School of Chemical and Environmental Engineering

Now offering two distinct diplomas: Chemical Engineering and Environmental Engineering

# Differential and Integral Calculus I

1. COURSE INFORMATION:

 School Chemical and Environmental Engineering Course Level Undergraduate Direction - Course ID MATH 101 Semester 1st Course Category Required Course Modules Instruction Hours per Week ECTS Lectures and Tutorial Exercises 5 Th=4, E=1, L=0 4 Course Type General Background Prerequisites Instruction/Exam Language Greek The course is offered to Erasmus students Yes Course URL https//www.eclass.tuc.gr/courses/MHPER314/ (in Greek)

2. LEARNING OUTCOMES

 Learning Outcomes The goal of the class Infinitesimal Calculus Ι is to provide the basic tools of mathematics needed by engineers in the theoretical part and the calculating part of his/her education.With the successful completeness of the course the student should know:The method of induction.Calculate limits of sequences, extremes of functions, Integrals, sums of series, areas of regions, volumes of solids with given sections, center of mass, moments of inertia.Expand functions to power series and calculate the values of basic functions to any given error.Study functions through their graphs.Approximate functions with polynomials and estimate the error of the approximation.Evaluate the work of a power in linear movement and the hydrostatic pressure in plane regions. General Competencies/Skills Search, analysis and synthesis of data and information.Independent work.Team work.Work in scientific environment.Produce free deductive thinking.

3. COURSE SYLLABUS

 Real numbers.Principle of Mathematical Induction.SequencesSeries (criteria of convergence).Limits and continuity of functions. Derivative of function, differential of functions.Application of derivatives in the study of functions.Definite Integral. Fundamental Theorems of Integral Calculus.Applications of the Integral.Calculation of areas, volumes, areas, and volumes of solids of revolution.Applications in Physics (Inertia and center of mass, Work, Hydrostatic pressure).Indefinite Integral. Techniques of Integration.Improper Integrals.Power series and Taylor series. Applications of Power series.

4. INSTRUCTION and LEARNING METHODS - ASSESSMENT

 Lecture Method Direct (face to face) Use of Information and Communication Technology Support by electronic platform e-class Instruction Organisation Activity Workload per Semester (hours) - Lectures 52 -Tutorial Exercises 13 - Independent, team study 35 Course Total 100 Assessment Method Final exam, written (100 %).