Differential and Integral Calculus I

1. COURSE INFORMATION:

School	Environmental Engineering
Course Level	Undergraduate
Course ID	MATH 101	Semester	1^st
Course Category	Required
Course Modules	Instruction Hours per Week		ECTS
Lectures and Tutorial Exercises	4 Th=3, E=1, L=0		5
Course Type	General Background
Prerequisites
Instruction/Exam Language	Greek
The course is offered to Erasmus students	No
Course URL	https//www.eclass.tuc.gr/courses/MHPER314/ (in Greek)

2. LEARNING OUTCOMES

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

3. COURSE SYLLABUS

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.

4. INSTRUCTION and LEARNING METHODS - ASSESSMENT

Lecture Method	Direct (face to face)
Use of Information and Communication Technology	E-class support
Instruction Organisation	Activity	Workload per Semester (hours)
	- Lectures	39
	- Lab assignments	13
	- Autonomous study	73
	Course Total	125
Assessment Method	Written final examination (100 %).

5. RECOMMENDED READING

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

6. INSTRUCTORS

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:

Differential and Integral Calculus I

Technical University of Crete

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1st Semester: MATH 101

Technical University of Crete

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