CALCULUS OF A SINGLE VARIABLE Sixth Edition

Transcription

1 CALCULUS OF A SINGLE VARIABLE Sixth Edition correlated to the Georgia Quality Core Curriculum Grade 9 12 Calculus (non-ap) McDougal Littell 5/2000

2 Georgia Quality Core Curriculum Subject Area: Textbook Title: Publisher: Mathematics Course: Grade 9-12 Calculus (non-ap) Calculus of a Single Variable, Sixth Edition 1998 Houghton Mifflin Calculus (non-ap) M Solves problems (including selecting appropriate approaches and tools and judging the reasonableness of results) throughout calculus. PE: A Preview of Calculus, 41-46; Motivating the Chapter, 2, 40, 90, 154, 240, 310, 406, 474, 546, 636; Explorations, 4, 12, 24, 44, 45, 47, 56, 67, 80, 91, 102, 125, 134, 141, 155, 172, 182, 221, 241, 258, 266, 274, 280, 287, 292, 311, 315, 321, 329, 333, 358, 377, 379, 445, 447, 461, 475, 481, 484, 499, 518, 525, 547, 558, 560, 588, 606, 689; Section Projects, 86, 140, 178, 195, 237, 286, 357, 402, 434, 453, 489, 498, 567, 573, 580, 661, 680; and problem-solving applications throughout (M below) IRG: Teaching Strategies, 2-15, 22-26; Motivating the Chapter, ; Explorations, ; Section Projects, PE: Pupil s Edition topics and pages; IRG: Instructor s Resource Guide: Strategies, Tests, and Special Feature Solutions for PE chapter/section page 1

3 M Relates concepts to real-world applications and to other concepts, using tools such as graphing calculators and computers. PE: Applications throughout, e.g.: Engineering and Physical Sciences, 2, 10, 13, 17, 19, 29, 30, 32, 34, 35, 36, 38, 40, 50, 66, 71, 78, 85, 88, 90, 108, 109, 112, 113, 120, 122, 123, 132, 133, 140, 142, 143, 144, 145, 146, 147, 148, 149, 151, 152, 154, 161, 162, 166, 167, 168, 175, 177, 178, 185, 186, 192, 194, 195, 205, 207, 208, 209, 210, 211, 212, 213, 214, 220, 223, 226, 227, 236, 238, 240, 247, 250, 251, 263, 279, 284, 285, 286, 298, 305, 306, 308, 310, 320, 326, 328, 346, 347, 348, 360, 362, 363, 364, 365, 376, 381, 384, 391, 395, 398, 399, 401, 402, 403, 404, 406, 415, 421, 424, 425, 426, 431, 433, 434, 438, 442, 443, 444, 445, 447, 448, 449, 450, 451, 452, 453, 454, 462, 463, 464, 466, 467, 468, 469, 470, 472, 474, 485, 488, 489, 498, 504, 506, 507, 516, 522, 531, 536, 541, 546, 563, 565, 566, 580, 614, 631, 633, 636, 641, 646, 647, 648, 649, 650, 651, 660, 661, 666, 669, 670, 680, 687, 692, 693, 695, 696, 697, A4, A16, A25, A26; PE: Pupil s Edition topics and pages; IRG: Instructor s Resource Guide: Strategies, Tests, and Special Feature Solutions for PE chapter/section page 2

