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Mathematical techniques for physiology and medicine

Author: William Simon
Publisher: New York : Academic Press, [1972]
Edition/Format:   eBook : Document : EnglishView all editions and formats
Database:WorldCat
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Mathematical Techniques For Physiology and Medicine.
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Simon, William, 1929-
Mathematical techniques for physiology and medicine.
New York, Academic Press [1972]
(DLC) 70190728
(OCoLC)354087
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: William Simon
ISBN: 9780323158015 0323158013
OCLC Number: 843220573
Reproduction Notes: Electronic reproduction. [S.l.] : HathiTrust Digital Library, 2010. MiAaHDL
Description: 1 online resource (xi, 267 pages) : illustrations
Details: Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002.
Contents: Front Cover; Mathematical Techniques for Physiology and Medicine; Copyright Page; Table of Contents; Preface; Chapter I. Review of Differential Calculus; 1. Dimensions; 2. The Concept of a Functional Relationship; 3. The Derivative; 4. The Function That Is Its Own Derivative; 5. Differential Equations; Problems; Chapter II. How Differential Equations Arise; 1. The One-Compartment Dilution Process; 2. One-Compartment Metabolic Turnover; 3. Radioactive Decay; 4. X-Ray Absorption; 5. One Compartment with Constant Injection; 6. The Two-Compartment Series Dilution; 7. Dimensionless Variables. 8. Mother-Daughter Radioactive Decay9. A Circular Reaction; Problems; Chapter III. Guessing the Solution of a Differential Equation; 1. Introduction: Quadratic Equations; 2. More about Exponential Functions; 3. Second Derivatives; 4. Solutions of Simple Differential Equations; 5. Linear and Nonlinear Equations; 6. Homogeneous and Inhomogeneous Equations; 7. The Forms of Solutions; 8. The Two-Compartment Series Dilution; 9. One Compartment with a Long Input; 10. Diffusion between Compartments; 11. A Simple Kinetic Reaction; Problems; Chapter IV. The Laplace Transform. 1. Introduction: Antiderivatives2. Area under a Curve; 3. The Split Integral Theorem; 4. Simultaneous Linear Equations; 5. Transforming the Differential Equation; 6. One Compartment with Nonzero Initial Concentration; 7. The Second Compartment of the Two-Compartment Series Dilution; 8. Diffusion between Compartments; 9. Finding New Transforms; 10. Three Special Cases; 11. The Partial Fraction Expansion; 12. The Convolution Integral; Problems; Chapter V. Compartmental Problems; 1. Introduction; 2. The One-Compartment Mixed Case; 3. The Two-Compartment Problem. 4. A Simple Three-Compartment Problem5. The Unit Impulse Response; 6. The Convolution Theorem; 7. Numerical Solutions from the Unit Impulse Response; 8. Working Backward; Problems; Chapter VI. Numerical Methods; 1. Euler's Method; 2. Verifying the Result; 3. Numerical Solution of a Circular Reaction with Changing Rate Constant; 4. Restricted Value Problems; 5. Numerical Solution of Higher-Order Equations; Problems; Chapter VII. Regulation and Oscillation; 1. The Sine and Cosine Functions; 2. Properties of Control Systems; 3. A Simple Regulator; 4. The Output Rate Error Response. 5. The Effect of Time Delay in the Feedback Loop6. Pooling Delay versus Pure Time Delay; 7. A Three-Compartment System; 8. Control of Biosynthesis; 9. Other Oscillators; Problems; Chapter VIII. Diffusion; 1. Introduction: Infinite Series; 2. Fourier Series; 3. The Thermal Diffusion Equation; 4. Chemical Diffusion; 5. Semi-Infinite Section with Mixed Loss; 6. Finite Section with Mixed Loss; 7. Threshold-Dependent Loss; 8. Semi-Infinite Section with Internal Generation; 9. Finite Section with Internal Generation; 10. Spherical Diffusion; 11. Cylindrical Diffusion and the Krogh Equation.
Responsibility: William Simon.

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Mathematical Techniques For Physiology and Medicine.

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