Advanced Calculus for Mathematical Modeling in Engineering and Physics
With Discrete and Numerical Analogies
- 1st Edition - June 14, 2024
- Imprint: Academic Press
- Author: David Stapleton
- Language: English
- Paperback ISBN:9 7 8 - 0 - 4 4 3 - 2 2 2 8 9 - 4
- eBook ISBN:9 7 8 - 0 - 4 4 3 - 2 2 2 8 8 - 7
Advanced Calculus for Mathematical Modeling in Engineering and Physics: With Discrete and Numerical Analogies introduces the principles and methods of advanced calculus for mathe… Read more
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Request a sales quoteAdvanced Calculus for Mathematical Modeling in Engineering and Physics: With Discrete and Numerical Analogies introduces the principles and methods of advanced calculus for mathematical modeling through a balance of theory and application using a state space approach with elementary functional analysis. This framework facilitates a deeper understanding of the nature of mathematical models, and of the behavior of their solutions. The work provides a variety of advanced calculus models for mathematical, physical science, and engineering audiences, with discussions on how calculus-based models and their discrete analogies are generated. This valuable textbook offers scientific computations driven by Octave/MATLAB script.
- Adopts a state space/functional analysis approach to advanced calculus-based models to provide a better understanding of the development of models and the behaviors of their solutions
- Uniquely includes discrete analogies to calculus-based models, as well as the derivation of many advanced calculus models of physics and engineering– instead of only seeking solutions to the models
- Offers online teaching support for qualified instructors (for selected solutions) and study materials for students (MATLAB/Octave scripts)
Advanced undergraduate and graduate students, taking courses in Advanced Calculus, Professionals / researchers / academics who require an introduction or refresher to the subject, especially with applications in applied math, physics, computer science, engineering, chemistry, and biology
- Cover image
- Title page
- Table of Contents
- Copyright
- About the author
- Preface
- Acknowledgments
- Chapter 1. Calculus models in state spaces
- 1.1. Abstract vector spaces
- 1.2. Basic models of science and engineering as state-space models
- 1.3. Metric, norm, and inner product
- 1.4. ∗Calculus and trigonometry in a Banach space (optional)
- 1.5. Vector calculus with an introduction to Hilbert Spaces
- 1.6. Homogeneous linear models
- 1.7. Nonhomogeneous linear models
- 1.8. ∗∗Quantitative error analysis and numerical methods for linear models (optional)
- 1.9. Problems 1
- Chapter 2. Ordinary differential equations and recurrence relations
- 2.1. Classical solutions to initial value problems
- 2.2. Series solution methods
- 2.3. Transform methods
- 2.4. Approximation of solutions to differential equations
- Chapter 3. Systems of differential equations and discrete analogies
- 3.1. Linear and nonlinear systems of DEs
- 3.2. Homogeneous linear systems
- 3.3. Nonhomogeneous linear systems
- 3.4. Qualitative analysis of autonomous nonlinear systems of DEs
- 3.5. Approximation of solutions
- Chapter 4. Integration for advanced calculus models
- 4.1. Integration in real Euclidean space
- 4.2. Functions and constants defined as integrals
- 4.3. Integral transforms and the discrete fourier transform analogy
- 4.4. Models through functional considerations
- 4.5∗. Continuous probability theory (optional)
- Chapter 5. Partial differential equations and applications
- 5.1. Boundary value problems
- 5.2. Solution by the method of characteristics
- Chapter 6. Calculus of variations
- 6.1. Simplest problem and applications
- 6.2. Problems in more variables
- Chapter 7. Calculus with complex numbers
- 7.1. Complex limit and derivative
- 7.2. Analytic continuation of familiar functions
- 7.3. Mapping with complex functions
- 7.4. Complex integration
- 7.5. Sequences and series
- 7.6. Power series and Laurent series
- 7.7. Residue theorem, contour integration, and improper integrals
- 7.8. Inverse Laplace transforms
- 7.9. Problems 7
- Chapter 8. Introduction to tensors
- 8.1. Cartesian tensors
- 8.2. Dual spaces
- 8.3. Tensors
- 8.4. Tensor fields on real manifolds
- 8.5. Tensor algebra
- 8.6. Covariant differentiation
- 8.7. Differential forms and integration
- 8.8. Problems 8
- Appendices
- Index
- Edition: 1
- Published: June 14, 2024
- Imprint: Academic Press
- No. of pages: 880
- Language: English
- Paperback ISBN: 9780443222894
- eBook ISBN: 9780443222887
DS
David Stapleton
David Stapleton received his BS from the University of California, Santa Barbara and MS from the University of California, San Diego, before earning his PhD from University of Arizona in 1990. Now a Professor at University of Central Oklahoma, Dr. Stapleton has taught courses in advanced calculus for applications, mathematical modeling, calculus of variations, tensors, numerical linear algebra, and other mathematical topics and has served three times as the Director of the Conference on Applied Mathematics. He has published articles in various journals and proceedings of the AIAA, SIAM, IEEE/ION PLANS, Navigation, Foundations of Physics, Physics Communications, AJCM, STAIF, FAA, ICAO, and more. He has also worked as a contractor to the FAA at the FAA Technical Center and Mike Monroney Aeronautical Center and also has experience as a contractor to the USAF at Cape Canaveral, Vandenberg AFB (now Vandenberg SFB), and Edwards AFB.
Affiliations and expertise
Professor, Department of Mathematics & Statistics University of Central Oklahoma Edmond, Oklahoma, USARead Advanced Calculus for Mathematical Modeling in Engineering and Physics on ScienceDirect