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Course Details
| Course Department: | Department of Mathematics and Statistics |
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| Course Code: | MAS 028 |
| Course Title: | Mathematics for CEE |
| Number of ECTS: | 5 |
| Level of Course: | 1st Cycle (Bachelor's Degree) |
| Year of Study (if applicable): | Year 2 Semester 1 |
| Semester/Trimester when the Course Unit is Delivered: | Fall Semester
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| Name of Lecturer(s): | Panagiotis Batakidis, Pavlos Kassotakis |
| Lectures/Week: | 2 (3 hours per lecture) |
| Laboratories/week: | 1 (1 hours per lecture) |
| Tutorials/Week: | -- |
| Course Purpose and Objectives: |
A brief introduction to differential equations with an emphasis on
solving simple equations. Understand basic mathematical methods from the calculus of many
variables that can be applied to engineering problems.
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| Learning Outcomes: |
The students: - understand what a differential equation is - solve first order differential equations - solve second-order linear differential equations - understand what vector functions are - calculate tangent and perpendicular vectors - understand the concept of curvature - understand the concept of function of two variables - the concept of partial derivative - they use the chain rule - calculate tangent planes - the concept of directed derivative - calculate maxima/minima of functions of two variables - calculate double integrals - calculate curves and surface integrals
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| Prerequisites: | MAS025 - Engineering Mathematics I |
| Co-requisites: | Not Applicable |
| Course Content: |
A brief introduction to differential equations: Basic definitions, Differential equations of first order (equations of separated variables, homogeneous, linear, exact). Linear differential equations of the second order (Homogeneous equations with fixed coefficients, solution of the inhomogeneous: Method of undetermined coefficients, Euler's differential equation). Infinite calculus: Vector functions (Calculus of vector functions, arc length, unit tangent and perpendicular vectors). Functions of several variables (Partial derivatives, chain rule, directed derivative - slope of a function of two variables, maxima - minima of functions of two variables). Multiple integrals (Computation of double integrals, double integrals in non-orthogonal regions, double integrals in polar coordinates, triple integrals). Curves and surface integrals. |
| Teaching Methodology: | Lectures (3hrs / week) and Tutorial (1 hr / week) |
| Bibliography: |
Elementary Differential Equations and Boundary Problems, W.E.Boyce & R.C. Diprima, 8th Edition, Wiley, 2005. CALCULUS (7th Edition), by H. Anton, I. Bivens, S. Davis, John Willey & Sons, 2003 Thomas’ Calculus (10th Edition), by G. B. Thomas, R. L. Finney, M. D. Weir, F. R. Giordano, Pearson Addison Wesley, 2000 |
| Assessment: | One midterm (40%) and one final exam (60%) |
| Language of Instruction: | Greek
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| Delivery Mode: | Face-To-Face |
| Work Placement(s): | Not Applicable |