INSTRUCTOR: Ms. Axel Gayondato
Course Overview
A. COURSE DESCRIPTION:
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 solution, select the appropriate methods of solution and interpret the obtained solution. Students are also expected to relate differential equations to various practical engineering and scientific problems as well as employ computer technology in solving and verifying solutions.
B. COURSE LEARNING OUTCOMES (CLO):
At the end of the course, the students should be able to:
CLO1. Determine the solution of the different types of differential equations.
CLO2. Apply differential equations to selected engineering problems.
C. Module and Unit Topics
To ensure the accomplishment of the learning outcomes, you need to master the following topics in this course:
Module 1: Definitions
1.1. Definition and Classifications of Differential Equations (D.E.) by type
1.2. Solution of a D.E. (General and Particular)
Module 2: Solution of Some 1st Order, 1st Degree D.E.
2.1. Variable Separable
2.2. Exact Equation
2.3 Linear Equation
2.4 Substitution Methods
2.4.1 Homogenous Coefficients
2.4.2. Bernoulli’s Equation
Module 3: Applications of 1st Order D.E.
3.1. Decomposition / Growth
3.2. Newton’s Law of Cooling
3.3. Mixing (Non-Reacting Fluids)
Module 4: Linear Differential Equation of Order n
4.1. Introduction
4.1.1. Standard form of a nth order Linear DE
4.1.2. Differential Operators
4.1.3. Principle of Superposition
4.1.4. Linear Independence of a Set of Functions
4.2. Homogeneous Linear Differential Equation with Constant Coefficients
4.2.1. Solution of a Homogeneous Linear Ordinary DE
4.2.2. Initial and Boundary Value Problems
Module 5: Laplace Transforms of Functions
5.1. Definition
5.2. Transform of Elementary Functions
5.3. Transform of e at f(t) – Theorem
5.4. Transform of t n f(t) – Derivatives of Transforms
5.5. Inverse Transforms
5.7. Transforms of Derivatives
5.8. Initial Value Problems
Module 6: The Heaviside Unit-Step
6.1. Definition
6.2. Laplace Transforms of Discontinuous Functions and Inverse Transform Leading to Discontinuous Functions
6.3. Solution of Initial Value Problems with Discontinuous Functions by Laplace Transform Method