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Record Nr. |
UNINA9910154935603321 |
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Autore |
Monahan Chris |
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Titolo |
Calculus II / / by Chris Monahan |
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Pubbl/distr/stampa |
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Indianapolis, Indiana : , : Alpha, , 2016 |
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ISBN |
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Edizione |
[First American edition.] |
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Descrizione fisica |
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1 online resource (1 volume) : illustrations |
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Collana |
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Disciplina |
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Soggetti |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di contenuto |
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Intro -- Contents iii -- Part 1: Review of Pre-Calculus and Calculus I 1 -- 1 Pre-Calculus Topics Used in Calculus II 3 -- Trigonometry 4 -- Exponents and Logarithms 6 -- Parametric Equations 8 -- Polar Coordinates 10 -- Geometric Sequences and Series 14 -- Partial Fractions 15 -- 2 Limits, Derivatives, and Basic Integration 19 -- Limits 20 -- Derivatives 23 -- Implicit Differentiation 28 -- Mean Value Theorem 29 -- Relative Extremes and Concavity 30 -- Applications of the Derivative 33 -- Related Rates 36 -- 3 Definite and Indefinite Integrals 41 -- Indefinite Integrals 42 -- u-Substitutions 46 -- Fundamental Theorem of Calculus 50 -- Numerical Approximation 54 -- Part 2: Length, Area, and Volumes 61 -- 4 Areas and Approximations 63 -- Riemann Sums 64 -- From Numerical Approximations to the True Area 76 -- Average Value of a Function 80 -- Area Between Two Curves 81 -- Simpson's Rule 86 -- 5 Volumes and Areas of Solids of Revolutions 91 -- Volumes of Solids with Defined Cross Sections 92 -- Disks and Washers 97 -- Cylindrical Shell Method 106 -- Arc Length 110 -- Surface Area 113 -- Part 3: More Definite and Indefinite Integrals 117 -- 6 More Integration Techniques 119 -- Integration by Parts 120 -- Polynomials and Transcendentals 123 -- Two Transcendentals 129 -- 7 Integration with Trigonometric Functions 133 -- Trigonometric Substitutions 134 -- Case I: a2 + x2 134 -- Case II: x2 - a2 136 -- Case III: a2 - x2 138 -- Integrals of the Form sinn(x) cosm(x) (When Either m or n Is Odd) 139 -- Case I: Both m and n Are Odd 139 -- Case II: Both m and n Are Even 140 -- Case III: Either m or n Is Odd 141 -- Integrals with Integrands of the Form tann |
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(x) secm(x) (m Is Even) 142 -- Integrals with Integrands of the Form tann(x) secm(x) (m Is Odd, n Is Even) 143 -- 8 Integration with Fractions 147 -- Completing the Square 148. |
Integration by Partial Fractions 152 -- Nonrepeating Linear Factors 152 -- Repeated Linear Factors 154 -- Irreducible Quadratic Factors 155 -- Part 4: The Infinite Series and More 159 -- 9 To Infinity and Beyond 161 -- Improper Integrals 162 -- Infinite Limits of Integration 162 -- Discontinuities in the Integrand 165 -- Comparison Test for Improper Integrals 168 -- 10 Parametric Equations 171 -- First and Second Derivatives of Parametric Curves 172 -- Arc Length of a Parametric Curve 178 -- 11 Polar Coordinates 181 -- Slope of the Tangent Line 182 -- Length of an Arc of a Polar Curve 187 -- Area Under a Curve 189 -- 12 Introduction to Vectors 195 -- Scalars and Vectors 196 -- 13 Differential Equations 205 -- Separable Differential Equations 206 -- Linear Approximations 212 -- Euler's Method 214 -- Slope Fields 217 -- First Order Linear Differential Equations 222 -- 14 Infinite Sequences 227 -- Convergence and Divergence of Sequences 228 -- Squeeze Theorem 231 -- Increasing, Decreasing, and Monotonic Sequences 233 -- 15 Infinite Series 237 -- Infinite Geometric Series 238 -- Tests of Convergence 239 -- Alternating Series 244 -- Estimating the Sum of Alternating Series 247 -- 16 Power Series 249 -- Power Series 250 -- MacLaurin Series 252 -- Taylor Series 258 -- Error Estimates for the MacLaurin and Taylor Series 260 -- 17 Calculus II Final Exam 263 -- Chapter 1 264 -- Chapter 2 264 -- Chapter 3 265 -- Chapter 4 266 -- Chapter 5 266 -- Chapter 6 267 -- Chapter 7 267 -- Chapter 8 268 -- Chapter 9 268 -- Chapter 10 268 -- Chapter 11 269 -- Chapter 12 269 -- Chapter 13 270 -- Chapter 14 270 -- Chapter 15 271 -- Chapter 16 271 -- Solutions 272 -- Chapter 1 272 -- Chapter 2 272 -- Chapter 3 273 -- Chapter 4 273 -- Chapter 5 274 -- Chapter 6 274 -- Chapter 7 274 -- Chapter 8 275 -- Chapter 9 275 -- Chapter 10 275 -- Chapter 11 275 -- Chapter 12 276. |
Chapter 13 276 -- Chapter 14 277 -- Chapter 15 277 -- Chapter 16 277 -- A Solutions to "You've Got Problems" 279 -- B Integration Practice Problems and Solutions 297 -- C Glossary 307 -- Index 313. |
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Sommario/riassunto |
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Idiot's Guides: Calculus II, like its counterpart Idiot's Guides: Calculus I, is a curriculum-based companion book that continues the tradition of taking the sting out of calculus by adding more explanatory graphs and illustrations in easy-to-understand language, practice problems, and even a test at the end. Idiot's Guides: Calculus II is geared for all students who need to succeed in calculus. |
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