Department of Information & Communication Systems Engineering
 SCHOOL OF ENGINEERING Department of Information & Communication Systems Engineering
 Information & Communication Systems Security Information Systems Artificial Intelligence Computer & Communication Systems Geometry, Dynamical Systems & Cosmology

 Title: Lesson Code: Semester: ECTS: Theory Hours: Lab Hours: Faculty:

Content outline

Mathematical induction. Completeness of the real numbers. Functions. Limits. Continuity, theorems of continuous functions. Uniform continuity. Differentiation, derivative of inverse functions, derivatives of trigonometric functions, differential. Applications of derivatives, extreme values of functions, concavity, curve sketching, Cauchy mean value theorem, L’ Hopital rule, graphical method of solving autonomous differential equations, Newton’s approximation method. Integral, indefinite, definite, techniques of integration. Volume of solids of revolution. Improper integrals. Transcendental functions. Separable, linear differential equations of first order. Taylor’s formula.

Learning outcomes

The purpose of the course is to give a complete and working knowledge of differential and integral calculus.

It covers and expands material presented in the last years of high school, including functions, basic calculus, limits, derivatives and integrals.

In addition, the objective of the course is to provide a solid background to the analysis of functions of a single variable and to expose the mathematical rigor through the proofs of most of the theorems and propositions.

Finally, the material of this course also focuses on direct applications on problems from everyday life, from geometry (areas, volumes), from physics and technology.

After the successful completion of this course, the student should be able to:

• understand basic notions of differential calculus, such as the limit, continuity, differentiation of functions in one variable.
• understand basic notions of integral calculus, such as the indefinite/definite integral and the area of a function.
• apply suitable integration techniques for functions in one variable.
• realize more advanced concepts of integral calculus, such as improper integrals, solving simple differential equations and the use of Taylor's theorem.
• realize the importance/use of calculus in everyday life problems, in problems related to geometry, physics and technology.

Prerequisites

Not required.

Basic Textbooks
1. Finney R.L, Weir M.D, Giordano F.R., Thomas’ Calculus, Vol I, Crete University Press.
2. Kravvaristis D. Analysis Courses, Tsotras Publications, 2017.
3. Instructor’s notes.

1. Calculus, Vol I, S. Negrepontis, S. Giotopoulos, E. Giannakoulias, Symmetria Edt.
2. Calculus, M. Spivak, Publish or Perish, Inc.
3. Answer Book for Calculus, M. Spivak, Publish or Perish, Inc.
4. A first course in Calculus, S. Lang, Springer.

Learning Activities and Teaching Methods

The course evaluation derives from:

• 3 compulsory exercises during the semester: counting 30% in the final grade.
• final exam: counting 70% in the final grade.

Final Grade = (0.3*M.V. Exercises) + (0.7*Final Exam)

A student must have: Final Grade >= 5

Lectures 39 hours
Review-Problem Session hours 26 hours
Personal study 57 hours
Final exams 3 hours
Course total 125 hours (5 ECTS)

Language of Instruction
Greek (English for Erasmus students)

Μode of delivery

Face-to-face.

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