Differential Equations

Course Overview

This is a typical introductory course in differential equations. It lays its foundations in the general theory of ODEs, provides a survey of methods and techniques, and discusses some of the applications of differential equations. The course will be divided mainly in three parts:

• Theoretical solutions to differential equations: Become familiar with the operations and techniques used for solving exactly differential equations ranging from first order, second order, higher order, homogeneous and non-homogeneous.

• Numerical solutions to differential equations: Understand in which cases one cannot expect to have an exact formula for the solution and how to approximate the solution at any point of interest with the aid of a calculator (computer).

• Applications of Differential Equations: Understand how to set up different problems involving differential equations and discover how do some natural and physical phenomena can be studied and how we can predict future outcomes with just the information we know today.

By the end of the semester, students will:

• Understand what is a differential equation and what does it mean to solve it.
• The student should be able to use numerical, graphical, analytic techniques to analyze and/or solve differential equations.
• The student should be able to demonstrate how differential equations arise from physical models.
• The student should be able to use differential equations to model physical phenomena.

Prerequisites

• MTH 142

Textbooks

• Open Source Textbook provided in Brightspace.

Grading

• Midterm Exam 1: 15%
• Midterm Exam 2: 15%
• Quizzes: 15%
• Homework: 30%
• Cumulative Final Exam: 25%