Mathematical Models In The Applied Sciences Fowler Pdf

Math 577: Mathematical Modeling (Spring 2022)

"You cannot understand the physical world in any deep or satisfying way without using mathematical reasoning." -- R. P. Feynman This course will present an introduction and survey of mathematical models for problems in the applied sciences and engineering. The real-world problems, coming from areas like mechanical systems, control theory, bio-chemical reactions, and heat transfer will be formulated as idealized mathematical models. Equations will be derived from first principles in geometry, physics and the calculus of variations. Mathematical techniques such as nondimensionalization, perturbation analysis, and self-similar solutions will then be introduced to simplify the models and yield insight into the underlying problems.

Prerequisites

Some background in solving ordinary and partial differential equations [Math 353 or Math 356] and basic physics/mechanics, multivariable calculus [Math 212].

Math 577-01 (4838) Mathematical Modeling

Lectures Wed/Fri 1:45-3:00pm, Room 235 Physics Bldg

First class meeting: ???, Jan ??, 2022 see Academic Calendar
?????? : No lecture (Spring break)
Lectures end: ???, Apr ??, 2022

Instructor

Thomas Witelski, Professor, Dept of Math
Office: Room 295 Physics Building

Office hours

Zoom meetings, Times to be announced, or by email request for an appointment for other times.

Textbook

Applied Mathematics by J. D. Logan, Wiley-Interscience [Amazon]

Problem sets

Course materials and web links

Course outline/syllabus (Old version: Spring 2021)
Lecture notes and Review sheets
- See the resources folders on Sakai Math.577.01.Sp22
Computer access: Duke OIT VPN or locally at any *.duke.edu computer
Software from Duke OIT: Maple, Mathematica/Wolfram AlphaPro

Reference books

Introduction to the Foundations of Applied Mathematics by Mark H. Holmes, Springer-Verlag
Mathematics Applied to Deterministic Problems in the Natural Sciences by C.C. Lin and L.A Segel, SIAM Press [Google books]
Practical Applied Mathematics:Modelling, Analysis, Approximation by S. Howison, Cambridge University Press
Mathematical Models in the Applied Sciences by A. C. Fowler, Cambridge University Press
Mathematical Physiology by J. Keener and J. Sneyd, Springer Verlag: See chapter 1