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E-raamat: Numerical and Statistical Methods for Bioengineering: Applications in MATLAB

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(Cornell University, New York), (Cornell University, New York)
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"Cambridge Texts in Biomedical Engineering provides a forum for high-quality accessible textbooks targeted at undergraduate and graduate courses in biomedical engineering. It will cover a broad range of biomedical engineering topics from introductory texts to advanced topics including, but not limited to, biomechanics, physiology, biomedical instrumentation, imaging, signals and systems, cell engineering, and bioinformatics. The series will blend theory and practice, aimed primarily at biomedical engineering students but will be suitable for broader courses in engineering, the life sciences and medicine"--

"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 modelling concepts, nonlinear root finding, and numerical integration, chapters on hypothesis testing, data regression and probability are interweaved. A unique feature of the book is the inclusion of examples from clinical trials and bioinformatics, which are not found in other numerical methods textbooks for engineers. With a wealth of biomedical engineering examples, case studies on topical biomedical research, and the inclusion of end of chapter problems, this is a perfect core text for a one-semester undergraduate course"--

Provided by publisher.

Arvustused

'I think this book is a winner [ it] is really easy to read and places frameworks for numerical analysis into realistic bioengineering concepts that students will find familiar and relevant. This is most evident in the excellent boxed examples, but also in many of the homework problems. I also really liked the 'key points to consider' at the end of the chapters - these are useful reminders for the students. Finally, the book presents bioinformatics in a manageable fashion that should help demystify this subject for interested students.' K. Jane Grande-Allen, Rice University

