Differential Equations

This course is designed to provide all engineering students with a solid mathematical foundation in differential equations, serving as essential preparation for more advanced, discipline-specific courses in engineering and applied sciences. The rationale lies in equipping students with the analytical tools necessary to model, analyze, and solve a wide range of dynamic systems encountered in engineering practice. The course focuses on the formulation and solution of first-order differential equations, higher-order linear differential equations, and systems of first-order linear equations. In addition, it introduces the Laplace Transform as a powerful method for solving initial value problems and analyzing linear systems. Emphasis is placed on understanding the structure and classification of differential equations, evaluating conditions for the existence and uniqueness of solutions, and applying appropriate analytical techniques to obtain and interpret solutions. By the end of the course, students will be able to identify different types of differential equations, select and implement suitable solution strategies, and apply their knowledge to model and solve real-world problems in engineering and science. This foundational course enhances students’ mathematical maturity and problem-solving skills, preparing them for future coursework and professional practice.

• Formulate differential equations, classify them based on their properties, and analyze conceptual problems in differential equations.

• Apply appropriate methods to solve both first-order and higher-order differential equations.

• Apply differential equations to model and solve real-world problems

• Apply Laplace transforms and inverse Laplace transforms to solve differential equations.

1. Lecture 1: Introduction to Differential Equations

2. Lecture 2: Formation of Differential Equations

3. Lecture 3: Separation of Variables

4. Lecture 4: Homogeneous Differential Equations

5. Lecture 5: Exact Differential Equations

6. Lecture 6: Integrating Factors 

7. Lecture 7: First-order Linear Differential Equations

8. Lecture 8: Bernoulli Differential Equations

9. Lecture 9: Applications of First-Order Differential Equations

10. Lecture 10: Homogenous Higher-Ordered Linear Differential Equations with Constant Coefficients

11. Lecture 11: Non-homogenous Higher-Ordered Linear Differential Equations with Constant Coefficients

12. Lecture 12: Laplace Transforms

1. Problem Set 1: Formation of Differential Equations

2. Problem Set 2: Separation of Variables and Homogenous Differential Equations

3. Problem Set 3: Exact and Non-exact Differential Equations

4. Problem Set 4: First-order Linear Differential Equations

5. Problem Set 5: Applications of First-order Linear Differential Equations

6. Problem Set 6: Homogenous Higher-Ordered Linear Differential Equations with Constant Coefficients and Reduction of Order

7. Problem Set 7: Method of Undetermined Coefficients

8. Problem Set 8: Variation of Parameters

9. Problem Set 9: Laplace Transforms and Initial Value Problems

10. Problem Set 10: Simultaneous ODEs and Applications

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1. Elementary Differential Equations by Rainville (8th Edition)

2. Schaum's Outlines in Differential Equations (4th Edition)

3. Differential Equations for Dummies by Holzner

4. Differential Equations by Dawkins

5. Differential Equations by Blanchard (4th Edition)

6. Differential Equations for Engineers by Lebl

7. Elementary Differential Equations Module by Polytechnic University of the Philippines

1. Differential Equations by Yu Jei Abat

2. Differential Equations by SkanCity Academy

3. Differential Equations by Isaiah James Maling

4. Ordinary Differential Equation by Gahendra Purohit

5. Differential Equations by Professor Leonard

6. Differential Equations by enginerdmath

7. Differential Equations Practice Problems by enginerdmath