A Course in Differential Equations with Boundary Value Problems, 2nd Edition adds additional content to the author's successful A Course on Ordinary Differential Equations, 2nd Edition. This text addresses the need when the course is expanded.
The focus of the text is on applications and methods of solution, both analytical and numerical, with emphasis on methods used in the typical engineering, physics, or mathematics student's field of study. The text provides sufficient problems so that even the pure math major will be sufficiently challenged.
The authors offer a very flexible text to meet a variety of approaches, including a traditional course on the topic. The text can be used in courses when partial differential equations replaces Laplace transforms. There is sufficient linear algebra in the text so that it can be used for a course that combines differential equations and linear algebra.
Most significantly, computer labs are given in MATLAB®, Mathematica®, and Maple(TM). The book may be used for a course to introduce and equip the student with a knowledge of the given software. Sample course outlines are included.
Features
- MATLAB®, Mathematica®, and Maple(TM) are incorporated at the end of each chapter
- All three software packages have parallel code and exercises
- There are numerous problems of varying difficulty for both the applied and pure math major, as well as problems for engineering, physical science and other students.
- An appendix that gives the reader a "crash course" in the three software packages
- Chapter reviews at the end of each chapter to help the students review
- Projects at the end of each chapter that go into detail about certain topics and introduce new topics that the students are now ready to see
- Answers to most of the odd problems in the back of the book
Autorentext
Stephen A. Wirkus is an associate professor of mathematics at Arizona State University, where he has been a recipient of the Professor of the Year Award and NSF AGEP Mentor of the Year Award. He has published over 30 papers and technical reports. He completed his Ph.D. at Cornell University under the direction of Richard Rand.
Randall J. Swift is a professor of mathematics and statistics at California State Polytechnic University, Pomona, where he has been a recipient of the Ralph W. Ames Distinguished Research Award. He has authored more than 80 journal articles, three research monographs, and three textbooks. He completed his Ph.D. at the University of California, Riverside under the direction of M.M. Rao.
Zusammenfassung
Bioreactors: Animal Cell Culture Control for Bioprocess Engineering presents the design, fabrication, and control of a new type of bioreactor meant especially for animal cell line culture. The new bioreactor, called the "e;see-saw bioreactor,"e; is ideal for the growth of cells with a sensitive membrane. The see-saw bioreactor derives its name from its principle of operation in which liquid columns in either limb of the reactor alternately go up and down. The working volume of the reactor is small, to within 15 L. However, it can easily be scaled up for large production in volume of cell mass in the drug and pharmaceutical industries.The authors describe the principle of operation of the see-saw bioreactor and how to automatically control the bioprocess. They discuss different control strategies as well as the thorough experimental research they conducted on this prototype bioreactor in which they applied a time delay control for yield maximization.To give you a complete understanding of the design and development of the see-saw bioreactor, the authors cover the mathematical model they use to describe the kinetics of fermentation, the genetic algorithms used for deriving the optimal time trajectories of the bioprocess variables, and the corresponding control inputs for maximizing the product yield. One chapter is devoted to the application of time delay control. Following a description of the bioreactor's working setup in the laboratory, the authors sum up their investigation and define the future scope of work in terms of design, control, and software sensors.
Inhalt
Traditional First-Order Differential Equations
Introduction to First-Order Equations
Separable Differential Equations
Linear Equations
Some Physical Models Arising as Separable Equations
Exact Equations
Special Integrating Factors and Substitution Methods
Bernoulli Equation
Homogeneous Equations of the Form g(y=x)
Geometrical and Numerical Methods for First-Order Equations
Direction Fields|the Geometry of Differential Equations
Existence and Uniqueness for First-Order Equations
First-Order Autonomous Equations|Geometrical Insight
Graphing Factored Polynomials
Bifurcations of Equilibria
Modeling in Population Biology
Nondimensionalization
Numerical Approximation: Euler and Runge-Kutta Methods
An Introduction to Autonomous Second-Order Equations
Elements of Higher-Order Linear Equations
Introduction to Higher-Order Equations
Operator Notation
Linear Independence and the Wronskian
Reduction of Order|the Case n = 2
Numerical Considerations for nth-Order Equations
Essential Topics from Complex Variables
Homogeneous Equations with Constant Coecients
Mechanical and Electrical Vibrations
Techniques of Nonhomogeneous Higher-Order Linear Equations
Nonhomogeneous Equations
Method of Undetermined Coecients via Superposition
Method of Undetermined Coecients via Annihilation
Exponential Response and Complex Replacement
Variation of Parameters
Cauchy-Euler (Equidimensional) Equation
Forced Vibrations
Fundamentals of Systems of Differential Equations
Useful Terminology
Gaussian Elimination
Vector Spaces and Subspaces
The Nullspace and Column Space
Eigenvalues and Eigenvectors
A General Method, Part I: Solving Systems with Real and Distinct or Complex
Eigenvalues
A General Method, Part II: Solving Systems with Repeated Real Eigenvalues
Matrix Exponentials
Solving Linear Nonhomogeneous Systems of Equations
Geometric Approaches and Applications of Systems of Differential Equations
An Introduction to the Phase Plane
Nonlinear Equations and Phase Plane Analysis
Systems of More Than Two Equations
Bifurcations
Epidemiological Models
Models in Ecology
Laplace Transforms
Introduction
Fundamentals of the Laplace Transform
The Inverse Laplace Transform
Laplace Transform Solution of Linear Differential Equations
Translated Functions, Delta Function, and Periodic Functions
The s-Domain and Poles
Solving Linear Systems Using Laplace Transforms
The Convolution
Series Methods
Power Series Representations of Functions
The Power Series Method
Ordinary and Singular Points
The Method of Frobenius
Bessel Functions
Boundary-Value Problems and Fourier Series
Two-Point Boundary-Value Problems
Orthogonal Functions and Fourier Series
Even, Odd, and Discontinuous Functions
Simple Eigenvalue-Eigenfunction Problems
Sturm-Liouville Theory
Generalized Fourier Series
Partial Differential Equations
Separable Linear Partial Differential Equations
Heat Equation
Wave Equation
Laplace Equation
Non-Homogeneous Boundary Conditions
Non-Cartesian Coordinate Systems
<…