Calculus from Graphical, Numerical, and Symbolic Points of View Volumes 1 and 2 Second Edition, and Multivariable Revised Preliminary Edition: Complete

Contents Note: Each chapter contains a Summary. 1. 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 2. 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 3. 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 4. Using the Derivative Slope Fields; More Differential Equation Models More on Limits: Limits Involving Infinity and l'HÔpital'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 5. 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 6. 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 7. 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 8. Symbolic Antidifferentiation Techniques Integration by Parts Partial Fractions Trigonometric Antiderivatives Miscellaneous Antiderivatives Interlude: Beyond Elementary Functions Interlude: First-Order Linear Differential Equations 9. Function Approximation Taylor Polynomials Taylor's Theorem: Accuracy Guarantees for Taylor Polynomials Fourier Polynomials: Approximating Periodic Functions Interlude: Splines--Connecting the Dots 10. Improper Integrals Improper Integrals: Ideas and Definitions Detecting Convergence, Estimating Limits Improper Integrals and Probability 11. 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 12. 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 13. 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 14. 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 15. Other Topics Linear, Circular, and Combined Motion Using the Dot Product: More on Curves Curvature Lagrange Multipliers and Constrained Optimization 16. 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 A. Machine Graphics B. Real Numbers and the Coordinate Plane C. Lines and Linear Functions D. Polynomials and Rational Functions E. Algebra of Exponentials and Logarithms F. Trigonometric Functions G. Real-World Calculus: From Words to Mathematics H. Selected Proofs I. A Graphical Glossary of FunctionsOstebee, Arnold is the author of 'Calculus from Graphical, Numerical, and Symbolic Points of View Volumes 1 and 2 Second Edition, and Multivariable Revised Preliminary Edition: Complete' with ISBN 9780618267477 and ISBN 0618267476.