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Course Description Course Name : Engineering Mathematics and Differential Equations Course Code : G 241 Course Type : Compulsory Level of Course : First Cycle Year of Study : 2 Course Semester : Fall (16 Weeks) ECTS : 4 Name of Lecturer(s) : Prof.Dr. MAHMUT ÇETİN Learning Outcomes of the Course : 1. Gains the ability to define engineering problems. 2. Develops analitical thinking and synthesizing skills. 3. Formulates a problem mathematically. 4. Analyses alterative solving techniques and chooses the optimal solution. 5. Analyses the solution approaches; compares the solution by synthesizing, and proves the solution if it is corect or not. Mode of Delivery : Face-to-Face Prerequisites and Co-Prerequisites : None Recommended Optional Programme Components : None Aim(s) of Course : Have students gain analitical thinking skills by teaching them to solve ways of engineeering problems to be faced in the real life and providing in-depth knowledge. Course Contents : Linear Algebra:Matrices and determinants, systems of linear equations; Eigenvalue Problems, Numeric Analysis, Linear Programming/Operations Reseaqrch, Taylor and Maclaurin Series, Ordinary Differential Equations Language of Instruction : Turkish Work Place : Classroom   Course Outline /Schedule (Weekly) Planned Learning Activities Week Subject Student's Preliminary Work Learning Activities and Teaching Methods 1 Introduction to Matrices and Linear Systems: General Concepts and Notations, and some definitions Sections from different chapters relevant to the subject Expression and examples 2 Unit Matrix, Scalar Matrix, Diagonal Matrix, Multiplication of Matrices Sections from different chapters relevant to the subject Expression and examples 3 Determinants of Square Matrices Sections from different chapters relevant to the subject Expression and examples 4 Introduction to Linear Systems of Equations, Rank of a Matrix; Elementary Operations for Equations Sections from different chapters relevant to the subject Expression and examples 5 Linear System, Coefficient Matrix, Augmented Matrix and Solution of Linear Systems of Equations by Gauss Elimination and Gauss–Jordan Elimination Methods Sections from different chapters relevant to the subject Expression and examples 6 Eigenvalues and Eigenvectors Sections from different chapters relevant to the subject Expression and examples 7 Linear Programming: Principles, Minimisatin, Maximisation, Feasible Solution, Optimal Solution Sections from different chapters relevant to the subject Expression and examples 8 Graphical Solution of Linear Programming Problems Sections from different chapters relevant to the subject Expression and examples 9 Introduction to Taylor and Maclaurin Series Sections from different chapters relevant to the subject Expression and examples 10 Mid-term exam Study all the subjects Questions including all the subjects 11 Numerical integration: Trapezoidal and Simpson´s Rule; Newton-Raphson Root-finding Algorithm Sections from different chapters relevant to the subject Expression and examples 12 Introduction to First-Order Ordinary Differential Equations: Definitions and Constructing Differential Equation Sections from different chapters relevant to the subject Expression and examples 13 Separable and Homogeneous Differential Equations Sections from different chapters relevant to the subject Expression and examples 14 Exact and Non-exact Differential Equations; Integrating Factors; Bernoulli Differential Equations Sections from different chapters relevant to the subject Expression and examples 15 Second Order Differential Equations: Homogenous and Euler–Cauchy Differential Equations Sections from different chapters relevant to the subject Expression and examples 16/17 Final exam Study all the subjects Questions including all the subjects   Required Course Resources Resource Type Resource Name Recommended Course Material(s)      Chapra, S. C., R. P., Conale, 1998. Numerical Methods for Engineers with Programming and Software. McGraw-Hill International Editions, 924 p.  Goldstein, L. J., Lay, D. C., Schneider, D. I., 1996. Calculus and Its Applications. Prentice-Hall International Editions, 795 p.   Hoffman, J. D., 1993. Numerical Methods for Engineers and Scientists. McGraw-Hill International Editions, 825 p.  James, G., Searl, J., Wright, J., 1996. Modern Engineering Mathematics. Addison-Wesley Publishing Company, 954 p.  Jeffrey, A., 1995. Essentials of Engineering Mathematics: Worked Examples and Problems. Chapman and Hall, Inc., 825 p.  KREYSZIG, E., KREYSZIG, H., NORMINTON, E. J., 2011. ADVANCED ENGINEERING MATHEMATICS. JOHN WILEY & SONS, INC., pp. 1283, http://www.wiley.com/college/kreyszig  Spiegel, M., 1967. Applied differential Equations. Second Edition, Prentice-Hall, Inc., USA, 412 p  Rabenstein, A. L., 1975. Elementary Differential Equations with Linear Algebra. Academic Press, Inc., 374 p.  KREYSZIG, E., KREYSZIG, H., NORMINTON, E. J., 2011. ADVANCED ENGINEERING MATHEMATICS. JOHN WILEY & SONS, INC., pp. 1283, http://www.wiley.com/college/kreyszig Required Course Material(s)   Assessment Methods and Assessment Criteria Semester/Year Assessments Number Contribution Percentage     Mid-term Exams (Written, Oral, etc.) 1 90     Homeworks/Projects/Others 4 10 Total 100 Rate of Semester/Year Assessments to Success 40   Final Assessments 100 Rate of Final Assessments to Success 60 Total 100   Contribution of the Course to Key Learning Outcomes # Key Learning Outcome Contribution* 1 Gains the ability to use knowledge and skills in his/her field. 4 2 Improve a process-based system using the methods of measurement and evaluation 4 3 Has knowledge in the fields of basic science, engineering and food science and technology 5 4 Determines, identifies and resolves the problems in the areas regarding food engineering and technology applications 5 5 Researches and analyzes complex systems using scientific methods 5 6 Uses objective and subjective methods to evaluate food quality and interprets the results 2 7 Selects and uses modern technical systems in food engineering and technology applications 2 8 Uses laboratories, does food analyses and evaluates, interprets and reports the results, 2 9 Has skills of Independent decision-making, self-confidence, creativity and the ability to take responsibility 5 10 Complies with teamwork 0 11 Analytically and critically evaluates the learned information. 5 12 Knows the necessity of lifelong learning. 4 13 Communicates effectively and healthily in the relevant field and uses communication technologies 0 14 Knows a foreign language at a level to follow the literature about foods and communicate 3 15 is respectful of professional ethics 3 16 Has ability to plan, implement and develop a food process 4 17 Knows the legislation and management systems related to foods 2 18 Constantly improves himself/herself determining his/her training needs in accordance with his/her interests and abilities in the scientific, cultural, artistic and social fields besides his/her professional development 4 * Contribution levels are between 0 (not) and 5 (maximum).   Student Workload - ECTS Works Number Time (Hour) Total Workload (Hour) Course Related Works     Class Time (Exam weeks are excluded) 14 3 42     Out of Class Study (Preliminary Work, Practice) 14 1 14 Assesment Related Works     Homeworks, Projects, Others 4 4 16     Mid-term Exams (Written, Oral, etc.) 1 10 10     Final Exam 1 10 10 Total Workload: 92 Total Workload / 25 (h): 3.68 ECTS Credit: 4