Helps Students Understand Mathematical Programming Principles and Solve Real-World Applications
Supplies enough mathematical rigor yet accessible enough for undergraduates
Integrating a hands-on learning approach, a strong linear algebra focus, Maple (TM) software, and real-world applications, Linear and Nonlinear Programming with Maple (TM): 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 real-world applications.
Hands-on activities that engage students
Throughout the book, student understanding is evaluated through "waypoints" that involve basic computations or short questions. Some problems require paper-and-pencil calculations; others involve more lengthy calculations better suited for performing with Maple. Many sections contain exercises that are conceptual in nature and/or involve writing proofs. In addition, six substantial projects in one of the appendices enable students to solve challenging real-world problems.
Paul E. Fishback is a professor in the Department of Mathematics at Grand Valley State University in Allendale, Michigan, USA.
LINEAR PROGRAMMING An Introduction to Linear Programming The Basic Linear Programming Problem Formulation Linear Programming: A Graphical Perspective in R2 Basic Feasible Solutions The Simplex Algorithm The Simplex Algorithm Alternative Optimal/Unbounded Solutions and Degeneracy Excess and Artificial Variables: The Big M Method A Partitioned Matrix View of the Simplex Method The Revised Simplex Algorithm Moving beyond the Simplex Method: An Interior Point Algorithm Standard Applications of Linear Programming The Diet Problem Transportation and Transshipment Problems Basic Network Models Duality and Sensitivity Analysis Duality Sensitivity Analysis The Dual Simplex Method Integer Linear Programming An Introduction to Integer Linear Programming and the Branch and Bound Method The Cutting Plane Algorithm NONLINEAR PROGRAMMING Algebraic Methods for Unconstrained Problems Nonlinear Programming: An Overview Differentiability and a Necessary First-Order Condition Convexity and a Sufficient First-Order Condition Sufficient Conditions for Local and Global Optimal Solutions Numeric Tools for Unconstrained Nonlinear Problems The Steepest Descent Method Newton's Method The Levenberg-Marquardt Algorithm Methods for Constrained Nonlinear Problems The Lagrangian Function and Lagrange Multipliers Convex Nonlinear Problems Saddle Point Criteria Quadratic Programming Sequential Quadratic Programming Appendix A: Projects Appendix B: Important Results from Linear Algebra Appendix C: Getting Started with Maple Appendix D: Summary of Maple Commands Bibliography Index Exercises appear at the end each section.