Numerical and statistical methods for bioengineering : applications in MATLAB /

Numerical and statistical methods for bioengineering : applications in MATLAB / Michael R. King and Nipa A. Mody.

Show other versions (1)

"The first MATLAB-based numerical methods textbook for bioengineers that uniquely integrates modelling concepts with statistical analysis, while maintaining a focus on enabling the user to report the error or uncertainty in their result. Between traditional numerical method topics of linear mod...

Full description

Saved in:
Bibliographic Details
Online Access: Full Text (via Cambridge)
Main Author: King, Michael R., 1973-
Other Authors: Mody, Nipa A., 1973-
Format: Electronic eBook
Language:English
Published: Cambridge ; New York : Cambridge University Press, 2010.
Series:Cambridge texts in biomedical engineering.
Subjects:
MATLAB.
Biomedical engineering > Statistical methods.
Biomedical engineering > Mathematics.
Table of Contents:
  • Cover
  • Half-title
  • Series-title
  • Title
  • Copyright
  • Contents
  • Preface
  • Format
  • Acknowledgements
  • 1 Types and sources of numerical error
  • 1.1 Introduction
  • 1.2 Representation of floating-point numbers
  • 1.2.1 How computers store numbers
  • 1.2.2 Binary to decimal system
  • 1.2.3 Decimal to binary system
  • 1.2.4 Binary representation of floating-point numbers
  • 1.3 Methods used to measure error
  • 1.4 Significant digits
  • 1.5 Round-off errors generated by floating-point operations
  • 1.6 Taylor series and truncation error
  • 1.6.1 Order of magnitude estimation of truncation error
  • 1.6.2 Convergence of a series
  • 1.6.3 Finite difference formulas for numerical differentiation
  • 1.7 Criteria for convergence
  • 1.8 End of Chapter 1: key points to consider
  • 1.9 Problems
  • References
  • 2 Systems of linear equations
  • 2.1 Introduction
  • 2.2 Fundamentals of linear algebra
  • 2.2.1 Vectors and matrices
  • 2.2.2 Matrix operations
  • 2.2.3 Vector and matrix norms
  • 2.2.4 Linear combinations of vectors
  • 2.2.5 Vector spaces and basis vectors
  • 2.2.6 Rank, determinant, and inverse of matrices
  • 2.3 Matrix representation of a system of linear equations
  • 2.4 Gaussian elimination with backward substitution
  • 2.4.1 Gaussian elimination without pivoting animalnhip
  • 2.4.2 Gaussian elimination with pivoting
  • 2.5 LU factorization
  • 2.5.1 LU factorization without pivoting
  • 2.5.2 LU factorization with pivoting
  • 2.5.3 The MATLAB lu function
  • 2.6 The MATLAB backslash (\) operator
  • 2.7 Ill-conditioned problems and the condition number
  • 2.8 Linear regression hemoglobin8211;oxygen binding
  • 2.9 Curve fitting using linear least-squares approximation
  • 2.9.1 The normal equations
  • 2.9.2 Coefficient of determination and quality of fit
  • 2.10 Linear least-squares approximation of transformed equations
  • 2.11 Multivariable linear least-squares regression
  • 2.12 The MATLAB function polyfit
  • 2.13 End of Chapter 2: key points to consider
  • 2.14 Problems
  • Solving systems of linear equations
  • References
  • 3 Probability and statistics
  • 3.1 Introduction
  • 3.2 Characterizing a population: descriptive statistics
  • 3.2.1 Measures of central tendency
  • 3.2.2 Measures of dispersion
  • 3.3 Concepts from probability
  • 3.3.1 Random sampling and probability
  • 3.3.2 Combinatorics: permutations and combinations
  • 3.4 Discrete probability distributions
  • 3.4.1 Binomial distribution
  • 3.4.2 Poisson distribution
  • 3.5 Normal distribution
  • 3.5.1 Continuous probability distributions
  • 3.5.2 Normal probability density
  • 3.5.3 Expectations of sample-derived statistics
  • 3.5.4 Standard normal distribution and the z statistic
  • 3.5.5 Confidence intervals using the z statistic and the t statistic
  • 3.5.6 Non-normal samples and the centralimit theorem
  • 3.6 Propagation of error
  • 3.6.1 Addition/subtraction of random variables
  • 3.6.2 Multiplication/division of random variables
  • 3.6.3 General functional relationship between two random variables
  • 3.7 Linear regression error
  • 3.7.1 Error in model parameters
  • 3.7.2 Error in model predictions
  • 3.8 End of Chapter 3: key points to consider
  • 3.9 Problems
  • References
  • 4 Hypothesis testing
  • 4.1 Introduction
  • 4.2 Formulating a hypothesis
  • T$29.

Similar Items