Instructor: Garyfallos Papaschinopoulos / Gesthimani Stefanidou
Lesson Code: TMC159
Semester: 1st
Weekly teaching hours: 6
Prerequisites: No
Course offered to Erasmus students: No
Course URL:

Learning Outcomes:
The scopus of the course is to introduce the students to basic concepts concerning Integral Calculus, Series, Vector spaces, Matrices, Functions of Several Variables and Vector Functions which are necessary for all students of School of Engineering.

General Skills:
Search, analysis and synthesis of data and information,
Critical thinking
Promoting free, creative and inductive reasoning

Course Content: 
Matrices and determinants. Rank of a matrix. Elementary Transformations. Inverse matrix. Linear systems. Eigenvalues and eigenvectors. Computation of the matrix An. Vector spaces. Linear dependence and linear independence. Basis and dimension of a vector space. Inverse Trigonometric Functions. Hyperbolic Functions. Definite and indefinite integrals. Integration techniques. Applications of integration. Improper integrals. Sequences. Series of real numbers. Power Series. Taylor series. Functions of Several Variables. Partial Derivatives of Functions of Several Variables. Chain Rules. Local Exrtema. Conditional Extrema. Vector Functions of one variable. Derivative of a Vector function. Vector Functions of Several Variables. Differential Operators (Gradient, Divergence, Rot).

Suggested Bibliography:
1. Advanced Mathematics (Schaum’s Outline Series), Murray R. Spiegel, Translation J. Schinas, 1982, ISBN 07-060229-8.
2. Introduction to Linear Algebra, C.J. Schinas and G. Papaschinoulos, Tziolas, ISBN 978-960-418-375-3.
3. Calculus of Functions of one Variable with Vector and Linear Algebra, X. Terzides, Christodoulides, ISBN 960-8183-56-1.
4. Exercises of Calculus of a Function of one Real Variable, B. Fragou, Ziti, 2005, ISBN 960-431-677-X.

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