Summary: Carefully developed for one-year courses that combine and integrate material from Precalculus through Calculus I, this text is ideal for instructors who wish to successfully bring students up to speed algebraically within precalculus and transition them into calculus. The Larson Calculus texts continue to offer instructors and students new and innovative teaching and learning resources. The Calculus series was the first to use computer-generated graphics (Third Editi...show moreon), to include exercises involving the use of computers and graphing calculators (Fourth Edition), to be available in an interactive CD-ROM format (Fifth Edition), to be offered as a complete, online calculus course (Sixth Edition), and to offer this two-semester Calculus I with Precalculus text. Every edition of the book has made the mastery of traditional calculus skills a priority, while embracing the best features of new technology and, when appropriate, calculus reform ideas. Now, the Eighth Edition is the first calculus program to offer algorithmic homework and testing created in Maple so that answers can be evaluated with complete mathematical accuracy.
Two primary objectives guided the authors in writing this book: 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 saves the instructor time. The Eighth Edition continues to provide an evolving range of conceptual, technological, and creative tools that enable instructors to teach the way they want to teach and students to learn they way they learn best. The Larson program offers a variety of options to address the needs of any calculus course and any level of calculus student, enabling the greatest number of students to succeed.
The explanations, theorems, and definitions have been thoroughly and critically reviewed. When necessary, changes have been made to ensure that the text is pedagogically sound, mathematically precise, and comprehensible.
The exercise sets have been carefully and extensively examined to ensure they cover all calculus topics appropriately. Many new exercises have been added at the suggestion of a number of calculus instructors.
A variety of exercise types are included in each exercise set. Questions involving skills, writing, critical thinking, problem-solving, applications, and real-data applications are included throughout the text. Exercises are presented in a variety of question formats, including matching, free response, true/false, modeling, and fill-in the blank.
The Eduspace online resources have been integrated into a comprehensive learning system that combines numerous dynamic calculus resources with online homework and testing materials.
The Integrated Learning System addresses the changing needs of today's instructors and students. Recognizing that the calculus course is presented in a variety of teaching and learning environments, the program resources are available in print, CD-ROM, and online formats.
Eduspace, powered by Blackboard provides instructors with online courses and content in multiple disciplines. By pairing the widely recognized tools of Blackboard with quality, text-specific content from Houghton Mifflin (HMCo), Eduspace makes it easy for instructors to create all or part of a course online. Homework exercises, quizzes, tests, tutorials, and supplemental study materials all come ready-to-use. Instructors can choose to use the content as is, modify it, or even add their own. Eduspace with eSolutions combines all the features of Eduspace with an electronic version of the textbook exercises and the complete solutions to the odd-numbered text exercises, providing students with a convenient and comprehensive way to do homework and view the course materials.
SMARTHINKING online tutoring brings students real-time, online tutorial support when they need it most.
3.1 A Preview of Calculus 3.2 Finding Limits Graphically and Numerically 3.3 Evaluating Limits Analytically 3.4 Continuity and One-Sided Limits 3.5 Infinite Limits Section Project: Graphs and Limits of Functions Progressive Summary 1: Flowchart of Calculus
4.1 The Derivative and the Tangent Line Problem 4.2 Basic Differentiation Rules and Rates of Change 4.3 The Product and Quotient Rules and Higher-Order Derivatives 4.4 The Chain Rule 4.5 Implicit Differentiation Section Project: Optical Illusions 4.6 Related Rates
5. Applications of Differentiation
5.1 Extrema on an Interval 5.2 Rolle's Theorem and the Mean Value Theorem 5.3 Increasing and Decreasing Functions and the First Derivative Test 5.4 Concavity and the Second Derivative Test 5.5 Limits at Infinity 5.6 A Summary of Curve Sketching 5.7 Optimization Problems Section Project: Connecticut River 5.8 Differentials
6.1 Antiderivatives and Indefinite Integration 6.2 Area 6.3 Riemann Sums and Definite Integrals 6.4 The Fundamental Theorem of Calculus Section Project: Demonstrating the Fundamental Theorem 6.5 Integration by Substitution 6.6 Numerical Integration Progressive Summary 2: Flowchart of Calculus
7. Exponential and Logarithmic Functions
7.1 Exponential Functions and Their Graphs 7.2 Logarithmic Functions and Their Graphs 7.3 Using Properties of Logarithms 7.4 Exponential and Logarithmic Equations 7.5 Exponential and Logarithmic Models Section Project: Comparing Models
8. Exponential and Logarithmic Functions and Calculus
8.1 Exponential Functions: Differentiation and Integration 8.2 Logarithmic Functions and Differentiation Section Project: An Alternate Definition of ln x 8.3 Logarithmic Functions and Integration 8.4 Differential Equations: Growth and Decay Progressive Summary 3: Flowchart of Calculus
9. Trigonometric Functions
9.1 Radian and Degree Measure 9.2 Trigonometric Functions: The Unit Circle 9.3 Right Triangle Trigonometry 9.4 Trigonometric Functions of Any Angle 9.5 Graphs of Sine and Cosine Functions Section Project: Approximating Sine and Cosine Functions 9.6 Graphs of Other Trigonometric Functions 9.7 Inverse Trigonometric Functions 9.8 Applications and Models
10. Analytic Trigonometry
10.1 Using Fundamental Identities 10.2 Verifying Trigonometric Identities 10.3 Solving Trigonometric Equations Section Project: Modeling a Sound Wave 10.4 Sum and Difference Formulas 10.5 Multiple-Angle and Product-Sum Formulas
11. Trigonometric Functions and Calculus
11.1 Limits of Trigonometric Functions Section Project: Graphs and Limits of Trigonometric Functions 11.2 Trigonometric Functions: Differentiation 11.3 Trigonometric Functions: Integration 11.4 Inverse Trigonometric Functions: Differentiation 11.5 Inverse Trigonometric Functions: Integration 11.6 Hyperbolic Functions Section Project: St. Louis Arch Progressive Summary 4: Flowchart of Calculus
12. Topics in Analytic Geometry
12.1 Introduction to Conics: Parabolas 12.2 Ellipses and Implicit Differentiation 12.3 Hyperbolas and Implicit Differentiation 12.4 Parametric Equations 12.5 Polar Coordinates 12.6 Graphs of Polar Coordinates 12.7 Polar Equations of Conics Section Project: Polar Equations of Planetary Orbits Progressive Summary 5: Flowchart of Calculus
13. Additional Topics in Trigonometry
13.1 Law of Sines 13.2 Law of Cosines 13.3 Vectors in the Plane Section Project: Adding Vectors Graphically 13.4 Vectors and Dot Products 13.5 Complex Numbers and Zeros. Section Project: The Mandelbrot Set. 13.6 Trigonometric Form of a Complex Number
14. Systems of Equations and Matrices
14.1 Systems of Linear Equations in Two Variables 14.2 Multivariable Linear Systems 14.3 Systems of Inequalities Section Project: Area Bounded by Concentric Circles 14.4 Matrices and Systems of Equations 14.5 Operations with Matrices 14.6 The Inverse of a Square Matrix 14.7 The Determinant of a Square Matrix Section Project: Cramer's Rule
A. Proofs of Selected Theorems B. Applications of Integration Perforated Tear out Nutshells 1. Algebraic Functions. 2. Limits of Algebraic Functions. 3. Differentiation of Algebraic Functions. 4. Calculus of Algebraic Functions. 5. Calculus of Exponential and Log Functions. 6. Trigonometric Functions. 7. Calculus of Trig and Inverse Trig.
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