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  • Produktbild: Numerical Methods and Analysis with Mathematical Modelling
  • Produktbild: Numerical Methods and Analysis with Mathematical Modelling

Numerical Methods and Analysis with Mathematical Modelling

Aus der Reihe Textbooks in Mathematics

297,99 €

inkl. gesetzl. MwSt., Versandkostenfrei

Beschreibung

Produktdetails

Einband

Gebundene Ausgabe

Erscheinungsdatum

07.08.2024

Abbildungen

130 SW-Abb., 130 Farbzeichn., 37 Tabellen

Verlag

Taylor & Francis

Seitenzahl

424

Maße (L/B/H)

24/16,1/2,7 cm

Gewicht

798 g

Sprache

Englisch

ISBN

978-1-03-269723-9

Beschreibung

Produktdetails

Einband

Gebundene Ausgabe

Erscheinungsdatum

07.08.2024

Abbildungen

130 SW-Abb., 130 Farbzeichn., 37 Tabellen

Verlag

Taylor & Francis

Seitenzahl

424

Maße (L/B/H)

24/16,1/2,7 cm

Gewicht

798 g

Sprache

Englisch

ISBN

978-1-03-269723-9

EU-Ansprechpartner

Taylor & Francis Verlag GmbH
Kaufingerstraße 24
80331 München
DE
GPSR@taylorandfrancis.com

Herstelleradresse

Taylor & Francis Group
5 Howick Place
SW1P 1WG London
UK
GPSR@taylorandfrancis.com

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  • Produktbild: Numerical Methods and Analysis with Mathematical Modelling
  • Produktbild: Numerical Methods and Analysis with Mathematical Modelling

