Calculus 1 with Precalculus : A One-Year Course

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

• ISBN13: 9780618087600
• ISBN10: 0618087605
• Edition: 1st
• Format: Hardcover
• Copyright: 2001-07-01
• Publisher: Brooks Cole

Summary

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.

Table of Contents

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.