Instructor: Nishant Malik
Office: 310 Kemeny Hall
Email: Nishant.Malik@dartmouth.edu
Phone: 603-646-9020

Class Room: 105 Kemeny Hall
Class Times: Monday, Wednesday and Friday 12:50 -1:55 PM
Office Hours: Tuesday and Thursday 3:00 PM - 4:30 PM [or by appointment].

X-hours: Tuesday 1:20 PM — 2:10 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.

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

Dimensional Analysis, Scaling, Differential Equations and Two-Dimensional Dynamical Systems. Perturbation Methods: Regular perturbation, The Poincare-Lindstedt Method, Asymptotic analysis, Singular perturbation, Boundary layers and uniform approximations, Initial layers, The WKB approximation, Asymptotic expansion of integrals, Boundary value problem. Eigenvalue Problems, Integral Equations, and Green's Functions: Sturm-Liouville problems, Orthogonal functions, Fourier Series, Integral Equations, Volterra Equations, Fredholm equations with Degenerate Kernels, Green’s function, Green’s function via eigenfunctions. Partial Differential Equations: Conservation laws, Several dimensions, Green’s identities, Energy method for uniqueness, Laplace and Poission equation, Separation of variables. Discrete Models: Difference Equations, Stochastic Models, Probability-Based Models.

*Note: This syllabus is only suggestive, and few topics may be removed depending on the availability of time during the course.
*Update (04/11): A list of topics with section numbers from the book that will be covered during spring 2018.

Percentage of total grades
One Midterm exam 25 %
Homework 20%
Class participation 5%
Project 20%
Final Exam 30%

Midterm: It will be 2hrs long.
Final Exam: It will be cumulative and 3hrs long.
Class Participation: Will be based on attendance (25%) and in-class activities (75%). Attendance may be taken randomly at instructor's discretion.
Project: For grading of the project, please see the link to the project (see menu at the top).

Exam and Project Schedule

1. Midterm
Date: May 03, 2018
Time: 5-7PM
Location: Kemeny 307

2. Project submission deadline: May 30, 2018.

3. Final Exam
Date: June 01, 2018
Time: 3:00 - 6:00PM
Location: TBA

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.