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Calculus: From Graphical, Numerical, and Symbolic Points of View

by: Ostebee, Arnold

Calculus: From Graphical, Numerical, and Symbolic Points of View

by: Ostebee, Arnold

ISBN 13:
9780030965784
ISBN 10:
0030965780
Edition: 1st
Format: Paperback
Copyright: 07/01/1996
Publisher: HOUGHTON MIFFLIN COMPANY (COLLEGE DIVISION)

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Functions and Derivatives: The Graphical View Functions, Calculus Style Graphs
A Field Guide to Elementary Functions
Amount Functions and Rate Functions: The Idea of the Derivative
Estimating Derivatives: A Closer Look
The Geometry of Derivatives
The Geometry of Higher-Order Derivatives
Interlude: Zooming in on Differences
Functions and Derivatives: The Symbolic View Defining the Derivative
Derivatives of Power Functions and Polynomials Limits
Using Derivative and Antiderivative Formulas
Differential Equations;
Modeling Motion Derivatives of Exponential and Logarithm Functions;
Modeling Growth Derivatives of Trigonometric Functions: Modeling Oscillation
Interlude: Tangent Lines in History
Interlude: Limit--The Formal Definition
New Derivatives from Old Algebraic Combinations: The Product and Quotient Rules
Composition and the Chain Rule Implicit
Functions and Implicit Differentiation
Inverse Functions and Their Derivatives;
Inverse Trigonometric Functions Miscellaneous
Derivatives and Antiderivatives Interlude: Vibrations--Simple and Damped
Interlude: Hyperbolic Functions
Using the Derivative Slope Fields;
More Differential Equation Models More on Limits: Limits Involving Infinity and l'Hocirc;pital's Rule Optimization
Parametric Equations, Parametric Curves Related Rates
Newton's Method: Finding Roots Building Polynomials to Order;
Taylor Polynomials Why Continuity Matters
Why Differentiability Matters: The Mean Value Theorem
Interlude: Growth with Interest
Interlude: Logistic Growth
Interlude: Digging Deeper for Roots
The Integral Areas and Integrals
The Area Function
The Fundamental Theorem of Calculus Finding Antiderivatives;
The Method of Substitution Integral Aids: Tables and Computers
Approximating Sums: The Integral as a Limit Working with Sums
Interlude: Mean Value Theorems and Integrals
Numerical Integration Approximating Integrals
Numerically Error Bounds for approximating Sums
Euler's Method: Solving DEs Numerically
Interlude: Simpson's Rule
Interlude: Gaussian Quadrature: Approximating Integrals Efficiently
Using the Integral Measurement and the Definite Integral;
Arc Length Finding Volumes by Integration Work
Separating Variables: Solving DEs Symbolically Present Value
Interlude: Mass and Center of Mass
Symbolic Antidifferentiation Techniques Integration by Parts
Partial Fractions Trigonometric Antiderivatives
Miscellaneous Antiderivatives
Interlude: Beyond Elementary Functions
Interlude: First-Order Linear Differential Equations
Function Approximation Taylor Polynomials
Taylor's Theorem: Accuracy Guarantees for Taylor Polynomials
Fourier Polynomials: Approximating Periodic Functions
Interlude: Splines--Connecting the Dots
Improper Integrals Improper Integrals: Ideas and Definitions Detecting Convergence, Estimating Limits
Improper Integrals and Probability
Infinite Series Sequences and Their Limits Infinite Series, Convergence, and Divergence Testing for Convergence;
Estimating Limits Absolute Convergence;
Alternating Series Power Series Power Series as Functions Taylor Series Interlude: Fourier Series V. Vectors and Polar Coordinates
Vectors and Vector-Valued Functions
Polar Coordinates and Polar Curves Calculus in Polar Coordinates M.
Multivariable Calculus: A First Look
Three-Dimensional Space Functions of Several Variables
Partial Derivatives Optimization and Partial Derivatives: A First Look
Multiple Integrals and Approximating Sums
Calculating Multiple Integrals by Iteration
Double Integrals in Polor Coordinates
Curves and Vectors
Three-dimensional Space Curves and Parametric Equations Vectors
Vector-valued Functions, Derivatives, and Integrals
Derivatives, Antiderivatives, and Motion
The Dot Product Lines and Planes in Three Dimensions
The Cross Product
Derivatives Functions of Several Variables
Partial Derivatives
Partial Derivatives and Linear Approximation
The Gradient and Directional Derivatives
Local Linearity: Theory of the Derivative
Higher Order Derivatives and Quadratic Approximation
Maxima, Minima, and Quadratic Approximation
The Chain Rule
Integrals Multiple Integrals and Approximating Sums
Calculating Integrals by Iteration
Double Integrals in Polar Coordinates
More on Triple Integrals;
Cylindrical and Spherical Coordinates
Multiple Integrals Overviewed;
Change of Variables
Other Topics Linear, Circular, and Combined Motion Using the Dot Product: More on Curves Curvature Lagrange Multipliers and Constrained Optimization
Vector Calculus Line Integrals
More on Line Integrals;
A Fundamental Theorem Relating Line and Area Integrals: Green's Theorem Surfaces and Their Parametrizations
Surface Integrals
Derivatives and Integrals of Vector Fields
Back to Fundamentals: Stokes' Theorem and the Divergence Theorem
Appendices
Machine Graphics
Real Numbers and the Coordinate Plane
Lines and Linear Functions
Polynomials and Rational Functions
Algebra of Exponentials and Logarithms
Trigonometric Functions
Real-World Calculus: From Words to Mathematics
Selected Proofs
A Graphical Glossary of Functions
Table of Contents provided by Publisher. All Rights Reserved.

Amazon no longer offers textbook rentals. We do!

Calculus: From Graphical, Numerical, and Symbolic Points of View

Calculus: From Graphical, Numerical, and Symbolic Points of View

9780030965784

0030965780

Table of Contents

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