Calculus IΙΙ

 

 

FACULTY

ENGINEERING

DEPARTMENT

CHEMICAL ENGINEERING

LEVEL OF STUDY

UNDERGRADUATE

SEMESTER OF STUDY

3o

COURSE TITLE

Calculus IΙΙ
COURSEWORK BREAKDOWNTEACHING WEEKLY HOURSECTS Credits
Lectures3
Laboratory0
Projects2

TOTAL

5
COURSE TYPE Compulsory
PREREQUISITES Calculus I and Linear Algebra Calculus II
LANGUAGE OF INSTRUCTION/EXAMSGreek
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.


General Skills

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
Method descriptionSemester Workload
Lectures80
Tutorial Exercises20
Independent Study25
Exams25
Course Total
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: