Calculus of a Single Variable : Early Transcendental Functions
ISBN: 9780538735520 | 053873552X
Edition: 5thFormat: Hardcover
Publisher: Cengage Learning
Pub. Date: 1/1/2010
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The Single Variable portion of Calculus: Early Transcendental Functions, 5/e, offers students innovative learning resources. Every edition from the first to the fifth of Calculus: Early Transcendental Functions, 5/e has made the mastery of traditional calculus skills a priority, while embracing the best features of new technology and, when appropriate, calculus reform ideas.
Larson writes a very clear, straight forward calculus book for students. The book has very good examples to help a student or teacher explain a topic. There are plenty of practice problems, with answers for the odd questions in the back. It provides examples and problems that also meet the AP Calculus AB and BC curriculum.
| 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 | |
| Limits and their Properties | |
| A Preview of Calculus | |
| Finding Limits Graphically and Numerically | |
| ... MORE | |
| Continuity and One-Sided Limits | |
| Infinite Limits | |
| Section Project: Graphs and Limits of Trigonometric Functions | |
| 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 | |
| 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 | |
| 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 | |
| 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 | |
| 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 | |
| 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'H?pital's Rule | |
| Improper Integrals | |
| 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 | |
| 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 | |
| Table of Contents provided by Publisher. All Rights Reserved. |
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