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School of Chemical and Environmental Engineering

Now offering two distinct diplomas: Chemical Engineering and Environmental Engineering

Differential and Integral Calculus I


School Environmental Engineering
Course Level Undergraduate
Course ID MATH 101 Semester 1st
Course Category Required
Course Modules Instruction Hours per Week ECTS
Lectures and Tutorial Exercises 4
Th=3, E=1, L=0
Course Type General Background
Instruction/Exam Language Greek
The course is offered to Erasmus students No
Course URL https// (in Greek)



Learning Outcomes

This course aims to provides the essential mathematical techniques that an engineer needs in the theoretical part of his training as well as  what he/she  shall need in the computational part of his work.

On completion of this course students will be expected to

  • apply the mathematical induction method
  • calculate limits of sequences and examine the convergence of series
  • compute derivatives and antiderivatives of functions
  •  find the extreme values of functions and solve optimization problems
  •  sketch the graph of functions
  • to evaluate  integrals using the basic techniques of integration
  • evaluate areas, volumes of solids with known cross sections, moments and center of mass, the work done by a variable force along the x-axis, the fluid force against a  vertical flat plate.
  • approximate functions by Taylor polynomial and calculate the errors bound
  • represent   certain functions as series and  evaluate the   values at a point up a desired error.
General Competencies/Skills
  • Review, analyse and synthesise data and information
  • Work autonomously
  • Work in teams
  • Work in an international frame
  • Advance free, creative  and causative thinking


Real variables. Principle of Mathematical induction. Sequences, limits of sequences, recursively defined sequences. Series (Convergence criteria) Functions of one real variable. Limits and continuity of functions. Derivatives. Geometric interpretation of the derivative. Differentials. Applications of the derivative. Definite integrals. Basic theorems of integral calculus. Applications of integration: Αreas between two curves,  volumes and surfaces of solids by revolution, arc length, moments and centroids, hydrostatic pressure.  Exponential Functions. Inverse functions. Hyperbolic functions. Indefinite integral. Integration techniques. Techniques of Integration: Integration by Parts,Trigonometric Integrals, Trigonometric Substitutions,Integration of Rational Functions by Partial Fractions, Improper Integrals. Power series and Taylor series. Applications of series.


Lecture Method Direct (face to face)
Use of Information and Communication Technology E-class support
Instruction Organisation Activity Workload per Semester
- Lectures 39
- Lab assignments 13
- Autonomous study 73
Course Total 125

Assessment Method

Written final examination (100 %).


  • THOMAS Calculus ,  George B. Thomas , Jr., Joel Hass, Christopher Heil, Maurice D. Weir,
  • Calculus, Briggs William, Cochran Lyle, Gillett Bernard


Course Instructor: Associate Professor A. Manoussakis (Faculty - EnvEng)
Lectures: Associate Professor A. Manoussakis (Faculty - EnvEng)
Tutorial exercises: Associate Professor A. Manoussakis (Faculty - EnvEng)
Laboratory Exercises: