ENGINEERING MATHEMATICS: DIFFERENTIAL EQUATIONS & LINEAR ALGEBRA
- Course
- MATH501 - ENGINEERING MATHEMATICS: DIFFERENTIAL EQUATIONS & LINEAR ALGEBRA
- Department
- Mechanical Engineering - English - Master
- Course Type
- Course
- Status
- Required
- Language
- English
- Credit
- 3
- ECTS
- 8
- T+P+L
- 3 + 0 + 0
- Course Coordinator(s)
- Assoc. Prof. Dr. Ali ÖZYAPICI
- Prerequisite
- -
Course Description
The course is held in two parts. The first part of the course covers review of the differential equations and linear algebra undergraduate topics: First-order and second order ordinary differential equations and their solutions. Laplace transforms and power series solutions. The linear algebra topics (the system solutions, vectors etc.), as well as their examples of applications in the field of engineering. In the second part, the higher order linear differential equations with variable coefficients, higher order nonlinear differential equations, Laplace Transforms, inverse Laplace transforms, Convolution and integral equations, solution of differential equations systems with Laplace transform, initial value and linear boundary value problems, Green's function, series solutions of differential equations are discussed.
ENGINEERING MATHEMATICS: DIFFERENTIAL EQUATIONS & LINEAR ALGEBRA
Evaluation Tools (Active Term)
| Item | Type | Weight (%) |
|---|---|---|
| Final | Final | 40 |
| Homework1 | Assignment | 30 |
| Homework2 | Assignment | 30 |
| Total | 100 | |
Course outcomes
No course outcomes have been defined yet.
Course Syllabus
| Week | Topic |
|---|---|
| Week 1 | Review of the first order differential equations and Its Applications |
| Week 2 | Review of Second order ordinary differential equations and their solutions |
| Week 3 | Definition of Laplace transforms and Inverse of Laplace Transform. Basic Theorems of Laplace Transform |
| Week 4 | Applications of Laplace Transform: Constant Coefficient Equations and System of Linear equations; |
| Week 5 | Applications of Laplace Transform: Differential Equations of Variable Coefficients |
| Week 6 | Series Solution of variable coefficient Differantial equation |
| Week 7 | Midterm |
| Week 8 | Nonlinear Differential Equations and their solutions: Trial Equation Method |
| Week 9 | Review of linear algebra: Matrices |
| Week 10 | Solutions of System of linear equations and their applications |
| Week 11 | Basics on Vector spaces |
| Week 12 | Eigenvalues and Eigenvectors |
| Week 13 | Application of Eigenvalues and Eigenvectors to the differantial Equations |
| Week 14 | completion of missing parts of lessons( if any) and Revision |
| Week 15 | Final Exam |
Reference Books & Course Materials
- 01 Advanced engineering mathematics, Tenth Edition, Erwın Kreyszıg , Wiley, 2011.
- 02 Linear Algebra and Its Applications,Fourth Edition, David C. Lay, Pearson 2012.
- 03 Differantial Equations and Boundary Value Problems, Fourth Edition, C. Henry Edwards, David, E. Penney, Pearson, 2008.
Learning Outcomes
No learning outcomes have been defined.
Program Outcomes
No program outcomes have been defined.
Po-Lo Matrix
The PO-LO matrix has not been populated yet.