Calculus of a Single Variable – Ron Larson – 7th Edition


Designed for the three-semester course for math and science majors, the Larson//Edwards series continues its tradition of success by being the first to offer both an Early Transcendental version as well as a new Calculus with text. This was also the first calculus text to use computer-generated (Third Edition), to include exercises involving the use of computers and calculators (Fourth Edition), to be available in an interactive CD-ROM format (Fifth Edition), and to be offered as a complete, online calculus course (Sixth Edition). Every edition of the has made the mastery of traditional calculus skills a priority, while embracing the best features of new technology and, when appropriate, calculus reform ideas. The Seventh Edition also expands its support package with an all-new set of text-specific videos.

P.S. Problem-Solving Sections, an additional set of thought-provoking exercises added to the end of each chapter, require students to use a variety of problem-solving skills and provide a challenging arena for students to work with calculus concepts.

Getting at the Concept Exercises added to each section exercise set check students’ understanding of the basic concepts. Located midway through the exercise set, they are both boxed and titled for easy .

Review Exercises at the end of each chapter have been reorganized to provide students with a more effective study tool. The exercises are now grouped and correlated by text section, enabling students to target concepts requiring review.

The icon “IC” in the text identifies examples that appear in the Interactive Calculus 3.0 CD-ROM and Internet Calculus 2.0 web site with enhanced opportunities for exploration and visualization using the program itself and/or a Computer Algebra System.

Think About It conceptual exercises require students to use their critical-thinking skills and help them develop an intuitive understanding of the underlying theory of the calculus.
Modeling Data multi-part questions ask students to find and interpret mathematical models to fit real-life data, often through the use of a graphing utility.

Section Projects, applications that appear at the end of selected exercise sets. may be used for individual, collaborative, or peer-assisted assignments.
True or False? Exercises, included toward the end of many exercises sets, help students understand the logical structure of calculus and highlight concepts, common errors, and the correct statements of definitions and theorems.

Motivating the Chapter sections opening each chapter present data- applications that explore the concepts to be covered in the context of a real-world setting.

Table of Content

Chapter 1
Limits and their properties
1.1 A preview of the calculation
1.2 Find limits graphically and numerically
1.3 Analytically Assessing Limits
1.4 Continuity and Limits of a face
1.5 Infinite limits
Episode 2
2.1 The problem of the derivative and the tangent line
2.2 Basic rules of differentiation and exchange rates
2.3 Rules of products and ratios and derivatives of higher order
2.4 The rule of the chain
2.5 Implicit differentiation
2.6 Related rates
Chapter 3
Differentiation applications
3.1 Extreme in an interval
3.2 Rolle's theorem and the mean value theorem
3.3 Increase and decrease functions and the first test of derivatives
3.4 Concavity and the second derivative test
3.5 Limits in Infinity
3.6 A summary of the curve tracing
3.7 Optimization problems
3.8 Newton's method
3.9 Differentials
Chapter 4
4.1 Antiderivatives and indefinite integration
4.2 Zone
4.3 Sums of Reimann and definite integrals
4.4 The Fundamental Theorem of Calculus
4.5 Integration by substitution
4.6 Numerical integration
Chapter 5
Logarithmic, exponential and other transcendental functions
5.1 Natural logarithmic function and differentiation
5.2 The function and natural logarithmic integration
5.3 Inverse functions
5.4 Exponential Functions: Differentiation and Integration
5.5 Different bases of e and applications
5.6 Differential equations: growth and decay
5.7 Differential equations: separation of variables
5.8 Inverse trigonometric functions and differentiation
5.9 Inverse trigonometric functions and integration
5.10 Hyperbolic functions
Chapter 6
Integration applications
6.1 Area of ​​a region between two curves
6.2 Volume: the disk method
6.3 Volume: the Shell method
6.4 Length of the arch and surfaces of the revolution
6.5 Work
6.6 Moments, Mass Centers and Centroids
6.7 Fluid pressure and fluid force
Chapter 7
Integration techniques, hospital rule and improper integrals
7.1 Basic rules of integration
7.2 Integration by parts
7.3 Trigonometric integrals
7.4 Trigonometric substitution
7.5 Partial fractions
7.6 Integration by tables and other integration techniques
7.7 Indeterminate forms and the L'Hôpital rule
7.8 Improper Integrals
Chapter 8
Infinite series
8.1 Sequences
8.2 Series and convergence
8.3 The integral test and the p series
8.4 Series Comparison
8.5 Alternating series
8.6 The reason and root tests
8.7 Taylor polynomials and approximations
8.8 Power series
8.9 Representation of functions by Power Series
8.10 Taylor and Maclaurian Series
Chapter 9
Conics, parametric equations and polar coordinates
9.1 Conics and Calculation
9.2 Flat curves and parametric equations
9.3 Parametric Equations and Calculation
9.4 Polar coordinates and polar graphics
9.5 Area and length of the arc in polar coordinates
9.6 Polar and Kepler equations

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