Calculus for cognitive scientists : partial differential equation models /: partial differential equation models. (2016)

• Record Type: Book
• Further Information: Note: James K. Peterson.
• Authors: Peterson, James K (James Kent)
• Contents: Acknowledgments; Contents; List of Figures; List of Tables; List of Code Examples; Abstract; History; Part I Introductory Matter; 1 Introduction; 1.1 Chapter Guide; 1.2 Code; References; Part II Quantitative Tools; 2 Graham -- Schmidt Orthogonalization; 2.1 Numerical Integration; 2.1.1 Evaluating Smk; 2.1.2 Homework; 2.1.3 Matlab Implementation; 2.1.4 Run Time Output; 2.2 Linearly Independent Functions; 2.2.1 Functions; 2.2.2 Homework; 2.3 Vector Spaces and Basis; 2.4 Inner Products; 2.5 Graham -- Schmidt Orthogonalization; 2.5.1 Making It Formal; 2.5.2 General MatLab GSO; Reference. 3 Numerical Differential Equations3.1 Approximating Solutions Numerically; 3.1.1 Expansions of F; 3.1.2 Minimizing Error; 3.1.3 The Matlab Implementation; 3.2 Runge -- Kutta Fehlberg Methods; 3.2.1 The RKF5 Flowchart; 3.2.2 Runge -- Kutta Fehlberg MatLab Implementation; References; Part III Deriving the Cable Model; 4 Biological Molecules; 4.1 Molecular Bonds; 4.1.1 Bond Comparisons; 4.2 Energy Considerations; 4.3 Hydrocarbons; 4.4 Amino Acids; 4.5 Peptide Bonds; 4.6 Chains of Amino Acids; 4.7 Nucleic Acids; 4.7.1 Sugars; 4.7.2 Nucleotides; 4.7.3 Complementary Base Pairing; 4.8 Making Proteins. 5 Ion Movement5.1 Membranes in Cells; 5.2 The Physical Laws of Ion Movement; 5.2.1 Ficke's Law of Diffusion; 5.2.2 Ohm's Law of Drift; 5.2.3 Einstein's Relation; 5.2.4 Space Charge Neutrality; 5.2.5 Ions, Volts and a Simple Cell; 5.3 The Nernst -- Planck Equation; 5.4 Equilibrium Conditions: The Nernst Equation; 5.4.1 An Example; 5.5 One Ion Nernst Computations in MatLab; 5.5.1 Homework; 5.6 Electrical Signaling; 5.6.1 The Cell Prior to K Gates; 5.6.2 The Cell with K+ Gates; 5.6.3 The Cell with NaCl Inside and Outside Changes; 5.6.4 The Cell with Na+ Gates. 5.6.5 The Nernst Equation for Two Ions5.6.6 The Nernst Equation for More Than Two Ions; 5.6.7 Multiple Ion Nernst Computations in MatLab; 5.7 Ion Flow; 5.7.1 Transport Mechanisms; 5.7.2 Ion Channels; 5.7.3 Active Transport Using Pumps; 5.7.4 A Simple Compartment Model; 5.8 Movement of Ions Across Biological Membranes; 5.8.1 Membrane Permeability; 5.8.2 The Goldman -- Hodgkin -- Katz (GHK) Model; 5.8.3 The GHK Voltage Equation; 5.8.4 Examples; 5.8.5 The Effects of an Electrogenic Pump; 5.9 Excitable Cells; References; 6 Lumped and Distributed Cell Models; 6.1 Modeling Radial Current. 6.2 Modeling Resistance6.3 Longitudinal Properties; 6.4 Current in a Cable with a Thin Wall; 6.5 The Cable Model; 6.5.1 The Core Conductor Model Assumptions; 6.5.2 Building the Core Conductor Model; 6.6 The Transient Cable Equations; 6.6.1 Deriving the Transient Cable Equation; 6.6.2 The Space and Time Constant of a Cable; 7 Time Independent Solutions to Infinite Cables; 7.1 The Infinite Cable; 7.2 Solving the Time Independent Infinite Cable Equation; 7.2.1 Variation of Parameters; 7.3 Modeling Current Injections; 7.3.1 Continuity in the Solution; 7.3.2 Continuity in the Derivative.
• Publisher Details: Singapore : Springer
• Publication Date: 2016
• Extent: 1 online resource (xxxi, 534 pages)
• Subjects: 515; Calculus; Differential equations, Partial; MATHEMATICS -- Calculus; MATHEMATICS -- Mathematical Analysis; Calculus; Differential equations, Partial; Engineering; Computational Intelligence; Theoretical, Mathematical and Computational Physics; Mathematical Models of Cognitive Processes and Neural Networks; Artificial Intelligence (incl. Robotics); Computer Imaging, Vision, Pattern Recognition and Graphics; Electronic books
• Languages: English
• ISBNs: 9789812878809; 9812878807; 9812878785; 9789812878786
• Related ISBNs: 9789812878786
• Notes: Note: Includes bibliographical references and index.; Note: Online resource; title from PDF title page (EBSCO, viewed February 22, 2016).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.