4 M (continued) M M Relates concepts to real-world applications and to other concepts, using tools such as graphing calculators and computers. (continued) Defines, identifies, and applies concepts of function and relation with respect to domain, range, intercepts, symmetry, asymptotes, zeros, odd, and even. Applies the algebra of functions by finding sum, product, quotient, composition, and inverse, where they exist. PE: Applications throughout (continued), e.g.: Business and Economics, 10, 17, 18, 19, 37, 78, 88, 113, 122, 162, 167, 177, 178, 186, 194, 212, 220, 226, 229, 230, 231, 232, 233, 234, 237, 238, 251, 283, 284, 286, 298, 307, 308, 320, 328, 336, 345, 346, 353, 355, 357, 361, 364, 365, 376, 403, 404, 415, 471, 488, 531, 541, 544, 556, 557, 565, 566, 567, 632, 633, A9, A15, A27; Social and Behavioral Sciences, 8, 34, 35, 85, 88, 113, 122, 149, 152, 195, 210, 213, 227, 284, 308, 341, 355, 356, 364, 471, 488, 542, 566, 567, 633; Life Sciences, 10, 13, 19, 29, 31, 78, 132, 177, 220, 249, 284, 308, 328, 353, 355, 356, 361, 364, 372, 376, 404, 507, 516, 522, 544, 557; General, 78, 283, 285, 285, 347, 376, 412, 414, 567, 580, 621, 648; see also detailed Index of Applications, xxxi-xxvi; Technology Boxes, 98, 107, 116, 173, 386, 468, 478, 482, 483, 491, 500, 513, 528, 549, 561, 583, 597, 653; Technology Notes throughout the text; and M above IRG: Teaching Strategies, 2-15, 22-26; Motivating the Chapter, ; Explorations, ; Technology Boxes, ; Section Projects, PE: Graphs and Models, 3-10; Functions and Their Graphs, IRG: P.1, P.3 PE: Functions and Their Graphs, 20-30; Inverse Functions, IRG: P.3, 5.3 PE: Pupil s Edition topics and pages; IRG: Instructor s Resource Guide: Strategies, Tests, and Special Feature Solutions for PE chapter/section page 3

5 M M M M M Identifies and applies properties of algebraic, trigonometric, exponential, and logarithmic functions. Includes the following: polynomial (existence, number, and location of zeros), trigonometric (fundamental identities, addition formulas, graphs, amplitude, periodicity), exponential and logarithmic (properties, graphs, inverse, the number e as a limit), and absolute value (f( x ), f(x) ). Evaluates limits of functions and applies properties of limits. Indicates where a function is continuous and where it is discontinuous. Defines the derivative of a function in various ways (e.g., as the slope of the tangent line, rate of change of the function, and instantaneous velocity). Differentiates algebraic, trigonometric, exponential, and logarithmic functions. PE: Functions and Their Graphs, 20-30; Polynomial Equations, 218, 220; Exponential Functions, , ; Review of Trigonometric Functions, A17-A27 IRG: P.3, 3.8, 5.4, 5.5, A.3 PE: Finding Limits Graphically and Numerically, 47-55; Evaluating Limits Analytically, 56-66; Continuity and One- Sided Limits, 67-78; Infinite Limits, 79-86; Limits at Infinity, IRG: 1.2, 1.3, 1.4, 1.5, 3.5 PE: Continuity and One-Sided Limits, 67-78; 333 IRG: 1.4 PE: The Derivative and the Tangent Line Problem, ; Rates of Change, IRG: 2.1, 2.2 PE: The Derivative and the Tangent Line Problem, ; Basic Differentiation Rules and Rates of Change, ; The Natural Logarithmic Function and Differentiation, ; Bases Other than e, IRG: 2.1, 2.2, 5.1, 5.5 PE: Pupil s Edition topics and pages; IRG: Instructor s Resource Guide: Strategies, Tests, and Special Feature Solutions for PE chapter/section page 4

6 M M Differentiates the sum, product, and quotient (including tan x and cot x) of functions. Differentiates a composite function using the chain rule, including differentiating a rational power of a function. PE: Basic Differentiation Rules and Rates of Change, ; The Product and Quotient Rules, , IRG: 2.2, 2.3 PE: The Chain Rule, ; Related Rates, IRG: 2.4, 2.6 M Differentiates an implicitly defined function. PE: Implicit Differentiation, IRG: 2.5 M Differentiates the inverse of a function, including inverse trigonometric functions. PE: Derivative of an Inverse Function, ; Derivatives of Inverse Trigonometric Functions, ; Differentiation of Inverse Hyperbolic Functions, IRG: 5.3, 5.8, 5.9 M Finds successive derivatives of functions. PE: Higher-Order Derivatives, 120, ; First Derivative Test, ; Second Derivative Test, IRG: 2.3, 3.3, 3.4 M M M States and applies Rolle's Theorem and the Mean Value Theorem. Relates differentiability and continuity (that differentiability implies continuity). Uses l'hôpital's Rule (quotient indeterminate forms). PE: Rolle s Theorem and the Mean Value Theorem, IRG: 3.2 PE: Differentiability and Continuity, IRG: 2.1 PE: Indeterminate Forms and L Hôpital s Rule, IRG: 7.7 PE: Pupil s Edition topics and pages; IRG: Instructor s Resource Guide: Strategies, Tests, and Special Feature Solutions for PE chapter/section page 5

