Courses

Mathematics I

General

Course Contents

  • Real analysis of single-variable functions:
    Continuity and limits of functions. Differentiation. Extreme values of functions. Application of derivatives in engineering. Integration. Integrals of elementary functions. Numerical integration. Trapezoidal rule and Simpson’s rule to approximate definite integrals. Application of integration in engineering.
  • An introduction to linear programming:
    Simplex method for linear optimization. A geometric interpretation of linear optimization problems with two variables. Application of Simplex method in optimal design.
  • Nonlinear equations:
    Solving exponential equations. Solving equations with complex numbers
  • Basic probability theory:
    Definitions of probability. Venn diagrams. Mathematical formulation of probability. Properties of probability. Conditional probability. Total probability and the Bayes’ theorem. Discrete and continuous random variables. Distribution functions. Expected values. Moments of random variables and the variance. Application of probability in engineering.

Educational Goals

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

  • Acquiring knowledge in the basic 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 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

ActivitySemester workload
Lectures50
Independent study100
Total150

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 Πρώτος, Θεσσαλονίκη,1982.
  2. R. Churchill, J. Brown, Μιγαδικές συναρτήσεις και εφαρμογές, 2η Έκδοση, Μετάφραση: Πανεπιστημιακές Εκδόσεις Κρήτης.
  3. Howard E. Taylor, Thomas L. Wade, University Calculus, New York,1982.
  4. Frank Ayres, Schaum’s outline of theory and problems of Matrices, Singapore,1983.
  5. Richard Bronson, Shaum’s outline of Modern Introductory Differential Equations, United States, 1973.