Math 46:Introduction to Applied Mathematics

Math 136: Applied Mathematics II

Spring 2019

Instructor: Dorothy Wallace

Office: 204 Kemeny Hall

Email: Dorothy.Wallace@dartmouth.edu

Phone: 603-646-3610

Class Room: tba

Class Times: Tuesday and Thursday 2:25-4:15 PM

Office Hours: Tuesday and Thursday 4:30 PM - 5:20 PM, Wednesday 4:30-5:30 [or by appointment].

X-hours: Wednesday 4:30 PM — 5:30 PM [Will be used intermittently at instructor's discretion for review of course material etc. Do not schedule anything regular in this X-hr. ].

Course Description

This course introduces a wide variety of mathematical tools and methods to analyze phenomena in the physical, life and social sciences. The focus of this course will be on analytical tools (the ones involving the use of pen and paper) rather than the computational tools (the ones involving the use of computers). However, students are encouraged to learn numerical skills with packages from programming languages like Python or Matlab or C++ (or whatever else a particular student prefers) and use them in their projects. Students enrolled in the graduate version of this course, Math 136, will be given more sophisticated assignments and problems to solve.

Prerequisite

MATH 22 and MATH23, or permission of the instructor..

Textbook

Title: Applied Mathematics

Edition: Fourth

Author: J. David Logan

Publisher: John Wiley & Sons

Tentative Syllabus

Ordinary Differential Equations: Review of linear systems and applications. Dynamical Systems. Intro to perturbation theory. Intro to mathematical control theory. Taylor series approximations. Partial Differential Equations: Heat, diffusion, and reaction diffusion equations. Eigenvalues and Fourier series solutions. Wave equation, vibrating string, vibrating drumhead. The “Laplacian” and introduction to the spectral theorem. The hyperbolic Laplacian. Schrodinger’s equation for the hydrogen atom and its solution.

*Note: This syllabus is only suggestive, and few topics may be removed depending on the availability of time during the course.

Grades

Midterm: It will be 1.5hrs long IN CLASS on April 30..

Homework: Will be graded collaboratively in class, fixed, and turned in when perfect. Marked done or not done.

Class Participation: Will be based on attendance and in-class activities. Attendance may be taken randomly at instructor's discretion.

Project: For grading of the project, those in Math 46 will create a poster to be shown at the Math undergraduate poster session. Those in Math 136 will write a research paper.

Exam and Project Schedule

1. Midterm

Date: April 30, 2019

Time: 5-7PM

Location: IN CLASS

2. Project proposal deadline: May 14, 2019.

3. Project submission deadline: May 28, 2019 (LAST DAY OF CLASS)

Special Needs

Students with a diagnosed learning disability are encouraged to discuss with the instructor any appropriate accommodations that might be helpful. All discussions will remain confidential, although the Student Accessibility Services office may be consulted.

Honor Principle

You are encouraged to work together on homework. However, the final write-up should be your own. On exams, all work should be entirely your own; no consultation of other persons, printed works, or online sources is allowed without the instructor's explicit permission. On the final project, your signature indicates that all coauthors contributed substantially to the research and writing and that the work is your own.

Religious observance: Some students may wish to take part in religious observances that occur during this academic term. If you have a religious observance that conflicts with your participation in the course, please meet with me before the end of the second week of the term to discuss appropriate accommodations.