Read more
Klappentext Calculus: Late Transcendentals, 11th EMEA Edition strives to increase student comprehension and conceptual understanding through a balance between rigor and clarity of explanations; sound mathematics; and excellent exercises, applications, and examples. Anton pedagogically approaches Calculus through the Rule of Four, presenting concepts from the verbal, algebraic, visual, and numerical points of view. Inhaltsverzeichnis 1 Limits and Continuity 1 1.1 Limits (An Intuitive Approach) 1 1.2 Computing Limits 13 1.3 Limits at Infinity; End Behavior of a Function 22 1.4 Limits (Discussed More Rigorously) 31 1.5 Continuity 40 1.6 Continuity of Trigonometric Functions 51 2 The Derivative 59 2.1 Tangent Lines and Rates of Change 59 2.2 The Derivative Function 69 2.3 Introduction to Techniques of Differentiation 80 2.4 The Product and Quotient Rules 88 2.5 Derivatives of Trigonometric Functions 93 2.6 The Chain Rule 98 2.7 Implicit Differentiation 105 2.8 Related Rates 112 2.9 Local Linear Approximation; Differentials 119 3 The Derivative in Graphing and Applications 130 3.1 Analysis of Functions I: Increase, Decrease, and Concavity 130 3.2 Analysis of Functions II: Relative Extrema; Graphing Polynomials 139 3.3 Analysis of Functions III: Rational Functions, Cusps, and Vertical Tangents 148 3.4 Absolute Maxima and Minima 157 3.5 Applied Maximum and Minimum Problems 164 3.6 Rectilinear Motion 177 3.7 Newton's Method 185 3.8 Rolle's Theorem; Mean-Value Theorem 191 4 Integration 203 4.1 An Overview of the Area Problem 203 4.2 The Indefinite Integral 208 4.3 Integration by Substitution 217 4.4 The Definition of Area as a Limit; Sigma Notation 223 4.5 The Definite Integral 233 4.6 The Fundamental Theorem of Calculus 242 4.7 Rectilinear Motion Revisited Using Integration 253 4.8 Average Value of a Function and its Applications 262 4.9 Evaluating Definite Integrals by Substitution 266 5 Applications of the Definite Integral in Geometry, Science, and Engineering 277 5.1 Area Between Two Curves 277 5.2 Volumes by Slicing; Disks and Washers 284 5.3 Volumes by Cylindrical Shells 294 5.4 Length of a Plane Curve 300 5.5 Area of a Surface of Revolution 306 5.6 Work 311 5.7 Moments, Centers of Gravity, and Centroids 319 5.8 Fluid Pressure and Force 328 6 Exponential, Logarithmic, and Inverse Trigonometric Functions 336 6.1 Exponential and Logarithmic Functions 336 6.2 Derivatives and Integrals Involving Logarithmic Functions 347 6.3 Derivatives of Inverse Functions; Derivatives and Integrals Involving Exponential Functions 353 6.4 Graphs and Applications Involving Logarithmic and Exponential Functions 360 6.5 L'Hôpital's Rule; Indeterminate Forms 367 6.6 Logarithmic and Other Functions Defined by Integrals 376 6.7 Derivatives and Integrals Involving Inverse Trigonometric Functions 387 6.8 Hyperbolic Functions and Hanging Cables 398 7 Principles of Integral Evaluation 412 7.1 An Overview of Integration Methods 412 7.2 Integration by Parts 415 7.3 Integrating Trigonometric Functions 423 7.4 Trigonometric Substitutions 431 7.5 Integrating Rational Functions by Partial Fractions 437 7.6 Using Computer Algebra Systems and Tables of Integrals 445 7.7 Numerical Integration; Simpson's Rule 454 7.8 Improper Integrals 467 8 Mathematical Modeling with Differential Equations 481 8.1 Modeling with Differential Equations 481 8.2 Separation of Variables 487 8.3 Slope Fields; Euler's Method 498 8.4 First-Order Differ...
