Calculus : early transcendentals /: early transcendentals. (2015)

• Record Type: Book
• Further Information: Note: Jon Rogawski, University of California, Los Angeles, Colin Adams, Williams College.
• Authors: Rogawski, Jon, 1955-2011; Adams, Colin Conrad
• Contents: Rogawski/Adams: Calculus Early Transcendentals 3e Table of Contents; Chapter 1: Precalculus Review; 1.1 Real Numbers, Functions, and Graphs; 1.2 Linear and Quadratic Functions; 1.3 The Basic Classes of Functions; 1.4 Trigonometric Functions; 1.5 Inverse Functions; 1.6 Exponential and Logarithmic Functions; 1.7 Technology: Calculators and Computers; Chapter Review Exercises; ; Chapter 2: Limits; 2.1 Limits, Rates of Change, and Tangent Lines; 2.2 Limits: A Numerical and Graphical Approach; 2.3 Basic Limit Laws; 2.4 Limits and Continuity; 2.5 Evaluating Limits Algebraically; 2.6 Trigonometric Limits; 2.7 Limits at Infinity; 2.8 Intermediate Value Theorem; 2.9 The Formal Definition of a Limit; Chapter Review Exercises; ; Chapter 3: Differentiation; 3.1 Definition of the Derivative; 3.2 The Derivative as a Function; 3.3 Product and Quotient Rules; 3.4 Rates of Change; 3.5 Higher Derivatives; 3.6 Trigonometric Functions; 3.7 The Chain Rule; 3.8 Implicit Differentiation; 3.9 Derivatives of General Exponential and Logarithmic Functions; 3.10 Related Rates; Chapter Review Exercises; ; Chapter 4: Applications of the Derivative; 4.1 Linear Approximation and Applications; 4.2 Extreme Values; 4.3 The Mean Value Theorem and Monotonicity; 4.4 The Shape of a Graph; 4.5 L'Hopital's Rule; 4.6 Graph Sketching and Asymptotes; 4.7 Applied Optimization; 4.8 Newton's Method; Chapter Review Exercises; ; Chapter 5: The Integral; 5.1 Approximating and Computing Area; 5.2 The Definite Integral; 5.3 The Indefinite Integral; 5.4 The Fundamental Theorem of Calculus, Part I; 5.5 The Fundamental Theorem of Calculus, Part II; 5.6 Net Change as the Integral of a Rate; 5.7 Substitution Method; 5.8 Further Transcendental Functions; 5.9 Exponential Growth and Decay; Chapter Review Exercises; ; Chapter 6: Applications of the Integral; 6.1 Area Between Two Curves; 6.2 Setting Up Integrals: Volume, Density, Average Value; 6.3 Volumes of Revolution; 6.4 The Method of Cylindrical Shells; 6.5 Work and Energy; Chapter Review Exercises; ; Chapter 7: Techniques of Integration; 7.1 Integration by Parts; 7.2 Trigonometric Integrals; 7.3 Trigonometric Substitution; 7.4 Integrals Involving Hyperbolic and Inverse Hyperbolic Functions; 7.5 The Method of Partial Fractions; 7.6 Strategies for Integration; 7.7 Improper Integrals; 7.8 Probability and Integration; 7.9 Numerical Integration; Chapter Review Exercises; ; Chapter 8: Further Applications of the Integral and Taylor Polynomials; 8.1 Arc Length and Surface Area; 8.2 Fluid Pressure and Force; 8.3 Center of Mass; 8.4 Taylor Polynomials; Chapter Review Exercises; ; Chapter 9: Introduction to Differential Equations; 9.1 Solving Differential Equations; 9.2 Models Involving y '=k(y-b); 9.3 Graphical and Numerical Methods; 9.4 The Logistic Equation; 9.5 First-Order Linear Equations; Chapter Review Exercises; ; Chapter 10: Infinite Series; 10.1 Sequences; 10.2 Summing an Infinite Series; 10.3 Convergence of Series with Positive Terms; 10.4 Absolute and Conditional Convergence; 10.5 The Ratio and Root Tests; 10.6 Power Series; 10.7 Taylor Series; Chapter Review Exercises; ; Chapter 11: Parametric Equations, Polar Coordinates, and Conic Sections; 11.1 Parametric Equations; 11.2 Arc Length and Speed; 11.3 Polar Coordinates; 11.4 Area and Arc Length in Polar Coordinates; 11.5 Conic Sections; Chapter Review Exercises; ; Chapter 12: Vector Geometry; 12.1 Vectors in the Plane; 12.2 Vectors in Three Dimensions; 12.3 Dot Product and the Angle Between Two Vectors; 12.4 The Cross Product; 12.5 Planes in Three-Space; 12.6 A Survey of Quadric Surfaces; 12.7 Cylindrical and Spherical Coordinates; Chapter Review Exercises; ; Chapter 13: Calculus of Vector-Valued Functions; 13.1 Vector-Valued Functions; 13.2 Calculus of Vector-Valued Functions; 13.3 Arc Length and Speed; 13.4 Curvature; 13.5 Motion in Three-Space; 13.6 Planetary Motion According to Kepler and Newton; Chapter Review Exercises; ; Chapter 14: Differentiation in Several Variables; 14.1 Functions of Two or More Variables; 14.2 Limits and Continuity in Several Variables; 14.3 Partial Derivatives; 14.4 Differentiability and Tangent Planes; 14.5 The Gradient and Directional Derivatives; 14.6 The Chain Rule; 14.7 Optimization in Several Variables; 14.8 Lagrange Multipliers: Optimizing with a Constraint; Chapter Review Exercises; ; Chapter 15: Multiple Integration; 15.1 Integration in Two Variables; 15.2 Double Integrals over More General Regions; 15.3 Triple Integrals; 15.4 Integration in Polar, Cylindrical, and Spherical Coordinates; 15.5 Applications of Multiple Integrals; 15.6 Change of Variables; Chapter Review Exercises; ; Chapter 16: Line and Surface Integrals; 16.1 Vector Fields; 16.2 Line Integrals; 16.3 Conservative Vector Fields; 16.4 Parametrized Surfaces and Surface Integrals; 16.5 Surface Integrals of Vector Fields; Chapter Review Exercises; ; Chapter 17: Fundamental Theorems of Vector Analysis; 17.1 Green's Theorem; 17.2 Stokes' Theorem; 17.3 Divergence Theorem; Chapter Review Exercises; ; Appendices; A. The Language of Mathematics; B. Properties of Real Numbers; C. Induction and the Binomial Theorem; D. Additional Proofs; ; Answers to Odd-Numbered Exercises; References; Index
• Publisher Details: Basingstoke : Palgrave Macmillan
• Publication Date: 2015
• Extent: 1 online resource (1050 pages)
• Subjects: 515.22; Calculus -- Textbooks
• Languages: English
• ISBNs: 9781319051716; 1319051715
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.