MAT 305 :  Elementary Differential Equations.
                                                      MW 5:20pm - 6:40pm, Earth & Space Engineering 181
               

SOLUTIONS TO PRACTICE PROBLEMS FOR FINAL : solutions to practice problems.pdf

THERE WERE A COUPLE OF TYPOS IN THE PRACTICE PROBLEMS,
HERE ARE THE CORRECTIONS :   correction to practice problems.pdf

PRACTICE PROBLEMS FOR FINAL : practice problems for final.pdf
 
 TAKE-HOME MIDTERM 2 AVAILABLE FOR DOWNLOAD:  mat305midterm2.pdf

Instructor : Kingshook Biswas
Office : 3-119 , Math Tower.
Email : kbiswas@math.sunysb.edu

Office hours : MW 4-5  (or email to set up an appointment)

Recitation : Th 5:20pm - 6:15pm, Earth & Space Engineering 181.
TA : Luis Lopez
Office : 2-122 , Math Tower
Email : llopez@math.sunysb.edu

Textbook: Boyce, DiPrima : Elementary Differential Equations and Boundary Value Problems, Wiley, 8th Edition.

About this course
Differential equations are of fundamental importance not only in mathematics, but also in the natural and social sciences. They are equations formulated in terms of rates of change of functional quantities, and possibly the independent variable(s) on which these functions depend. For single variable functions this leads to ordinary differential equations, whereas for functions of several variables one has partial differential equations. We will study different kinds of differential equations and the methods used to solve them.

Syllabus :

First order equations : Chapter 2 , including Section 2.1 (linear equations), Section 2.2 (separable equations),  Section 2.4, Section 2.5, Section 2.6 (exact equations) and Section 2.8 (the existence and uniqueness theorem);

Second order linear equations (both homogeneous and non-homogeneous) : Chapter 3 , sections 3.1 to 3.7;

Power series solutions of second order differential equations  : Chapter 5 , sections 5.1 to 5.7;

And selected topics as time permits from : Systems of first order linear equations (chapters 4 and 7), nonlinear differential equations and stability (chapter 9), and some basic partial differential equations and methods used to solve them including Fourier series (chapter 10).

Prerequisites:
This is an upper division's course. Knowledge of basic calculus (Fundamental Theorem, Separable Differential Equations) is expected, knowledge of material from MAT 203/205 is beneficial, especially for the last part of the course on partial differential equations.

Grading Policy:

Your grade will be determined by your scores on

  • Midterm 1 :      20%
  • Midterm 2 :      20%
  • Final :               35%
  • Recitations :     25%
    • Homework: Homework problems will be assigned weekly each Wednesday, and will be due on the following Wednesday in class. The T.A. will assign a recitation grade at the end of the course based on your graded homework problems and your performance in recitations classes.

    Notes: Notes will be posted when necessary for material covered in class which is not in the textbook.

    NOTES #1 : Differential Operators.

    NOTES #2 : Differential Equations and their groups of symmetry transformations.

    Midterm 1: Wed. March 1st, 5:20pm - 6:40pm.

    Syllabus for Midterm 1 includes :

    1)  First-order linear differential equations : Method of integrating factors, initial-value problems, Existence-Uniqueness Theorem for first-order linear DEs.

    2) Separable Equations : Separation of variables, initial-value problems.

    3) Exact Equations : Necessary condition for exactness, Sufficiency of condition for rectangles, Solution of exact equations, initial-value problems.

    4) Integrating factors for non-exact equations.

    5) Intervals of definition for solutions to first-order DEs (linear, separable and exact), dependence on inital-condition.

    6) Existence-Uniqueness Theorem for general first-order DEs. Method of Successive Approximations.

    PRACTICE MIDTERM #1

    Final: Wed. May 10th, 5:00 - 7:30pm.

     Homework #1 (Assigned Jan30, Due Feb 6) 

    Homework #2 (Assigned Feb 7, due Feb 15)

    Homework #3 (Assigned Feb 16, due Feb 22)

    Homework #4 (Assigned Feb 21, due Mar 1)

    Homework #5 (Assigned Mar 21, due Mar 29)