odd 9.6 The Ratio and Root Tests Objectives: (1) Use the Ratio Test to determine whether an infinite series converges or diverges; (2) Use the Root Test to determine whether an infinite series converges or diverges; (3) Review the tests for convergence and divergence of an infinite series. Day 1: p. 645 # 1 - 4 ALL, 13 - 29 odd Day 2: p. 645 # 37 - 49 odd Day 3: p. 645 # 51 - 65 odd Day 4: p. BC Packet p. 176 9.7 Taylor Polynomials and Approximations Objectives: (1) Find polynomial approximations of elementary functions and compare them with the elementary function; (2) Find Taylor and Maclaurin polynomial approximations of elementary functions; (3) Use the remainder of a Taylor polynomial. Day 1: p. 656 # 1 - 4 ALL, 13 - 23 odd Day 2: p. 656 # 33, 34, 45, 47 9.8 Power Series Objectives: (1) Understand the definition of a power series; (2) Find the radius and interval of convergence of a power series; (3) Determine the endpoint convergence of a power series. Day 1: p. 666 # 5 - 29 odd 9.9 Representations of Functions by Power Series Objectives: (1) Find a geometric power series that represents a function; (2) Construct a power series using series operations. Day 1: p. 674 # 1 - 15 odd [Use your calculator to observe the graph of the first few terms of the series along with the original functions.] 9.10 Taylor and Maclaurin Series Objectives: (1) Find a Taylor and a Maclaurin series for a function; (2) Use a basic list of Taylor series to find other Taylor series. Day 1: p. 685 # 1 – 7 Day 2: p. 685 # 21 – 29 odd Chapter 10 - Parametric Equations and Polar Coordinates 10.2 Plane Curves and Parametric Equations Objectives: (1) Sketch the graph of a curve given by a set of parametric equations; (2) Eliminate the parameter in a set of parametric equations. Day 1: p. 716 # 1 - 31 odd 10.3 Parametric Equations and Calculus Objectives: (1) Find the slope of a tangent line to a curve given by a set of parametric equations; (2) Find arc length of a curve given by a set of parametric equations. Day 1: Arc length: p. 724 # 5 - 13 odd, 17 – 25 odd Day 2: 27 – 41 odd 10.4 Polar Coordinates and Polar Graphs Objectives: (1) Understand the polar coordinate system; (2) Rewrite rectangular equations in polar form and vice versa; (3) Sketch the graph of an equation given its specific polar form; (4) Find the slope of a tangent line to a polar graph; (5) Identify several types of special polar graphs. Day 1: p. 736 # 1 – 41 odd Day 2: p. 736 # 61 - 79 odd 10.5 Area and Arc Length in Polar Coordinates Objectives: (1) Find the area of a region bounded by a polar graph. Day 1: p. 745 # 7 - 16 More on Differential Equations Objectives: (1) Find numerical solutions of differential equations using Euler’s Method; (2) Solve logistic differential equations and use them in modeling. Days 1-3: Packet on Euler’s Method and logistic differential equations Vector-Valued Functions Objectives: (1) Analyze curves in vector form, and find derivatives of vector functions. AP Review