Calculus With Analytic Geometry - Rilegato

Simmons, George

Rilegato

ISBN 10: 0070576424 ISBN 13: 9780070576421

Casa editrice: McGraw-Hill Education, 1995

Riassunto

Written by acclaimed author and mathematician George Simmons, this revision is designed for the calculus course offered in two and four year colleges and universities. It takes an intuitive approach to calculus and focuses on the application of methods to real-world problems. Throughout the text, calculus is treated as a problem solving science of immense capability.

Su questo libro

L'autore

GEORGE F. SIMMONS has academic degree from the CAlifornia Institute of Technology, the university of chicago, and Yale University. He taught at several colleges and universities before joining the faculty of Colorado college in 1962, where he is a professor of mathematics. He is also the author of introduction to topology and Modern Analysis, Precalculus Mathematics in a Nutshell and calculus with Analytic Geometry.

Contenuti

CHAPTER 1: Numbers, Functions, and Graphs

1-1 Introduction

1-2 The Real Line and Coordinate Plane: Pythagoras

1-3 Slopes and Equations of Straight Lines

1-4 Circles and Parabolas: Descartes and Fermat

1-5 The Concept of a Function

1-6 Graphs of Functions

1-7 Introductory Trigonometry

1-8 The Functions Sin O and Cos O

CHAPTER 2: The Derivative of a Function

2-0 What is Calculus ?

2-1 The Problems of Tangents

2-2 How to Calculate the Slope of the Tangent

2-3 The Definition of the Derivative

2-4 Velocity and Rates of Change: Newton and Leibriz

2-5 The Concept of a Limit: Two Trigonometric Limits

2-6 Continuous Functions: The Mean Value Theorem and Other Theorem

CHAPTER 3: The Computation of Derivatives

3-1 Derivatives of Polynomials

3-2 The Product and Quotient Rules

3-3 Composite Functions and the Chain Rule

3-4 Some Trigonometric Derivatives

3-5 Implicit Functions and Fractional Exponents

3-6 Derivatives of Higher Order

CHAPTER 4: Applications of Derivatives

4-1 Increasing and Decreasing Functions: Maxima and Minima

4-2 Concavity and Points of Inflection

4-3 Applied Maximum and Minimum Problems

4-4 More Maximum-Minimum Problems

4-5 Related Rates

4-6 Newtons Method for Solving Equations

4-7 Applications to Economics: Marginal Analysis

CHAPTER 5: Indefinite Integrals and Differential Equations

5-1 Introduction

5-2 Differentials and Tangent Line Approximations

5-3 Indefinite Integrals: Integration by Substitution

5-4 Differential Equations: Separation of Variables

5-5 Motion Under Gravity: Escape Velocity and Black Holes

CHAPTER 6: Definite Integrals

6-1 Introduction

6-2 The Problem of Areas

6-3 The Sigma Notation and Certain Special Sums

6-4 The Area Under a Curve: Definite Integrals

6-5 The Computation of Areas as Limits

6-6 The Fundamental Theorem of Calculus

6-7 Properties of Definite Integrals

CHAPTER 7: Applications of Integration

7-1 Introduction: The Intuitive Meaning of Integration

7-2 The Area between Two Curves

7-3 Volumes: The Disk Method

7-4 Volumes: The Method of Cylindrical Shells

7-5 Arc Length

7-6 The Area of a Surface of Revolution

7-7 Work and Energy

7-8 Hydrostatic Force

PART II

CHAPTER 8: Exponential and Logarithm Functions

8-1 Introduction

8-2 Review of Exponents and Logarithms

8-3 The Number e and the Function y = e <^>x

8-4 The Natural Logarithm Function y = ln x

8-5 Applications

Population Growth and Radioactive Decay

8-6 More Applications

CHAPTER 9: Trigonometric Functions

9-1 Review of Trigonometry

9-2 The Derivatives of the Sine and Cosine

9-3 The Integrals of the Sine and Cosine

9-4 The Derivatives of the Other Four Functions

9-5 The Inverse Trigonometric Functions

9-6 Simple Harmonic Motion

9-7 Hyperbolic Functions

CHAPTER 10 : Methods of Integration

10-1 Introduction

10-2 The Method of Substitution

10-3 Certain Trigonometric Integrals

10-4 Trigonometric Substitutions

10-5 Completing the Square

10-6 The Method of Partial Fractions

10-7 Integration by Parts

10-8 A Mixed Bag

10-9 Numerical Integration

CHAPTER 11: Further Applications of Integration

11-1 The Center of Mass of a Discrete System

11-2 Centroids

11-3 The Theorems of Pappus

11-4 Moment of Inertia

CHAPTER 12: Indeterminate Forms and Improper Integrals

12-1 Introduction. The Mean Value Theorem Revisited

12-2 The Interminate Form 0/0. L'Hospital's Rule

12-3 Other Interminate Forms

12-4 Improper Integrals

12-5 The Normal Distribution

CHAPTER 13: Infinite Series of Constants

13-1 What is an Infinite Series ?

