Course Information

Course Department:

Department of Mathematics and Statistics

Course Code:

MAS 020

Course Title:

Introductory Mathematics II for Chemistry

Number of ECTS:

Level of Course:

1st Cycle (Bachelor's Degree)

Year of Study (if applicable):

Semester/Trimester when the Course Unit is Delivered:

Spring Semester

Name of Lecturer(s):

Andreas Karageorghis

Lectures/Week:

2 (1.5 hours per lecture)

Laboratories/week:

Tutorials/Week:

1 (1 hours per lecture)

Course Purpose and Objectives:

This is the second out of two introductory Mathematics courses offered to Chemistry students. It aims to enable students understand basic calculus methods and basic concepts of Linear Algebra, which could find application when addressing problems in Chemistry. This is a mandatory course, reflecting its importance for other courses in the Chemistry degree, especially those of the Physical Chemistry sector, which routinely use the language of Mathematics. This course is prerequisite for Quantum Chemistry (CHE241).

Learning Outcomes:

After successful completion of this course, students will be expected to:

Use differential equations as models to address physical problems.
Solve differential equations of first order and linear differential equations of second order.
Understand the concept of the complex numbers, be able to perform operations of complex numbers and solve problems involving applications of complex numbers.
Understand the concept of a function of two variables.
Understand the concept of partial derivative.
Apply the chain rule.
Determine maximum/minimum of functions of two variables.
Be familiar with the concept of double integrals and be able to determine simple double integrals.
Solve linear systems.
Understand the concept of matrix and determinant.
Provide the definition of vector space.
Be familiar with the concept of linear independence.
Be familiar with the concept of a base of a vector space.
Determine eigenvalues and eigenfunctions.
Diagonize a matrix.

Prerequisites:

MAS018 (Introductory Mathematics I)

Co-requisites:

Not Applicable

Course Content:

DIFFERENTIAL EQUATIONS
First order – Linear second order – Special forms of differential equations

COMPLEX NUMBERS
Complex numbers and their properties – Polar and exponential forms – Applications – Relations between trigonometric and hyperbolic functions

FUNCTIONS OF TWO VARIABLES
Definitions – Limits and continuity – Partial derivatives – Maxima and minimum – Double integrals

LINEAR ALGEBRA
Systems of linear systems – Matrices -Determinants – Vectors – Vector spaces – Inner product spaces - Eigenvalues and eigenfunctions – Linear transformations

Teaching Methodology:

Lectures and problem-solving tutorials

Bibliography:

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.
Calculus with Analytic Geometry, by H. C. Edwards, D. E. Penney, Prentice Hall, 1997.
Calculus with analytic geometry, 4th ed., by R. Ellis, D. Gulick, Harcourt Brace Jovanovich, 1990.
Calculus with analytic geometry, 2nd ed., by D. G. Zill, PWS-KENT Publishing Company, 1998.
H. Anton and C. Rorres, Elementary Linear Algebra, 6th edition, Wiley, 1991
S.F. Andrilli and D. Hecker, Elementary Linear Algebra, 3rd ed., Elsevier Academic Press, 2003

Assessment:

Mid-term exams (40%) and Final exam (60%)

Language of Instruction:

Greek

Delivery Mode:

Face-To-Face

Work Placement(s):

Not Applicable

Course Details