MTH 201: Elementary Differential Equation I

Course Description

MATH 201: Elementary Differential Equation I Unijos Lecture note pdf introduces students to the basic principles and methods of solving ordinary differential equations (ODEs). The course emphasizes analytical techniques, mathematical modeling, and applications in science and engineering. Students gain a foundation in formulating and solving first- and second-order differential equations relevant to real-world problems.

Course Structure

First-Order Differential Equations

• Separable, linear, and exact equations

• Applications: population growth, cooling laws, and mixing problems

• Integrating factors and substitution methods

Higher-Order Differential Equations

• Homogeneous and non-homogeneous linear equations

• Solutions with constant coefficients

• Method of undetermined coefficients and variation of parameters

Systems of Differential Equations

• Introduction to systems of first-order linear equations

• Matrix methods and eigenvalue problems (introductory concepts)

Laplace Transform

• Definition and basic properties

• Inverse Laplace transform

• Solving initial value problems using Laplace methods

Applications and Modeling

• Mechanical vibrations

• Electrical circuits

• Motion under resistance

Learning Outcomes

By the end of the course, students should be able to:

• Solve different types of first- and second-order differential equations

• Apply appropriate solution methods to physical and engineering problems

• Use Laplace transforms to solve initial value problems

• Analyze simple systems modeled by differential equations

• Interpret the results of mathematical models in real-life contexts

Assessment Methods

• Exams and Quizzes: Evaluate problem-solving accuracy and conceptual understanding

• Homework Assignments: Reinforce weekly lessons and practice key techniques

• Projects/Case Studies: Apply theory to model and solve practical problems

• Class Participation: Engagement during tutorials and problem-solving sessions

This course lays a crucial foundation for advanced mathematics and engineering courses, equipping students with the skills to analyze and solve real-world dynamic systems using differential equations.