Calculus of a Single Variable: Early Transcendental Functions
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品牌: Ron LarsonBruce Edwards
基本信息出版社:
Brooks/Cole; International ed of 5th revised ed (2011年2月10日)平装:944页正文语种:英语ISBN:0538735538条形码:9780538735537商品尺寸:26.2 x 21.4 x 3.4 cm商品重量:1.8 KgASIN:0538735538商品描述内容简介Known for its continued excellence, "Calculus of a Single Variable: Early Transcendental Functions, 5e, International Edition" offers instructors and students innovative teaching and learning resources. The Larson team always has two main objectives for text revisions: to develop precise, readable materials for students that clearly define and demonstrate concepts and rules of calculus; and, to design comprehensive teaching resources for instructors that employ proven pedagogical techniques and save time. The Larson/Edwards Calculus program offers a solution to address the needs of any calculus course and any level of calculus student. Every edition from the first to the fifth of "Calculus of a Single Variable: Early Transcendental Functions, 5e" has made the mastery of traditional calculus skills a priority, while embracing the best features of new technology and, when appropriate, calculus reform ideas.目录1. PREPARATION FOR CALCULUS. Graphs and Models. Linear Models and Rates of Change. Functions and Their Graphs. Fitting Models to Data. Inverse Functions. Exponential and Logarithmic Functions. 2. LIMITS AND THEIR PROPERTIES. A Preview of Calculus. Finding Limits Graphically and Numerically. Evaluating Limits Analytically. Continuity and One-Sided Limits. Infinite Limits.Section Project: Graphs and Limits of Trigonometric Functions. 3. DIFFERENTIATION. The Derivative and the Tangent Line Problem. Basic Differentiation Rules and Rates of Change. Product and Quotient Rules and Higher-Order Derivatives. The Chain Rule. Implicit Differentiation. Section Project: Optical Illusions. Derivatives of Inverse Functions. Related Rates. Newton's Method. 4. APPLICATIONS OF DIFFERENTIATION. Extrema on an Interval. Rolle's Theorem and the Mean Value Theorem. Increasing and Decreasing Functions and the First Derivative Test. Section Project: Rainbows. Concavity and the Second Derivative Test. Limits at Infinity. A Summary of Curve Sketching. Optimization Problems. Section Project: Connecticut River. Differentials. 5. INTEGRATION. Antiderivatives and Indefinite Integration. Area. Riemann Sums and Definite Integrals. The Fundamental Theorem of Calculus. Section Project: Demonstrating the Fundamental Theorem. Integration by Substitution. Numerical Integration. The Natural Logarithmic Function: Integration. Inverse Trigonometric Functions: Integration. Hyperbolic Functions. Section Project: St. Louis Arch. 6. DIFFERENTIAL EQUATIONS. Slope Fields and Euler's Method. Differential Equations: Growth and Decay. Differential Equations: Separation of Variables. The Logistic Equation. First-Order Linear Differential Equations. Section Project: Weight Loss. Predator-Prey Differential Equations. 7. APPLICATIONS OF INTEGRATION. Area of a Region Between Two Curves. Volume: The Disk Method. Volume: The Shell Method. Section Project: Saturn. Arc Length and Surfaces of Revolution. Work. Section Project: Tidal Energy. Moments, Centers of Mass, and Centroids. Fluid Pressure and Fluid Force. 8. INTEGRATION TECHNIQUES, L'HOPITAL'S RULE, AND IMPROPER INTEGRALS. Basic Integration Rules. Integration by Parts. Trigonometric Integrals. Section Project: Power Lines. Trigonometric Substitution. Partial Fractions. Integration by Tables and Other Integration Techniques. Indeterminate Forms and L'Hopital's Rule. Improper Integrals. 9. INFINITE SERIES. Sequences. Series and Convergence. Section Project: Cantor's Disappearing Table. The Integral Test and p-Series. Section Project: The Harmonic Series. Comparisons of Series. Section Project: Solera Method. Alternating Series. The Ratio and Root Tests. Taylor Polynomials and Approximations. Power Series. Representation of Functions by Power Series. Taylor and Maclaurin Series. 10. CONICS, PARAMETRIC EQUATIONS, AND POLAR COORDINATES. Conics and Calculus. Plane Curves and Parametric Equations. Section Projects: Cycloids. Parametric Equations and Calculus. Polar Coordinates and Polar Graphs. Section Project: Anamorphic Art. Area and Arc Length in Polar Coordinates. Polar Equations of Conics and Kepler's Laws.