7 M M Applies the derivative to finding slope and to finding tangent and normal lines to a curve. Uses derivatives to sketch graphs by showing functions increasing or decreasing, finding relative and absolute maximum and minimum points, and showing concavity and finding points of inflection (Includes such functions as e x, e xsin x, f(x), f( x ).) PE: The Derivative and the Tangent Line Problem, ; Newton s Method, ; Differentials, ; Parametric Equations and Calculus, ; Slope and Tangent Lines to a Polar Graph, IRG: 2.1, 3.8, 3.9, 9.3, 9.4 PE: Increasing and Decreasing Functions and the First Derivative Test, ; Concavity and the Second Derivative Test, ; Limits at Infinity, ; A Summary of Curve Sketching, IRG: 3.3, 3.4, 3.5, 3.6 M Applies extreme value to problem situations. PE: Extrema on an Interval, ; Optimization Problems, IRG: 3.1, 3.7 M M M M Applies definition of derivative to problem situations involving speed, velocity, and acceleration, and involving average, instantaneous, or related rates of change. Defines the antiderivative and applies its properties. Applies the antiderivative to problems such as those involving distance and velocity from acceleration with initial conditions, and growth and decay. Relates the definite integral to the concept of the area under a curve. PE: Related Rates, ; Business and Economics Applications, IRG: 2.6, 3.10 PE: Antiderivatives and Indefinite Integration, IRG: 4.1 PE: Antiderivatives and Indefinite Integration, IRG: 4.1 PE: Riemann Sums and Definite Integrals, IRG: 4.3 PE: Pupil s Edition topics and pages; IRG: Instructor s Resource Guide: Strategies, Tests, and Special Feature Solutions for PE chapter/section page 6

8 M M M M M M M Approximates areas by using inscribed and circumscribed rectangles and other appropriate methods; includes using calculators and computers. Calculates areas by evaluating sums using sigma notation. Defines and applies the properties of the definite integral. Identifies and uses the Fundamental Theorem of Calculus in evaluating definite integrals. Integrates by substitution, by using identities, by changing variables, and by parts. Applies the integral to the average or mean value of a function on an interval. Finds the area between curves using integration formulas. PE: Area, IRG: 4.2 PE: Area, IRG: 4.2 PE: Riemann Sums and Definite Integrals, IRG: 4.3 PE: The Fundamental Theorem of Calculus, IRG: 4.4 PE: Integration by Substitution, ; Basic Integration Rules, ; Integration by Parts, ; Trigonometric Integrals, ; Trigonometric Substitution, ; Partial Fractions, ; Other Integration Techniques, IRG: 4.5, 7.1, 7.2, 7.3, 7.4, 7.5, 7.6 PE: The Fundamental Theorem of Calculus, ; Numerical Integration, IRG: 4.4, 4.6 PE: Area of a Region Between Two Curves, IRG: 6.1 M Finds the volume of a solid of revolution. PE: Volume: The Disc Method, ; Volume: The Shell Method, IRG: 6.2, 6.3 PE: Pupil s Edition topics and pages; IRG: Instructor s Resource Guide: Strategies, Tests, and Special Feature Solutions for PE chapter/section page 7

9 M Interprets ln x as the area under the curve of f(x) = 1/x. PE: The Number e, 314 IRG: 5.1 PE: Pupil s Edition topics and pages; IRG: Instructor s Resource Guide: Strategies, Tests, and Special Feature Solutions for PE chapter/section page 8