Mathematics II

General

• Code: 276-190201
• Semester: 2nd
• Study Level: Undergraduate
• Course type: Υποχρεωτικό, Γενικού υποβάθρου
• Teaching and exams language: Greek
• Teaching Methods (Hours/Week): Lectures (3) / Practical Exercises (2)
• ECTS Units: 7.5
• Course homepage: https://exams-geo.the.ihu.gr/course/view.php?id=209
• Instructors: Zoumakis Nikolaos

Course Contents

• Functions of several real variables:
  Limits and continuity of multivariable functions. Partial and total differentiation. Critical points, local maximum, local minimum and saddle points.  Optimization with constraints. The Lagrange multiplier method. Application of partial derivatives in engineering. Introduction to multivariable integration.
• Ordinary differential equations:
  First order differential equations. Higher order linear differential equations with constant coefficients. General solution. Particular solution. Initial conditions. Applications in food technology leading to the differential equations.
• Taylor and Maclaurin series:
  Application of Taylor series in finding approximations of non-trivial functions and integrals.
• Introduction to Statistics for food manufacturing industry:
  Descriptive Statistics and graphical analysis. Probability distribution functions for discrete and continuous random variables. Normal and Student’s t distributions and their applications in food industry. Introduction to statistical hypothesis testing. The null and alternative hypothesis in Statistics. Regression and correlation. Least square method. Pearson correlation coefficient. Spearman correlation. Generalized correlation coefficient. Probabilistic interpretation of regression and correlation.

Educational Goals

The course aims to achieve the following learning outcomes for students:

• Acquiring knowledge in advanced Mathematics concepts and skills for food science and technology.
• Application of Mathematics in the food industry in the form of computational exercises.

General Skills

• Students must be capable of using advanced mathematical methods for solving problems in food science and technology.
• Promotion of analytical, creative and inductive thinking.
• Decision-making.
• Autonomous work.
• Teamwork.

Teaching Methods

Face to face:

• Lectures (theory and exercises) in the classroom.

Use of ICT means

• Lectures with PowerPoint slides using PC and projector.
• Notes, solved and unsolved problems in electronic format. Each session involved both a faculty lecture and student participation in problem-solving exercises.
• Posting course material and communicating with students on the Moodle online platform.

Teaching Organization

Students Evaluation

Evaluation methods:

• Attendance at class and participation in discussions, and solving exercises in the classroom is rewarded with 20% of the final grade.
• Written final exams (80% of the final grade).

The evaluation criteria are presented and analyzed to the students at the beginning of the semester and are available at the course website.

Recommended Bibliography

1. Θωμά Κυβεντίδη, Διαφορικές Εξισώσεις, Τόμος Δεύτερος, Θεσσαλονίκη,1983.
2. Γεώργιος Χ. Ζιούτας, Πιθανότητες για Μηχανικούς – Μέθοδοι – Εφαρμογές, Εκδόσεις Σοφία, Θεσσαλονίκη, 2005.
3. Murray R. Spiegel, Shaum’s outline of Theory and Problems of Advanced Mathematics for Engineers and Scientists, United States, 1971.
4. Seymour Lipschutz, Shaum’s outline of Theory and Problems of Linear Algebra, United States, 1987.

Related Research Journals

• Journal of Engineering Mathematics.
• Journal of Applied and Engineering Mathematics.
• Journal of Mathematics and Statistics Research.
• Journal of Computational and Applied Mathematics.
• Journal of Numerical Analysis, Industrial and Applied Mathematics.