Paul E. Fishback is a professor in the Department of Mathematics at Grand Valley State University in Allendale, Michigan, USA.
Helps Students Understand Mathematical Programming Principles and Solve Real-World Applications
Supplies enough mathematical rigor yet accessible enough for undergraduatesIntegrating a hands-on learning approach, a strong linear algebra focus, Maple™ software, and real-world applications, Linear and Nonlinear Programming with Maple™: An Interactive, Applications-Based Approach introduces undergraduate students to the mathematical concepts and principles underlying linear and nonlinear programming. This text fills the gap between management science books lacking mathematical detail and rigor and graduate-level books on mathematical programming.
Essential linear algebra tools
Throughout the text, topics from a first linear algebra course, such as the invertible matrix theorem, linear independence, transpose properties, and eigenvalues, play a prominent role in the discussion. The book emphasizes partitioned matrices and uses them to describe the simplex algorithm in terms of matrix multiplication. This perspective leads to streamlined approaches for constructing the revised simplex method, developing duality theory, and approaching the process of sensitivity analysis. The book also discusses some intermediate linear algebra topics, including the spectral theorem and matrix norms.
Maple enhances conceptual understanding and helps tackle problems
Assuming no prior experience with Maple, the author provides a sufficient amount of instruction for students unfamiliar with the software. He also includes a summary of Maple commands as well as Maple worksheets in the text and online. By using Maple´s symbolic computing components, numeric capabilities, graphical versatility, and intuitive programming structures, students will acquire a deep conceptual understanding of major mathematical programming principles, along with the ability to solve moderately sized rea
LINEAR PROGRAMMING: An Introduction to Linear Programming. The Simplex Algorithm. Standard Applications of Linear Programming. Duality and Sensitivity Analysis. Integer Linear Programming. NONLINEAR PROGRAMMING: Algebraic Methods for Unconstrained Problems. Numeric Tools for Unconstrained Nonlinear Problems. Methods for Constrained Nonlinear Problems. Appendices. Bibliography. Index.
Integrating a hands-on learning approach, a strong linear algebra focus, Maple™ software, and real-world applications, this text introduces the mathematical concepts and principles underlying linear and nonlinear programming. It draws on the simplex method to develop the major ideas of duality and sensitivity analysis and provides applications and exercises from zoology, chemistry, and game theory to illustrate how linear and nonlinear programming are invaluable problem solving tools. The text solves problems using Maple and includes explicit Maple instructions, important commands, and sample worksheets. Maple worksheets and code are available on the book´s website.
Integrating a learning approach, a linear algebra focus, Maplea software, and real-world applications, this text introduces the mathematical concepts and principles underlying linear and nonlinear programming. It solves problems using Maple and includes explicit Maple instructions, important commands, and sample worksheets.
Über den Autor
Paul E. Fishback is a professor in the Department of Mathematics at Grand Valley State University in Allendale, Michigan, USA.
Klappentext
Using Maple(TM) throughout, this innovative text is based on the multiplication of partitioned matrices as opposed to the older, more traditional approach that becomes bogged down with summation formulas as special cases. Endorsed by the Linear Algebra Curriculum Study Group, the multiplication of partitioned matrices is considered an important idea in a first course on linear algebra. Each chapter contains pedagogical devices where readers can check their understanding of the material by performing basic computations or responding to short answer questions. The book also presents various activities for group assignments and in-class assessments of applications, such as game theory, breast cancer diagnosis, and waste management.
