Mathematics & Statistics Texas Tech University Kent Pearce Department of Mathematics and Statistics Texas Tech University Lubbock, Texas 79409-1042 Voice: (806)742-2566 x 226 FAX: (806)742-1112 Email: kent.pearce@ttu.edu

Homework -- Calculus II
 Math 1352-002 Summer II 2000 Bradley and Smith Calculus, 2nd Ed. Prentice Hall Upper Saddle River, New Jersey

 Content Homework Hours 6.1: Area Between Curves f(x) >= g(x) f, g intersecting horizontal strips economics examples Multiples of 3 (3-27, 33-42) 2 6.2: Volume by Cross-Sectional Area cross-sectional area solids of revolution disk method washer method Multiples of 3 (3-48) 2 6.3: Volume by Shells Multiples of 3 (3-33) 2 6.4: Arc Length and Surface Area arclength y = f(x) arclength x = g(y) surface area: solids of revolution Multiples of 3 (3-27) 1 6.5: Applications work Hooke's law fluid force centroids and moments theorem of Pappus Multiples of 3 (6-42) 3

 Content Homework Hours 7.1: Review anti-differnetiation formulae substitution tables Multiples of 3 (3-42, 48-60) 2 7.2: Integration by Parts formula definite integrals repetition Multiples of 3 (3-45) 1 7.3: Trigonometric Methods powers of sinmx cosnx powers of tanmx secnx trigonometric substitution Multiples of 5 (5-60) 1 7.4: Partial Fractions reduced form single linear factors repeated linear factors single quadactic factors repeated quadratic factors Heavyside covering method rational functions of sin x and cos x Multiples of 5 (5-55) 2 7.5: Summary of Methods (a) simplification (b) basic formulae (c) substitution (d) integration by parts (e) trigonometric functions: reduction, identities (f) radical functions: trigonometric substitution (g) rational functions: partial fraction decomposition Computer Algebra Software Summary: Multiples of 7 (7-84) Software: [Multiples of 7] + 1 (8-71) 1 7.6: First Order Differential Equations review separable equations linear differential equations initial value problems modelling exponential growth modelling logistic growth Multiples of 3 (3-15, 21-30) 34, 39, 42 2 7.7: Improper Integrals unbounded domains unbounded integrands Multiples of 3 (3-42) 43, 46, 49, 51 2 7.8: Hyperbolic Functions definitions identities differentiation formulae integration formulae inverse functions differentiation / integration formulae Multiples of 3 (3-51) 2

 Content Homework Hours 8.1: Sequences definitions limits: intuitive and formal limit theorems composition theorems sandwich (squeeze) theorem bounded and monotonic sequences Multiples of 3 (3-45) 2 8.2: Infinite and Geometric Series definitions convergence and divergence convergence (limit) theorems telescoping series geometric series decimals and proportional decay Multiples of 3 (3-27) 32, 39, 41, 48, 51, 54 2 8.3: Integral Test and p-series divergence test series with non-negative terms (s.n.n.t.) integral test p-series Multiples of 5 (5-55) 1 8.4: Comparison Tests for s.n.n.t. direct comparison test convergence and divergence limit comparison test convergence and divergence 1, 2 Multiples of 5 (5-50) 2 8.5: Ratio and Root Tests for s.n.n.t. ratio test convergence, divergence and inconclusive root test convergence, divergence and inconclusive 1, 2 Multiples of 3 (3-45) 1 8.6: Alternating Series and Absolute Convergence alternating series test error estimates absolute convergence definition absolute convergence implies convergence conditional convergence definition rearrangement of terms 1, 2 Multiples of 5 (5-40) 44, 45 2 8.7: Power Series definition convergence theorem radius of convergence ratio test interval of convergence series in (x-c) term-by-term differentiation term-by-term integration 1, 2 Multiples of 3 (3-42) 43, 46, 47 2 8.8: Taylor Series Taylor polynomials Taylors theorem remainder and representation Taylor series known representations error estimates operations on Taylor series binomial series Multiples of 5 (5-55) 53 2

 Content Homework Hours 9.1: Polar Coordinates polar coordinate system multiple representations conversion between coordinate systems polar graphs Multiples of 3 (3-60) 1 9.2: Graphing table of values symmetry standard curves cardiod, rose, limacon, lemniscate, linear 4, 5, 6 Multiples of 5 (10-60) 61, 62 1 9.3: Area and Tangent Lines intersection points area via integration tangent lines at pole area between polar curves tangent slopes to polar graphs Multiples of 5 (5-60) 2 9.4: Parametric Equations graphing differentiation arclength area under curves Multiples of 3 (3-48) 1

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