  • Chapter 1 Review of Differential Calculus

    1.1. Introduction

    1.2 Limits

    1.3 Continuity

    1.3 Differentiation

    1.3.1 Increasing and decreasing functions

    Example 8

    1.3.2 Higher Derivatives

    1.4 Convex and Concave Functions

    Example 13. The 2nd derivative theorem

    Exercises

    1.5 Accumulation and Integration

    Exercises 1.5

    1.6 Taylor Polynomials

    Exercises 1.7

    1.7 Errors

    1.8. Algorithms Accuracy

    References and Further Readings

    Chapter 2 Mathematical Modeling and Introduction to Technology: Perfect Partners

    2.1 OVERVIEW AND THE PROCESS OF MATHEMATICAL MODELING..

    2.2 THE MODLEING PROCESS

    2.3 Making ASSUMPTIONS

    2.4 ILLUSTRATE EXAMPLES

    2.5 Technology

    Exercises Chapter 2

    References and Additional Readings

    Chapter 3 Modeling with Discrete Dynamical Systems and Modeling Systems of DDS

    3.1 Introduction Modeling with Discrete Dynamical Systems

    3.2 Equilibrium and Stability Values and Long-Term Behavior

    3.3 Using Python for a drug problem

    3.4 Introduction to Systems of Discrete Dynamical Systems

    3.4.1 Iteration and Graphical Solution

    3.5 Modeling of Predator - Prey model, SIR Model, and Military Models

    3.6 Technology Examples for Discrete Dynamical Systems

    3.6.1 Excel for Linear and Nonlinear DDS

    3.6.2 Maple for Linear and Nonlinear DDS

    3.6.3 R for Linear and Nonlinear DDS

    Example 2. Population dynamics using R

    Exercises Chapter 3

    Projects

    References and Suggested Future Readings

    CHAPTER 4 Numerical Solutions to Equations in One Variable

    4.1 Introduction and Scenario

    4.2 Archimedes' design of ships

    4.3 Bisection Method

    4.4 Fixed Point Algorithm

    4.5 Newton's Method

    4.6 Secant Method

    4.6.1 Archimedes' Example with secant method

    Example 4.6.2 Buying a car using Secant method

    4.7 Root Find as a DDS

    4.7.1 Example of Newton's Using EXCEL

    4.7.1 Root finding with Python

    Exercises

    Projects

    References and Further Readings

    CHAPTER 5 Interpolation and Polynomial Approximation

    5.1 Introduction

    5.2 Methods

    5.2.1 Lagrange Polynomials

    5.3 Lagrange Polynomials

    5.4 Divided Differences

    5.5 Cubic Splines

    5.6 Telemetry Modeling and Lagrange Polynomials

    5.7 Method of Divided Differences with Telemetry Data

    5.8 NATURAL CUBIC SPLINE INTERPOLATION to Telemetry Data

    5.9 Comparisons for Methods

    5.10 Estimating the Error

    5.11 Radiation Dosage Model

    Exercises

    Projects

    References and Further Readings

    Chapter 6 Numerical Differentiation and Integration

    6.1 Introduction and Scenario

    6.2 Numerical Differentiation

    6.3 Numerical Integration

    6.3 Car traveling problem

    6.4 Revisit a Telemetry Model

    6.5 Volume of Water in a Tank

    EXERCISES/Projects

    CHAPTER 7 Modeling with Numerical Solutions to Differential Equations---IVP for ODEs

    7.1 Introduction and Scenario

    Bridge Bungee Jumping

    Spread of a Contagious Disease

    7.2 Numerical Methods

    7.2.1 Euler's Method

    7.2.2 Improved Euler's Method (Heun's method)

    7.2.3 Runge-Kutta Methods

    7.3 Population Modeling

    7.4 Spread of a contagious disease

    7.5 Bungee Jumping

    7.6 Revisit Bungee as a 2nd order ODE IVP

    7.6 Harvesting a Species

    EXERCISES

    7.7 System of ODEs

    Projects

    CHAPTER 8 Iterative Techniques in Matrix Algebra

    8.1 Gauss Seidel and Jacobi

    8.1.1 Gauss-Seidel Iterative Method

    8.1.2 Jacobi Method

    8.2 A Bridge Too Far

    8.2 The Leontief Input-Output Economic Model

    8.3 Markov Chains with Eigenvalues and Eigenvectors

    8.4 Cubic Splines with Matrices

    Exercises

    Projects

    References and Further Readings

    CHAPTER 9 Modeling with Single Variable Unconstrained Optimization and Numerical Methods

    9.1 Introduction

    9.2 Single Variable Optimization and Basic Theory

    9..3 Models with Basic Applications of Max-Min Theory (calculus review)

    9.3 Applied Single Variable Optimization Models

    9.3.1 Oil Rig Location Problem

    9.4 Single Variable Numerical Search Techniques

    9.4.1 Unrestricted Search

    9.4.2 Dichotomous Search

    9.4.3 Golden Section Search

    9.4.4 Fibonacci Search

    9.5 INTERPLOATION WITH DERIVATIVES: NEWTON'S METHOD FOR NONLINEAR OPTIMZATION

    Exercises 9.5

    Projects

    Reference and Further Readings

    Chapter 10 Multivariable Numerical Search Methods

    10.1 Introduction

    10.1.1 Background theory

    10.2 Gradient Search Methods

    10.3 Modified Newton's Method

    10.4 Applications

    10.4.1 Manufacturing

    10.4.2 TV Manufacturing

    EXERCISES

    Projects

    References and FURTHER READING

    CHAPTER 11 Boundary Value Problems in ODE

    11.1 Introduction

    11.2 Linear Shooting Method

    11.3 Linear Finite Differences Method

    11.4 Applications

    11.4.1 Motorcycle suspension

    11.4.2 Parachuting by skydiving Free Fall

    11.4.3 Free Fall

    11.4.4 Bungee Two

    11.4.5 Heat transfer

    11.6 Beam Deflection

    Exercises

    Projects

    References and Further Readings

    CHAPTER 12 Approximation Theory and Curve Fitting

    12.1 Introduction

    12.2 Model Fitting

    12.3 Application of Planning and Production Control

    12.3 Continuous Least Squares

    12.4 Co-Sign Out a Cosine

    Exercises

    Projects

    Exercises

    References and Further readings

    Chapter 13 Numerical Solutions to Partial Differential Equations

    13.1 Introduction, Methods, and Applications

    13.1.2 Methods

    13.1.2 Application Scenario

    13.2 Solving the Heat Equation with Homogeneous Boundary Conditions

    13.3 Methods with Python

    Exercises

    Projects

    References and Furthe Readings