Differential Equations

This course is intended for all engineering students to have a firm foundation on differential equations in preparation for their degree-specific advanced mathematics courses. It covers first-order differential equations, nth-order linear differential equations, and systems of first-order linear differential equations. It also introduces the concept of Laplace Transforms in solving differential equations. The students are expected to be able to recognize different kinds of differential equations, determine the existence and uniqueness of the solution, select the appropriate methods of solution, and interpret the obtained solution. Students must also relate differential equations to various practical engineering and scientific problems. 

• 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