Calculus 1 with Precalculus : A One-Year Course

, by Larson, Ron; Hostetler, Robert P.; Edwards, Bruce H.

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ISBN: 9780618087600 | 0618087605
Cover: Hardcover
Copyright: 7/1/2001

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From the successful team of Larson, Hostetler, and Edwards comes a new text 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.

Note: Each chapter concludes with Review Exercises and P.S. Problem Solving. P. Prerequisites P.1 Solving Equations P.2 Solving Inequalities P.3 Graphical Representation of Data P.4 Graphs of Equations P.5 Linear Equations in Two Variables
Functions and Their Graphs
Functions
Analyzing Graphs of Functions
Shifting, Reflecting, and Stretching Graphs
Combinations of Functions
Inverse Functions
Mathematical Modeling
Polynomial and Rational Functions
Quadratic Functions
Polynomial Functions of Higher Degree
Polynomial and Synthetic Division
Complex Numbers
Zeros of Polynomial Functions
Rational Functions
Limits and Their Properties
A Preview of Calculus
Finding Limits Graphically and Numerically
Evaluating Limits Analytically
Continuity and One-Sided Limits
Infinite Limits
Differentiation
The Derivative and the Tangent Line Problem
Basic Differentiation Rules and Rates of Change
The Product and Quotient Rules and Higher-Order Derivatives
The Chain Rule
Implicit Differentiation
Related Rates
Applications of Differentiation
Extrema on an Interval
Rolle's Theorem and the Mean Value Theorem
Increasing and Decreasing Functions and the First Derivative Test
Concavity and the Second Derivative Test
Limits at Infinity
A Summary of Curve Sketching
Optimization Problems
Differentials
Integration
Antiderivatives and Indefinite Integration
Area
Riemann Sums and Definite Integrals
The Fundamental Theorem of Calculus
Integration by Substitution
Numerical Integration
Exponential and Logarithmic Functions
Exponential Functions and Their Graphs
Logarithmic Functions and Their Graphs
Properties of Logarithms
Exponential and Logarithmic Equations
Exponential and Logarithmic Models
Exponential and Logarithmic Functions and Calculus
Exponential Functions: Differentiation and Integration
Logarithmic Functions and Differentiation
Logarithmic Functions and Integration
Differential Equations: Growth and Decay
Trigonometric Functions
Radian and Degree Measure
Trigonometric Functions: The Unit Circle
Right Triangle Trigonometry
Trigonometric Functions of Any Angle
Graphs of Sine and Cosine Functions
Graphs of Other Trigonometric Functions
Inverse Trigonometric Functions
Applications and Models
Analytic Trigonometry
Using Fundamental Identities
Verifying Trigonometric Identities
Solving Trigonometric Equations
Sum and Difference Formulas
Multiple-Angle and Product-Sum Formulas
Trigonometric Functions and Calculus
Limits of Trigonometric Functions
Trigonometric Functions: Differentiation
Trigonometric Functions: Integration
Inverse Trigonometric Functions: Differentiation
Inverse Trigonometric Functions: Integration
Hyperbolic Functions
Additional Topics in Trigonometry
Law of Sines
Law of Cosines
Vectors in the Plane
Vectors and Dot Products
Trigonometric Form of a Complex Number
Systems of Equations and Matrices
Systems of Linear Equations in Two Variables
Multivariable Linear Systems
Systems of Inequalities
Matrices and Systems of Equations
Operations with Matrices
The Inverse of a Square Matrix
The Determinant of a Square Matrix
Topics in Analytic Geometry
Introduction to Conics: Parabolas
Ellipses and Implicit Differentiation
Hyperbolas and Implicit Differentiation
Parametric Equations
Polar Coordinates
Graphs of Polar Equations
Polar Equations of Conics
Proofs of Selected Theorems Answers to Odd-Numbered Exercises
Index of Applications
Index
Table of Contents provided by Publisher. All Rights Reserved.

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Calculus 1 with Precalculus : A One-Year Course

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Table of Contents

Supplemental Materials