13-2 Convergent Sequences

13-3 Convergent and Divergent Series

13-4 General Properties of Convergent Series

13-5 Series on Non-negative Terms: Comparison Tests

13-6 The Integral Test

13-7 The Ratio Test and Root Test

13-8 The Alternating Series Test

CHAPTER 14: Power Series

14-1 Introduction

14-2 The Interval of Convergence

14-3 Differentiation and Integration of Power Series

14-4 Taylor Series and Taylor's Formula

14-5 Computations Using Taylor's Formula

14-6 Applications to Differential Equations

14. 7 (optional) Operations on Power Series

14. 8 (optional) Complex Numbers and Euler's Formula

PART III

CHAPTER 15: Conic Sections

15-1 Introduction

15-2 Another Look at Circles and Parabolas

15-3 Ellipses

15-4 Hyperbolas

15-5 The Focus-Directrix-Eccentricity Definitions

15-6 (optional) Second Degree Equations

CHAPTER 16: Polar Coordinates

16-1 The Polar Coordinate System

16-2 More Graphs of Polar Equations

16-3 Polar Equations of Circles, Conics, and Spirals

16-4 Arc Length and Tangent Lines

16-5 Areas in Polar Coordinates

CHAPTER 17: Parametric Equations

17-1 Parametric Equations of Curves

17-2 The Cycloid and Other Similar Curves

17-3 Vector Algebra

17-4 Derivatives of Vector Function

17-5 Curvature and the Unit Normal Vector

17-6 Tangential and Normal Components of Acceleration

17-7 Kepler's Laws and Newton's Laws of Gravitation

CHAPTER 18: Vectors in Three-Dimensional Space

18-1 Coordinates and Vectors in Three-Dimensional Space

18-2 The Dot Product of Two Vectors

18-3 The Cross Product of Two Vectors

18-4 Lines and Planes

18-5 Cylinders and Surfaces of Revolution

18-6 Quadric Surfaces

18-7 Cylindrical and Spherical Coordinates

CHAPTER 19: Partial Derivatives

19-1 Functions of Several Variables

19-2 Partial Derivatives

19-3 The Tangent Plane to a Surface

19-4 Increments and Differentials

19-5 Directional Derivatives and the Gradient

19-6 The Chain Rule for Partial Derivatives

19-7 Maximum and Minimum Problems

19-8 Constrained Maxima and Minima

19-9 Laplace's Equation, the Heat Equation, and the Wave Equation

19-10 (optional) Implicit Functions

CHAPTER 20: Multiple Integrals

20-1 Volumes as Iterated Integrals

20-2 Double Integrals and Iterated Integrals

20-3 Physical Applications of Double Integrals

20-4 Double Integrals in Polar Coordinates

20-5 Triple Integrals

20-6 Cylindrical Coordinates

20-7 Spherical Coordinates

20-8 Areas of curved Surfaces

CHAPTER 21: Line and Surface Integrals

21-1 Green's Theorem, Gauss's Theorem, and Stokes' Theorem

21-2 Line Integrals in the Plane

21-3 Independence of Path

21-4 Green's Theorem

21-5 Surface Integrals and Gauss's Theorem

21-6 Maxwell's Equations : A Final Thought

Appendices

A: The Theory of Calculus

A-1 The Real Number System

A-2 Theorems About Limits

A-3 Some Deeper Properties of Continuous Functions

A-4 The Mean Value theorem

A-5 The Integrability of Continuous Functions

A-6 Another Proof of the Fundamental Theorem of Calculus

A-7 Continuous Curves With No Length

A-8 The Existence of e = lim h->0 (1 + h) <^>1/h

A-9 Functions That Cannot Be Integrated

A-10 The Validity of Integration by Inverse Substitution

A-11 Proof of the Partial fractions Theorem

A-12 The Extended Ratio Tests of Raabe and Gauss

A-13 Absolute vs Conditional Convergence

A-14 Dirichlet's Test

A-15 Uniform Convergence for Power Series

A-16 Division of Power Series

A-17 The Equality of Mixed Partial Derivatives

A-18 Differentiation Under the Integral Sign

A-19 A Proof of the Fundamental Lemma

A-20 A Proof of the Implicit Function Theorem

A-21 Change of Variables in Multiple Integrals

B: A Few Review Topics

B-1 The Binomial Theorem

B-2 Mathematical Induction

Dettagli dell?edizione

• Editore: McGraw-Hill Education
• Data di pubblicazione: 1995
• ISBN 10: 0070576424
• ISBN 13: 9780070576421
• Rilegatura: Copertina rigida
• Lingua: Inglese
• Numero edizione: 2
• Numero di pagine: 887