Advanced 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.
Key Features
- 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)
2. Ordinary Differential Equations and Recurrence Relations
3. Systems Of Differential Equations and Discrete Analogies
4. Integration For Advanced Calculus Models
5. Partial Differential Equations and Applications
6. Calculus Of Variations
7. Calculus With Complex Numbers
8. Introduction to Tensors
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
