Math 5710  Introduction to Applied Mathematics
M W F   11:50 am - 12:40 pm    LCB 121
  
                                   Mathematics is the Queen that rules the Universe   

 Text: Gilbert Strang, Introduction to Applied Mathematics, 1986

 Instructor:   Professor Elena Cherkaev
   Office:   LCB 206        ph: 801-581-7315  
   Email:   elena@math.utah.edu
   Office hours on zoom: M  1:30 - 2:30 pm and by appointment

When you are sending me an email please include '5710'  in the subject line

Class webpage:  http://www.math.utah.edu/~elena/M5710/5710.html

Students are requested to wear masks during in-person lectures.
Course description: The course gives an overview of methods, problems, and models of applied mathematics, emphasizing parallels between continuous and discrete approaches. We will see how differential equations and matrix equations reinforce each other and go in parallel. "To see the cooperation between calculus and linear algebra is to see one of the best parts of modern applied mathematics." /from the Preface of the textbook/   

Optimality and duality is a focus of the course (and another best part of modern applied mathematics), which expresses itself as a fundamental principle of energy minimization (or stationarity of the energy). This principle governs all the processes in the world, and we will see mathematical justification of that through the same mathematical framework held for all the problems and topics discussed in the course. Particular covered topics include optimization and duality, partial differential equations (potential flows, electricity and magnetism, equilibrium of fluids and solids, heat equation and wave equation),  ordinary differential equations (stability, chaos and fractals, nonlinear conservation laws), networks (electric, mechanic, social, internet) and transportation problem. 

About the textbook: Renowned mathematician Gilbert Strang teaches applied mathematics with the clear explanations, examples and insights of an experienced teacher. This book progresses steadily through a range of topics from symmetric linear systems to differential equations to least squares and optimization. It clearly demonstrates the power of matrix algebra in engineering problem solving. This is an ideal book (beloved by many readers) for a first course on applied mathematics and a reference for more advanced applied mathematicians.  /Google books/
Table of Contents:   http://www-math.mit.edu/~gs/books/itam_toc.html

Prerequisites:  Calculus, Linear Algebra, and Differential Equations.

Course objectives and expected learning outcomes:
The course gives an overview of ideas, models, and methods in the Applied Mathematics with focus on uniform framework and parallels between continuous and discrete approaches.

Upon successful completion of the course, a student should be able to: 
-  Understand, utilize, and manipulate basic concepts of optimality in discrete and continuous problems
-  To be able to solve optimization problems with constraints and Lagrange multipliers
-  Have a basic understanding of equilibrium in mechanical systems, fluids, and solids
-  Learn characteristics and properties of electrical networks
- To be able to solve least squares estimation problems
-  Distinguish different kinds of vector fields, such as gradients and curls
-  Have a knowledge of differential equations of equilibrium

Exams:  There will be one midterm, an optional project, and final exam.
Final test:  Tuesday, December 14, 2021
10:30 am – 12:30 pm

Exams policy: Exams will be closed book except that you may bring a "cheat sheet," an 8.5" x 11" piece of paper with notes on both sides. Your text, notes, homework papers, calculators, laptops, tablets, phones, text messaging devices, and books will not be allowed.

Optional Project/Independent study:  The research project based on the material covered in the course. 

Grading: The grade will be based on the homework (30%) and the exams (70%).
With optional project: on the homework (30%), the exams (60%), and project (10%).

Plagiarism: Plagiarism is unacceptable and results in  F  grade.

Last day to add, drop (delete) classes:    Friday, September 3

Holidays:   Labor Day holiday:     Monday, September 6  
                   Thanksgiving break:   Thurs.-Sun., Nov. November 25-28
Fall break:     October 10‐17
Classes end:  Thursday, December 9

Health Guidance Message:
University leadership has urged all faculty, students, and staff to model the vaccination, testing, and masking behaviors we want to see in our campus community.
These include:
Vaccination
Masking indoors
If unvaccinated, getting weekly asymptomatic coronavirus testing
https://attheu.utah.edu/feature/we-need-your-help-to-stop-the-spread/

ADA: The "American with Disabilities Act" requires that reasonable accommodations be made for students with physical, sensory, cognitive, systemic, learning and psychiatric disabilities. Please contact me at the beginning of the semester to discuss any such accommodation for the course.