Calculus IΙΙ
FACULTY | ENGINEERING | ||||
DEPARTMENT | CHEMICAL ENGINEERING | ||||
LEVEL OF STUDY | UNDERGRADUATE | ||||
SEMESTER OF STUDY | 3o | ||||
COURSE TITLE | Calculus IΙΙ | ||||
| COURSEWORK BREAKDOWN | TEACHING WEEKLY HOURS | ECTS Credits | |||
| Lectures | 3 | ||||
| Laboratory | 0 | ||||
| Projects | 2 | ||||
TOTAL | 5 | ||||
| COURSE TYPE | Compulsory | ||||
| PREREQUISITES | Calculus I and Linear Algebra Calculus II | ||||
| LANGUAGE OF INSTRUCTION/EXAMS | Greek | ||||
| COURSE DELIVERED TO ERASMUS STUDENTS | - | ||||
MODULE WEB PAGE (URL) | https://eclass.uowm.gr/ | ||||
2. LEARNING OUTCOMES
Learning Outcomes | |
| After successful completion of the course, students will be able to: • know the mathematical models for specific physical problems, • recognize the general form of differential equations, • apply appropriate methods to find general and partial solutions, • solve initial and boundary value problems, • find solutions in the form of series, • utilize the Laplace transform, • solve systems of differential equations, • graphically solve specific classes of differential equations, • address basic complex analysis issues. | |
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| The student will become familiar with all the mathematical processes that refer to the optimization of scientific processes and situations. Such a high-level course fosters creative and inductive thinking and becomes an essential tool for scientific completion. Other skills Search, analyze and synthesize data and information, using the necessary technologies Decision making Critical Thinking Autonomous work Teamwork |
3. COURSE CONTENTS
| 1. Differential equations of the first order i) Concept, definition, order, degree and general solution of differential equation ii) Differential equations of separable variables iii) Homogeneous Differential equations iv) Linear Differential equations v) Bernoulli differential equations vi) Method of solving non-linear equations vi) Initial value problem vii) Problems for engineers 2. Complex numbers - Complex functions i) Definition of Complex, Image, Vector Radius, Measure and Argument of Complex, Conjugate of Complex, Properties of Conjugate and Measure, Properties of Argument ii) Sum, Difference, Product and Quotient of complex numbers iii) Powers of imaginary unit i, Quadratic complex equation iv) Complex locus v) Complex Functions, Definition, Polynomials, Exponential, Exponential Function, Trigonometric Functions, Complex Logarithm, Properties of Complex Functions vi) Transformations of complex functions, Linear transformation vii) Derivative and rules for derivation of complex functions 3. Differential equations of 2nd and higher order i) The simplest form of differential equation of order n ii) Case of differential equation of order n in which the dependent variable y(x) does not exist iii) Case of differential equation of order n in which the independent variable x does not exist iv) Linear differential equations of higher order, General solution of homogeneous Linear differential equation of higher order, General solution of non-homogeneous Linear differential equation of higher order v) General solution of a 2nd order homogeneous linear differential equation with constant coefficients and General solution of a 2nd order nonhomogeneous linear differential equation with constant coefficients 4. Systems of linear differential equations i) System of n linear differential equations of order a, System in the form of matrices, General solution of the system ii) Homogeneous Systems of linear differential equations with constant coefficients 5. Laplace transform – Solving differential equations i) Basic concepts, Properties ii) Unit step function, Climbing function iii) Inverse Laplace Transform iv) Properties for solving differential equations, Solving differential equations v) Laplace transforms of basis functions |
4. TEACHING METHODS – ASSESSMENT
| MODE OF DELIVERY | Lectures (Face to face), Tutorial Exercises | ||||||||||||||||||||||||
| USE OF INFORMATION AND COMMUNICATION TECHNOLOGY | Projectors, computers, e-class, lectures using power point, computing tools | ||||||||||||||||||||||||
TEACHING METHODS |
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| ASSESSMENT METHODS | Written final exam, Optional midterm exam. |
5. RESOURCES
Suggested bibliography : |
| 1. ORDINARY DIFFERENTIAL EQUATIONS, TRAHANAS STEFANOS Details 2. Differential Equations, Transformations and Complex Functions, Mylonas Nikos - Schinas Christos |
Related academic journals: |