Calculus with Analytic Geometry 1st Edition by George F Simmons ISBN 0070574197 9780070574199

Calculus with Analytic Geometry 1st Edition by George F Simmons – Ebook PDF Instant Download/Delivery: 0070574197 ,9780070574199
Full download Calculus with Analytic Geometry 1st Edition after payment

Product details:

ISBN 10: 0070574197
ISBN 13: 9780070574199
Author: George F Simmons

Calculus with Analytic Geometry 1st Edition Table of contents:

Chapter 1: Numbers, Functions, and Graphs

• Introduction

• The Real Line and Coordinate Plane: Pythagoras

• Slopes and Equations of Straight Lines

• Circles and Parabolas: Descartes and Fermat

• The Concept of a Function

• Graphs of Functions

• Introductory Trigonometry

• The Functions sin θ and cos θ

Chapter 2: The Derivative of a Function

• What is Calculus?

• The Problems of Tangents

• How to Calculate the Slope of the Tangent

• The Definition of the Derivative

• Velocity and Rates of Change: Newton and Leibniz

• The Concept of a Limit: Two Trigonometric Limits

• Continuous Functions: The Mean Value Theorem and Other Theorems

Chapter 3: The Computation of Derivatives

• Derivatives of Polynomials

• The Product and Quotient Rules

• Composite Functions and the Chain Rule

• Some Trigonometric Derivatives

• Implicit Functions and Fractional Exponents

• Derivatives of Higher Order

Chapter 4: Applications of Derivatives

• Increasing and Decreasing Functions: Maxima and Minima

• Concavity and Points of Inflection

• Applied Maximum and Minimum Problems

• More Maximum-Minimum Problems

• Related Rates

• Newton’s Method for Solving Equations

• Applications to Economics: Marginal Analysis

Chapter 5: Indefinite Integrals and Differential Equations

• Differentials and Tangent Line Approximations

• Indefinite Integrals: Integration by Substitution

• Differential Equations: Separation of Variables

• Motion Under Gravity: Escape Velocity and Black Holes

Chapter 6: Definite Integrals

• The Problem of Areas

• The Sigma Notation and Certain Special Sums

• The Area Under a Curve: Definite Integrals

• The Computation of Areas as Limits

• The Fundamental Theorem of Calculus

• Properties of Definite Integrals

Chapter 7: Applications of Integration

• The Intuitive Meaning of Integration

• The Area between Two Curves

• Volumes: The Disk Method

• Volumes: The Method of Cylindrical Shells

• Arc Length

• The Area of a Surface of Revolution

• Work and Energy

• Hydrostatic Force

(Part II)

Chapter 8: Exponential and Logarithmic Functions

• Review of Exponents and Logarithms

• The Number e and the Function y = eˣ

• The Natural Logarithm Function y = ln x

• Applications: Population Growth and Radioactive Decay

Chapter 9: Trigonometric Functions

• Review of Trigonometry

• Derivatives of Sine and Cosine

• Integrals of Sine and Cosine

• Derivatives of the Other Four Trigonometric Functions

• The Inverse Trigonometric Functions

• Simple Harmonic Motion

• Hyperbolic Functions

Chapter 10: Methods of Integration

• The Method of Substitution

• Certain Trigonometric Integrals

• Trigonometric Substitutions

• Completing the Square

• The Method of Partial Fractions

• Integration by Parts

• A Mixed Bag

• Numerical Integration

Chapter 11: Further Applications of Integration

• The Center of Mass of a Discrete System

• Centroids

• The Theorems of Pappus

• Moment of Inertia

Chapter 12: Indeterminate Forms and Improper Integrals

• The Mean Value Theorem Revisited

• The Indeterminate Form 0/0: L’Hôpital’s Rule

• Other Indeterminate Forms

• Improper Integrals

• The Normal Distribution

Chapter 13: Infinite Series of Constants

• What is an Infinite Series?

• Convergent Sequences

• Convergent and Divergent Series

• General Properties of Convergent Series

• Comparison Tests for Series with Non-negative Terms

• The Integral Test

• The Ratio and Root Tests

• The Alternating Series Test

Chapter 14: Power Series

• Introduction

• The Interval of Convergence

• Differentiation and Integration of Power Series

• Taylor Series and Taylor’s Formula

• Computations Using Taylor’s Formula

• Applications to Differential Equations

• Optional: Operations on Power Series / Complex Numbers and Euler’s Formula

Part III

Chapter 15: Conic Sections

• Introduction

• Circles and Parabolas Revisited

• Ellipses

• Hyperbolas

• Focus–Directrix–Eccentricity Definitions

• Optional: Second-Degree Equations

Chapter 16: Polar Coordinates

• The Polar Coordinate System

• Graphs of Polar Equations

• Polar Equations of Circles, Conics, and Spirals

• Arc Length and Tangent Lines

• Areas in Polar Coordinates

Chapter 17: Parametric Equations

• Parametric Equations of Curves

• The Cycloid and Related Curves

• Vector Algebra

• Derivatives of Vector Functions

• Curvature and the Unit Normal Vector

• Tangential and Normal Components of Acceleration

• Kepler’s Laws and Newton’s Laws of Gravitation

Chapter 18: Vectors in Three-Dimensional Space

• Coordinates and Vectors in 3D Space

• The Dot Product

• The Cross Product

• Lines and Planes

• Cylinders and Surfaces of Revolution

• Quadric Surfaces

• Cylindrical and Spherical Coordinates

Chapter 19: Partial Derivatives

• Functions of Several Variables

• Partial Derivatives

• The Tangent Plane to a Surface

• Increments and Differentials

• Directional Derivatives and the Gradient

• The Chain Rule for Partial Derivatives

• Maximum and Minimum Problems

• Constrained Maxima and Minima

• Laplace’s Equation, the Heat Equation, and the Wave Equation

• Optional: Implicit Functions

Chapter 20: Multiple Integrals

• Volumes as Iterated Integrals

• Double Integrals and Iterated Integrals

• Physical Applications of Double Integrals

• Double Integrals in Polar Coordinates

• Triple Integrals

• Cylindrical Coordinates

• Spherical Coordinates

• Areas of Curved Surfaces

Chapter 21: Line and Surface Integrals

• Green’s Theorem, Gauss’ Theorem, and Stokes’ Theorem

• Line Integrals in the Plane

• Path Independence

• Green’s Theorem

• Surface Integrals and Gauss’ Theorem

• Maxwell’s Equations: A Final Thought

People also search for Calculus with Analytic Geometry 1st Edition:

purcell calculus with analytic geometry
    
calculus with analytic geometry richard silverman
    
calculus with trigonometry and analytic geometry quizlet
    
analytic geometry calculus
    
calculus and analytic geometry quizlet

Tags: George F Simmons, Calculus, Analytic Geometry