Differential Equations

Rationale:

This course builds a comprehensive and application-oriented foundation in differential equations, intended for engineering students who must analyze, model, and interpret time-dependent and spatially varying processes in physical, chemical, and biological systems. Engineering problems require a strong grasp of differential equations to formulate mathematically coherent models. This course addresses the need for students to develop the conceptual understanding and mathematical fluency necessary to connect physical principles with analytical and semi-analytical solutions.

Focus:

Students begin with first-order ordinary differential equations, including separable, homogeneous, exact, linear, Bernoulli, and non-exact equations, as well as those linear in both dependent and independent variables. Emphasis is placed on choosing appropriate solving methods based on structure and initial conditions, while reinforcing interpretation of solutions in the context of real-world engineering behavior. The course advances to higher-order linear differential equations with constant coefficients, supported by systematic solution strategies such as reduction of order, method of undetermined coefficients, and variation of parameters. Special attention is given to the structure and classification of equations to promote methodical problem-solving and physical insight. The Laplace Transform is introduced as a powerful tool to handle discontinuous or piecewise inputs and solve initial value problems systematically. Students also explore the use of power series techniques to construct solutions for linear differential equations with variable coefficients, particularly near ordinary or singular points. Throughout the course, students are trained to verify assumptions, assess boundary and initial condition relevance, and evaluate the physical interpretability of their solutions.

Outcome:

By the end of the course, students will have developed the ability to model engineering systems using first-order and higher-order differential equations. They will be able to apply appropriate solution techniques with precision, supported by rigorous mathematical justification. Students will interpret analytical solutions to explain system behavior, identify limitations, and validate physical plausibility. They will be equipped to integrate differential equations into engineering decision-making processes, prepare for more advanced topics such as partial differential equations and numerical methods, and support engineering design or analysis tasks that involve transient or dynamic behavior.

• Develop analytical solutions to first-order ordinary linear differential equations using traditional and advanced methods, and assess their applicability in solving initial value problems.

• Develop analytical solutions to mathematical models of real-world engineering phenomena using first-order and higher-order linear differential equations in describing physical, chemical, or biological systems.

• Develop analytical solutions to higher-order linear differential equations using traditional and advanced methods, and assess their applicability in solving initial value problems.

1. Lecture 0: Introduction to Differential Equations

2. Lecture 1: Formation of Differential Equations

3. Lecture 2: Separation of Variables

4. Lecture 3: Homogeneous Differential Equations

5. Lecture 4: Exact Differential Equations

6. Lecture 5: Non-Exact Differential Equations 

7. Lecture 6: First-order Linear Differential Equations

8. Lecture 7: Bernoulli Differential Equations

9. Lecture 8: Differential Equations Linear in Two Variables

10. Lecture 9: Lecture 9: Applications (Exponential Growth and Decay, Newton's Law of Cooling, Dissolution, Chemical Mixing, Heat Conduction, Flow through an Orifice, Chemical Kinetics, etc.) 

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

12. Lecture 11: Reduction of Order

13. Lecture 12: Method of Undetermined Coefficients

14. Lecture 13: Variation of Parameters

15. Lecture 14: Laplace and Inverse Laplace Transforms

16. Lecture 15: Applications of Laplace Transforms (Simultaneous ODEs, Vibration of Springs, Mixing, etc.)

17. Lecture 16: Power Series Solution to Linear Differential Equations

Please visit this link for the class recordings: 2CHE-A and 2CHE-B.

Please visit this link for the updated class schedule.

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

2. Differential Equations by Blanchard (4th Edition)

3. Schaum's Outlines in Differential Equations by Bronson (4th Edition)

4. Differential Equations by Dawkins

5. Differential Equations for Dummies by Holzner

6. Differential Equations for Engineers by Lebl

7. Ordinary Differential Equations by Nagy

8. Handbook of Differential Equations by Zwillinger

9. 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