# Math for Engineers

### 1. COURSE CONTENTS:

1. Basic Definition and Terminology:

Motivation, Definition, Classification by type, order, linearity and solutions.

2. First Order Differential Equations:

Initial-value problem, Separable variables, Homogeneous equations, Exact equations. Linear equations, Integrating factor, Bernoulli equation, Applications.

3. Second Order Differential Equations:

Initial-value and Boundary-value problems, Linear differential operators, Reduction. Of order, Homogeneous equations with constant coefficients, Nonhomogeneous equations, Method of undetermined coefficients, Method of variation of parameters, Some non-linear equations, Applications, Higher order Differential Equations.

4. Laplace Transform:

Definitions, Properties, Inverse Laplace transforms, Solving initial-value problems. Special functions: Heaviside unit step function, Periodic function, Dirac delta function, Convolution theorem.

5. Linear Algebra:

Definitions, Matrices and Determinants, Linear systems, Eigenvalues and Eigenvectors, Diagonalization.

6. System of Linear Differential Equations:

Homogeneous linear systems, Solving systems by Eigenvalues and Eigenvectors Method, Solving systems by Laplace transforms.

7. Partial Differential Equations:

Some mathematical models, Fourier series solutions, Method of separation of variables, Applications.

### 2. COURSE OBJECTIVES:

1. To acquaint students with the necessary theories and methods in both Differential and Partial Differential Equations.

2. To acquaint students with Differential Equations and their applications.

3. To Introduce, among others, the Laplace Transform method which is an efficient tool for solving Engineering problems in an elegant way

4. To present students with some realistic problems

5. To equip students with a number of methods for solving differential equation, concentrating on those which are of practical importance.

### 3. LEARNING OUTCOMES:

The students are expected to be able to:

1. Classify differential equations by type, order and linearity

2. Determine the general solution of different types of differential equations by using different techniques

3. Solve non-homogeneous differential equations by using the method of undetermined coefficients and the method of variation of parameters

4. Solve some non-linear differential equations

5. Determine eigenvalues and eigenvectors of matrices to comprehend the diagonalization process.