What you will learn in Differential Equations for Engineers Course
Solve separable and linear first-order differential equations and apply them to real-world problems.
Analyze homogeneous and inhomogeneous second-order differential equations, including resonance phenomena.
Utilize the Laplace transform and series methods to solve linear ordinary differential equations.
Model and solve systems of linear differential equations using matrix methods.
Understand the basics of partial differential equations and their applications.
Program Overview
First-Order Differential Equations
⏳ 4 hours
- Introduction to differential equations, classification, Euler method, and analytical solutions for separable and linear first-order equations.
- Applications include compound interest, terminal velocity, and RC circuits.
Homogeneous Linear Differential Equations
⏳ 4 hours
- Second-order linear differential equations with constant coefficients, superposition principle, Wronskian, and characteristic equations.
Inhomogeneous Linear Differential Equations
⏳ 4 hours
- Solving non-homogeneous equations using undetermined coefficients and variation of parameters. Applications include RLC circuits, mass-spring systems, and pendulums.
The Laplace Transform and Series Solution Methods
⏳ 4 hours
- Introduction to the Laplace transform for solving ODEs with discontinuous or impulsive forcing functions. Series solutions for linear ODEs.
Systems of Differential Equations
⏳ 4 hours
- Solving coupled systems of first-order linear differential equations using matrix methods and eigenvalue problems. Applications include coupled harmonic oscillators.
Partial Differential Equations
⏳ 4 hours
- Introduction to partial differential equations, classification, and basic solution techniques.
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Job Outlook
Enhances mathematical proficiency for careers in engineering, data science, and computational modeling.
Provides a solid foundation for advanced studies in mathematical theory and analysis.
Completing this course can bolster qualifications for roles requiring strong analytical and problem-solving skills.
Specification: Differential Equations for Engineers
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