Calculus: From Graphical, Numerical, and Symbolic Points of View
, by Ostebee, ArnoldNote: Supplemental materials are not guaranteed with Rental or Used book purchases.
- ISBN: 9780030169779 | 0030169771
- Cover:
- Copyright: 10/1/1996
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. |
What is included with this book?
The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any access cards, study guides, lab manuals, CDs, etc.
The Used, Rental and eBook copies of this book are not guaranteed to include any supplemental materials. Typically, only the book itself is included. This is true even if the title states it includes any access cards, study guides, lab manuals, CDs, etc.