Calculus II
FACULTY | ENGINEERING | ||||
DEPARTMENT | CHEMICAL ENGINEERING | ||||
LEVEL OF STUDY | UNDERGRADUATE | ||||
SEMESTER OF STUDY | 2o | ||||
COURSE TITLE | Calculus II | ||||
| COURSEWORK BREAKDOWN | TEACHING WEEKLY HOURS | ECTS Credits | |||
| Lectures | 4 | ||||
| Laboratory | 0 | ||||
| Projects | 0 | ||||
TOTAL | 4 | ||||
| COURSE TYPE | Compulsory | ||||
| PREREQUISITES | Calculus I and Linear algebra | ||||
| LANGUAGE OF INSTRUCTION/EXAMS | Greek | ||||
| COURSE DELIVERED TO ERASMUS STUDENTS | - | ||||
MODULE WEB PAGE (URL) | https://eclass.uowm.gr/ | ||||
2. LEARNING OUTCOMES
Learning Outcomes | |
| The course aims to: 1) To provide high-level knowledge concerning functions of many variables and especially functions of two independent variables which refer to matters of three-dimensional space. 2) To develop the students analytical ability to be able to understand a phenomenon in order to be able to study it and then solve a series of problems related to it. 3) To train and become knowledgeable about all the mathematical processes that refer to the optimization of scientific processes and situations. Optimization is one of the basic concerns of every scientist and especially of an engineer who models and studies issues of his specialty. 4) A good knowledge of the material of this course will also contribute to the production of new scientific and research ideas. | |
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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
| SECTION 1 FUNCTIONS OF MANY VARIABLES Definition, domain, set of values, equality of functions, isosceles and isosceles curves, basic surfaces in space SECTION 2 LIMIT AND CONTINUITY OF FUNCTIONS OF MANY VARIABLES Limit along a curve, limit of a function, properties of limits, non-convergence criteria, criterion interpolation, limit and composition, polar and spherical coordinates. Continuity and Properties, continuity and synthesis, basic theorems. SECTION 3 VECTOR FUNCTIONS Definition of vector function, Limit and continuity of vector function. Producer vector function. Arc length of curve. Tangent vector to curve, perpendicular plane to curve. Frenet trihedron, curvature, torsion. Frenet levels. SECTION 4 SOME FUNCTION DERIVATIVES Some first-order derivatives. Tangent surface plane. Total first differential class. Linear function approximation. Some higher order derivatives. Total differential higher class. Basic operators. The chain rule. The Cauchy-Riemann equations. THE Laplaces equation. The heat equation. Basic theorems. SECTION 5 OPTIMIZATIONS. EXTREMES OF FUNCTIONS OF MANY VARIABLES Slope of a function. Hessian function matrix. Local extrema of a function. Local extrema with limitations. Applications to the method of least squares. SECTION 6 DOUBLE INTEGER Double integral. Changing variables in the double integral. Key places in the level. Calculation of volume of solid. Calculation of surface area. Mass-center of mass of plane place. Flat locus centroid. Moments of inertia. Average function value. SECTION 7 TRIPLE INTEGER Triple integral. Change of variables in the triple integral. Cylindrical Coordinates. Global coordinates. Calculation of the volume of basic Solids. Mass-center of mass of a solid. Centroid of a solid. Moments of inertia. SECTION 8 VECTOR ANALYSIS Vector fields in the plane. Vector fields in space. Slope of a function. Its operator slope. The Laplace operator. Function deviation. Vector function vorticity. Conservative vector fields and function potential. SECTION 9 CURVED INTEGRALS Circumferential integral. Computation of a curvilinear integral. The mean value theorem. Mass-center of mass curve. Centroid of curve. Moments of inertia. Circumferential integral vector function. Vector fields and circumflex integral. Vector flow field through a closed curve. Project of strength. Basic theorems. SECTION 10 SURFACE INGREDIENTS Surface integral. Orientation of non-parametric surfaces. Calculation surface integral. Surface mass-center of mass. Surface centroid. Moments inactivity. Vector field flow through a surface. The divergence theorem. THE Stokes theorem. |
4. TEACHING METHODS – ASSESSMENT
| MODE OF DELIVERY | Lectures (Face to face) | ||||||||||||||||||||||||
| 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. Calculus of functions of many variables and introduction to differential equations, Mylonas Nikos - Schinas Christos - Papaschoinopoulos G. |
Related academic journals: |