Muu info

The first MATLAB-based numerical methods textbook specifically for bioengineers, including topics on hypothesis testing and examples exclusively from bioengineering applications.
Preface ix
1 Types and sources of numerical error
1(46)
1.1 Introduction
1(3)
1.2 Representation of floating-point numbers
4(12)
1.2.1 How computers store numbers
7(1)
1.2.2 Binary to decimal system
7(2)
1.2.3 Decimal to binary system
9(1)
1.2.4 Binary representation of floating-point numbers
10(6)
1.3 Methods used to measure error
16(2)
1.4 Significant digits
18(2)
1.5 Round-off errors generated by floating-point operations
20(6)
1.6 Taylor series and truncation error
26(13)
1.6.1 Order of magnitude estimation of truncation error
28(4)
1.6.2 Convergence of a series
32(1)
1.6.3 Finite difference formulas for numerical differentiation
33(6)
1.7 Criteria for convergence
39(1)
1.8 End of
Chapter 1: key points to consider
40(1)
1.9 Problems
40(6)
References
46(1)
2 Systems of linear equations
47(94)
2.1 Introduction
47(6)
2.2 Fundamentals of linear algebra
53(22)
2.2.1 Vectors and matrices
53(3)
2.2.2 Matrix operations
56(8)
2.2.3 Vector and matrix norms
64(2)
2.2.4 Linear combinations of vectors
66(3)
2.2.5 Vector spaces and basis vectors
69(2)
2.2.6 Rank, determinant, and inverse of matrices
71(4)
2.3 Matrix representation of a system of linear equations
75(1)
2.4 Gaussian elimination with backward substitution
76(11)
2.4.1 Gaussian elimination without pivoting
76(8)
2.4.2 Gaussian elimination with pivoting
84(3)
2.5 LU factorization
87(9)
2.5.1 LU factorization without pivoting
88(5)
2.5.2 LU factorization with pivoting
93(2)
2.5.3 The MATLAB lu function
95(1)
2.6 The MATLAB backslash (\) operator
96(1)
2.7 III-conditioned problems and the condition number
97(4)
2.8 Linear regression
101(6)
2.9 Curve fitting using linear least-squares approximation
107(11)
2.9.1 The normal equations
109(6)
2.9.2 Coefficient of determination and quality of fit
115(3)
2.10 Linear least-squares approximation of transformed equations
118(5)
2.11 Multivariable linear least-squares regression
123(1)
2.12 The MATLAB function polyfit
124(1)
2.13 End of
Chapter 2: key points to consider
125(2)
2.14 Problems
127(12)
References
139(2)
3 Probability and statistics
141(68)
3.1 Introduction
141(3)
3.2 Characterizing a population: descriptive statistics
144(3)
3.2.1 Measures of central tendency
145(1)
3.2.2 Measures of dispersion
146(1)
3.3 Concepts from probability
147(10)
3.3.1 Random sampling and probability
149(5)
3.3.2 Combinatorics: permutations and combinations
154(3)
3.4 Discrete probability distributions
157(9)
3.4.1 Binomial distribution
159(4)
3.4.2 Poisson distribution
163(3)
3.5 Normal distribution
166(20)
3.5.1 Continuous probability distributions
167(2)
3.5.2 Normal probability density
169(2)
3.5.3 Expectations of sample-derived statistics
171(4)
3.5.4 Standard normal distribution and the z statistic
175(2)
3.5.5 Confidence intervals using the z statistic and the t statistic
177(6)
3.5.6 Non-normal samples and the central-limit theorem
183(3)
3.6 Propagation of error
186(5)
3.6.1 Addition/subtraction of random variables
187(1)
3.6.2 Multiplication/division of random variables
188(2)
3.6.3 General functional relationship between two random variables
190(1)
3.7 Linear regression error
191(8)
3.7.1 Error in model parameters
193(3)
3.7.2 Error in model predictions
196(3)
3.8 End of
Chapter 3: key points to consider
199(3)
3.9 Problems
202(6)
References
208(1)
4 Hypothesis testing
209(101)
4.1 Introduction
209(1)
4.2 Formulating a hypothesis
210(9)
4.2.1 Designing a scientific study
211(6)
4.2.2 Null and alternate hypotheses
217(102)
4.3 Testing a hypothesis
219(12)
4.3.1 The p value and assessing statistical significance
220(6)
4.3.2 Type I and type II errors
226(2)
4.3.3 Types of variables
228(2)
4.3.4 Choosing a hypothesis test
230(1)
4.4 Parametric tests and assessing normality
231(4)
4.5 The z test
235(9)
4.5.1 One-sample z test
235(6)
4.5.2 Two-sample z test
241(3)
4.6 The t test
244(7)
4.6.1 One-sample and paired sample t tests
244(5)
4.6.2 Independent two-sample t test
249(2)
4.7 Hypothesis testing for population proportions
251(9)
4.7.1 Hypothesis testing for a single population proportion
256(1)
4.7.2 Hypothesis testing for two population proportions
257(3)
4.8 One-way ANOVA
260(14)
4.9 Chi-square tests for nominal scale data
274(14)
4.9.1 Goodness-of-fit test
276(5)
4.9.2 Test of independence
281(4)
4.9.3 Test of homogeneity
285(3)
4.10 More on non-parametric (distribution-free) tests
288(11)
4.10.1 Sign test
289(3)
4.10.2 Wilcoxon signed-rank test
292(4)
4.10.3 Wilcoxon rank-sum test
296(3)
4.11 End of
Chapter 4: key points to consider
299(1)
4.12 Problems
299(9)
References
308(2)
5 Root-finding techniques for nonlinear equations
310(44)
5.1 Introduction
310(2)
5.2 Bisection method
312(7)
5.3 Regula-falsi method
319(1)
5.4 Fixed-point iteration
320(7)
5.5 Newton's method
327(9)
5.5.1 Convergence issues
329(7)
5.6 Secant method
336(2)
5.7 Solving systems of nonlinear equations
338(8)
5.8 MATLAB function fzero
346(2)
5.9 End of
Chapter 5: key points to consider
348(1)
5.10 Problems
349(4)
References
353(1)
6 Numerical quadrature
354(55)
6.1 Introduction
354(7)
6.2 Polynomial interpolation
361(10)
6.3 Newton---Cotes formulas
371(16)
6.3.1 Trapezoidal rule
372(8)
6.3.2 Simpson's 1/3 rule
380(4)
6.3.3 Simpson's 3/8 rule
384(3)
6.4 Richardson's extrapolation and Romberg integration
387(4)
6.5 Gaussian quadrature
391(11)
6.6 End of
Chapter 6: key points to consider
402(1)
6.7 Problems
403(5)
References
408(1)
7 Numerical integration of ordinary differential equations
409(71)
7.1 Introduction
409(1)
7.2 Euler's methods
409(22)
7.2.1 Euler's forward method
416(1)
7.2.2 Euler's backward method
417(11)
7.2.3 Modified Euler's method
428(3)
7.3 Runge-Kutta (RK) methods
431(9)
7.3.1 Second-order RK methods
434(4)
7.3.2 Fourth-order RK methods
438(2)
7.4 Adaptive step size methods
440(11)
7.5 Multistep ODE solvers
451(5)
7.5.1 Adams methods
452(2)
7.5.2 Predictor-corrector methods
454(2)
7.6 Stability and stiff equations
456(5)
7.7 Shooting method for boundary-value problems
461(11)
7.7.1 Linear ODEs
463(1)
7.7.2 Nonlinear ODEs
464(8)
7.8 End of
Chapter 7: key points to consider
472(1)
7.9 Problems
473(5)
References
478(2)
8 Nonlinear model regression and optimization
480(59)
8.1 Introduction
480(7)
8.2 Unconstrained single-variable optimization
487(13)
8.2.1 Newton's method
488(4)
8.2.2 Successive parabolic interpolation
492(3)
8.2.3 Golden section search method
495(5)
8.3 Unconstrained multivariable optimization
500(23)
8.3.1 Steepest descent or gradient method
502(7)
8.3.2 Multidimensional Newton's method
509(4)
8.3.3 Simplex method
513(10)
8.4 Constrained nonlinear optimization
523(7)
8.5 Nonlinear error analysis
530(3)
8.6 End of
Chapter 8: key points to consider
533(1)
8.7 Problems
534(4)
References
538(1)
9 Basic algorithms of bioinformatics
539(21)
9.1 Introduction
539(1)
9.2 Sequence alignment and database searches
540(14)
9.3 Phylogenetic trees using distance-based methods
554(3)
9.4 End of
Chapter 9: key points to consider
557(1)
9.5 Problems
558(1)
References
558(2)
Appendix A Introduction to MATLAB 560(16)
Appendix B Location of nodes for Gauss-Legendre quadrature 576(2)
Index for MATLAB commands 578(1)
Index 579
Michael R. King is an Associate Professor of Biomedical Engineering at Cornell University. He is an expert on the receptor-mediated adhesion of circulating cells, and has developed new computational and in vitro models to study the function of leukocytes, platelets, stem and cancer cells under flow. He has co-authored two books and received numerous awards, including the 2008 ICNMM Outstanding Researcher Award from the American Society of Mechanical Engineers and received the 2009 Outstanding Contribution for a Publication in the international journal Clinical Chemistry. Nipa A. Mody is currently a postdoctoral research associate at Cornell University in the Department of Biomedical Engineering. She received her Ph.D. in Chemical Engineering from the University of Rochester in 2008 and has received a number of awards including a Ruth L. Kirschstein National Research Service Award (NRSA) from the NIH in 2005 and the Edward Peck Curtis Award for Excellence in Teaching from the University of Rochester in 2004.
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