George Brinton Thomas

Bio: George Brinton Thomas is an academic researcher. The author has contributed to research in topics: Integration by substitution & Function of several real variables. The author has an hindex of 2, co-authored 2 publications receiving 798 citations.

Calculus and Analytic Geometry

Abstract: (NOTE: Every chapter ends with Questions to Guide Your Review, Practice Exercises, and Additional Exercises.) P. Preliminaries. Real Numbers and the Real Line. Coordinates, Lines, and Increments. Functions. Shifting Graphs. Trigonometric Functions. 1. Limits and Continuity. Rates of Change and Limits. Rules for Finding Limits. Target Values and Formal Definitions of Limits. Extensions of the Limit Concept. Continuity. Tangent Lines. 2. Derivatives. The Derivative of a Function. Differentiation Rules. Rates of Change. Derivatives of Trigonometric Functions. The Chain Rule. Implicit Differentiation and Rational Exponents. Related Rates of Change. 3. Applications of Derivatives. Extreme Values of Functions. The Mean Value Theorem. The First Derivative Test for Local Extreme Values. Graphing with y e and y . Limits as x a a, Asymptotes, and Dominant Terms. Optimization. Linearization and Differentials. Newton's Method. 4. Integration. Indefinite Integrals. Differential Equations, Initial Value Problems, and Mathematical Modeling. Integration by Substitution--Running the Chain Rule Backward. Estimating with Finite Sums. Riemann Sums and Definite Integrals. Properties, Area, and the Mean Value Theorem. Substitution in Definite Integrals. Numerical Integration. 5. Applications of Integrals. Areas Between Curves. Finding Volumes by Slicing. Volumes of Solids of Revolution--Disks and Washers. Cylindrical Shells. Lengths of Plan Curves. Areas of Surfaces of Revolution. Moments and Centers of Mass. Work. Fluid Pressures and Forces. The Basic Pattern and Other Modeling Applications. 6. Transcendental Functions. Inverse Functions and Their Derivatives. Natural Logarithms. The Exponential Function. ax and logax. Growth and Decay. L'Hopital's Rule. Relative Rates of Growth. Inverse Trigonomic Functions. Derivatives of Inverse Trigonometric Functions Integrals. Hyperbolic Functions. First Order Differential Equations. Euler's Numerical Method Slope Fields. 7. Techniques of Integration. Basic Integration Formulas. Integration by Parts. Partial Fractions. Trigonometric Substitutions. Integral Tables and CAS. Improper Integrals. 8. Infinite Series. Limits of Sequences of Numbers. Theorems for Calculating Limits of Sequences. Infinite Series. The Integral Test for Series of Nonnegative Terms. Comparison Tests for Series of Nonnegative Terms. The Ratio and Root Tests for Series of Nonnegative Terms. Alternating Series, Absolute and Conditional Convergence. Power Series. Taylor and Maclaurin Series. Convergence of Taylor Series Error Estimates. Applications of Power Series. 9. Conic Sections, Parametrized Curves, and Polar Coordinates. Conic Sections and Quadratic Equations. Classifying Conic Sections by Eccentricity. Quadratic Equations and Rotations. Parametrizations of Plan Curves. Calculus with Parametrized Curves. Polar Coordinates. Graphing in Polar Coordinates. Polar Equations for Conic Sections. Integration in Polar Coordinates. 10. Vectors and Analytic Geometry in Space. Vectors in the Plane. Cartesian (Rectangular) Coordinates and Vectors in Space. Dot Products. Cross Products. Lines and Planes in Space. Cylinders and Quadric Surfaces. Cylindrical and Spherical Coordinates. 11. Vector-Valued Functions and Motion in Space. Vector-Valued Functions and Space Curves. Modeling Projectile Motion. Arc Length and the Unit Tangent Vector T. Curvature, Torison, and the TNB Frame. Planetary Motion and Satellites. 12. Multivariable Functions and Partial Derivatives. Functions of Several Variables. Limits and Continuity. Partial Derivatives. Differentiability, Linearization, and Differentials. The Chain Rule. Partial Derivatives with Constrained Variables. Directional Derivatives, Gradient Vectors, and Tangent Planes. Extreme Values and Saddle Points. Lagrange Multipliers. Taylor's Formula. 13. Multiple Integrals. Double Integrals. Areas, Moments, and Centers of Mass. Double Integrals in Polar Form. Triple Integrals in Rectangular Coordinates. Masses and Moments in Three Dimensions. Triple Integrals in Cylindrical and Spherical Coordinates. Substitutions in Multiple Integrals. 14. Integration in Vector Fields. Line Integrals. Vector Fields, Work, Circulation, and Flux. Path Independence, Potential Functions, and Conservative Fields. Green's Theorem in the Plane. Surface Area and Surface Integrals. Parametrized Surfaces. Stokes's Theorem. The Divergence Theorem and a Unified Theory. Appendices. Mathematical Induction. Proofs of Limit Theorems in Section 1.2. Complex Numbers. Simpson's One-Third Rule. Cauchy's Mean Value Theorem and the Stronger Form of L'Hopital's Rule. Limits that Arise Frequently. The Distributive Law for Vector Cross Products. Determinants and Cramer's Rule. Euler's Theorem and the Increment Theorem.

How does the brain build a cognitive code

Abstract: This article provides a self-contained introduction to my work from a recent perspective. A thought experiment is offered which analyses how a system as a whole can correct errors of hypothesis testing in a fluctuating environment when none of the system’s components, taken in isolation, even knows that an error has occurred. This theme is of general philosophical interest: How can intelligence or knowledge be ascribed to a system as a whole but not to its parts? How can an organism’s adaptive mechanisms be stable enough to resist environmental fluctuations which do not alter its behavioral success, but plastic enough to rapidly change in response to environmental demands that do alter its behavioral success? To answer such questions, we must identify the functional level on which a system’s behavioral success is defined.

A Directional Theory of Issue Voting.

Abstract: From Stokes's (1963) early critique on, it has been clear to empirical researchers that the traditional spatial theory of elections is seriously flawed. Yet fully a quarter century later, that theory remains the dominant paradigm for understanding mass-elite linkage in politics. We present an alternative spatial theory of elections that we argue has greater empirical verisimilitude. Based on the ideas of symbolic politics, the directional theory assumes that most people have a diffuse preference for a certain direction of policy-making and that people vary in the intensity with which they hold those preferences. We test the two competing theories at the individual level with National Election Study data and find the directional theory more strongly supported than the traditional spatial theory. We then develop the implications of the directional theory for candidate behavior and assess the predictions in light of evidence from the U.S. Congress.

Memory Systems: Cache, DRAM, Disk

Abstract: Is your memory hierarchy stopping your microprocessor from performing at the high level it should be? Memory Systems: Cache, DRAM, Disk shows you how to resolve this problem. The book tells you everything you need to know about the logical design and operation, physical design and operation, performance characteristics and resulting design trade-offs, and the energy consumption of modern memory hierarchies. You learn how to to tackle the challenging optimization problems that result from the side-effects that can appear at any point in the entire hierarchy.As a result you will be able to design and emulate the entire memory hierarchy. . Understand all levels of the system hierarchy -Xcache, DRAM, and disk. . Evaluate the system-level effects of all design choices. . Model performance and energy consumption for each component in the memory hierarchy.

Curvature attributes and their application to 3D interpreted horizons

Abstract: The advent of the interpretation workstation has allowed the generation and analysis of horizon attributes to develop rapidly.