Description of Individual Course Units
Course Unit CodeCourse Unit TitleType of Course UnitYear of StudySemesterNumber of ECTS Credits
MAT151MATHEMATICS ICompulsory115
Level of Course Unit
First Cycle
Objectives of the Course
The aim of course is to gain the ability of systematic and analytic approach to the statistics problems for students. The fundemantal concepts and methods of mathematic is thought during this course.
Name of Lecturer(s)
Doç.Dr.Tahsin ÖNER
Learning Outcomes
1Will be able to recognise properties of functions and their inverses, to use properties of polynomials, rational functions, exponential, logarithmic, trigonometic and inverse trigonometric functions.
2Will be able to understand conceptual and visual representatioan of limits, continuity, diferentiability, and tangent line approximations for functions at a point.
3Will be able to apply limit theorems, the Squeeze Theorem, left and right limits, and limits involving infinity and l’hospital’s rule.
4Will be able to obtain linear and Taylor polynomial approximations of functions and to approximate the values of functions
5Will be able to apply the power rule, product rule, quotient rule and the chain rulet o functions explicity and implicity for finding deribatives,.
6Will be able to use derivatives in practical applications, such as distance, velocity, acceleration, related rates and extereme value problems,
7Will be able to use first and second derivatives tests to optimize functions and to find critical points, inflections points, extreme values.
Mode of Delivery
Face to Face
Prerequisites and co-requisities
None
Recommended Optional Programme Components
None
Course Contents
Preliminaries: Real Numbers and the Real Line, Cartesian Coordinates in the Plane, Graphs of Quadratic Equations; Functions and Their Graphs, Combining Functions to Make New Functions, Polynomials and Rational Functions, The Trigonometric Functions; Limits of Functions; Limits at Infinity and Infinity Limits; Continuity; Tangent Lines and Their Spoles; The Derivative; Diferentiations Rules; The Chain Rule; Derivatives of Trigonometric Functions; Higher-Order Derivatives; Using Differentials and Derivatives (Derivatives in Economics) ; The Mean-Value Theorem; Implicit Differantiation; Inverse Functions; Exponential and Logarithmic Functions; The Natural Logarithm and Exponential; The Inverse Trigonometric Functions; Related Rates; Indeterminate Forms; Extreme Values; Concavity and Inflections; Extreme-Values Problems; Sketching the Graph of a Functions.
Weekly Detailed Course Contents
WeekTheoreticalPracticeLaboratory
1Preliminaries: Real Numbers and the Real Line, Cartesian Coordinates in the Plane, Graphs of Quadratic Equations; Functions and Their GraphsGiving some information about course
2Preliminaries: Combining Functions to Make New Functions, Polynomials and Rational Functions, The Trigonometric FunctionsSolving problems with a mentor
3Limits of FunctionsSolving problems with a mentor
4Limits at Infinity and Infinity LimitsSolving problems with a mentor
5Continuity; Tangent Lines and Their SpolesSolving problems with a mentor
6The DerivativeSolving problems with a mentor
7Diferentiations Rules; The Chain Rule; Derivatives of Trigonometric FunctionsSolving problems with a mentor
8Midterm examSolving problems with a mentor
9Higher-Order Derivatives; Using Differentials and Derivatives (Derivatives in Economics)
10The Mean-Value Theorem; Implicit DifferantiationSolving problems with a mentor
11Inverse Functions; Exponential and Logarithmic Functions; The Natural Logarithm and Exponential; The Inverse Trigonometric FunctionsSolving problems with a mentor
12Related RatesSolving problems with a mentor
13Indeterminate Forms; Extreme Values; Concavity and InflectionsSolving problems with a mentor
14Extreme-Values ProblemsSolving problems with a mentor
15Sketching the Graph of a FunctionsSolving problems with a mentor
16Final Exam
Recommended or Required Reading
1. Robert A. Adams and Christopher Essex, "Calculus A Complete Course", Pearson, 7th Edition, ("Kalkülüs - Eksiksiz Bir Ders" - Cilt I, Prof.Dr.M.Terziler, Doç.Dr.T.ÖNER, Palme Yayıncılık, 2012), (2010). 2. William L. Briggs, Lyle Cochran and Bernard Gillett, "Single Variable Calculus", Pearson, (2002). 3. Elgin H. Johnston and Jerry Mathews, Pearson, (2014).
Planned Learning Activities and Teaching Methods
Assessment Methods and Criteria
Term (or Year) Learning ActivitiesQuantityWeight
Midterm Examination1100
SUM100
End Of Term (or Year) Learning ActivitiesQuantityWeight
Final Examination1100
SUM100
Term (or Year) Learning Activities40
End Of Term (or Year) Learning Activities60
SUM100
Language of Instruction
Turkish
Work Placement(s)
None
Workload Calculation
ActivitiesNumberTime (hours)Total Work Load (hours)
Midterm Examination122
Final Examination122
Quiz111
Attending Lectures16348
Practice16116
Individual Study for Homework Problems11515
Individual Study for Mid term Examination12121
Individual Study for Final Examination13535
Individual Study for Quiz11010
TOTAL WORKLOAD (hours)150
Contribution of Learning Outcomes to Programme Outcomes
PO
1
PO
2
PO
3
PO
4
PO
5
PO
6
PO
7
PO
8
PO
9
PO
10
PO
11
PO
12
PO
13
PO
14
PO
15
PO
16
PO
17
PO
18
PO
19
PO
20
PO
21
PO
22
PO
23
PO
24
LO1   4 4 444   4   4     3
LO2   4 4 444   4   4     3
LO3   4 3 444   4   4     3
LO4   4 4 444   4   4     3
LO5   4 4 444   4   4     3
LO6   5 4 444   4   4     3
LO7   5 4 444   4   4     3
* Contribution Level : 1 Very low 2 Low 3 Medium 4 High 5 Very High
 
Ege University, Bornova - İzmir / TURKEY • Phone: +90 232 311 10 10 • e-mail: intrec@mail.ege.edu.tr