The aim of the course is to teach the basic mathematical techniques, introducing at the same time a number of mathematical skills which can be used for the analysis of problems. The emphasis is on the practical usability of mathematics; this goal is mainly pursued via a large variety of examples and applications from these disciplines

Learning Outcomes

CTPO

TOA

Upon successful completion of the course, the students will be able to :

LO - 1 :

clasify numbers and understand functions and their properties

1,2,3,4,5,6,7,8,9,10,11,12,13

1

LO - 2 :

know the concepts of limit and continuity of functions

1,2

1

LO - 3 :

know the concepts of derivatives of functions

1,2

1

LO - 4 :

apply of the derivative to some engineering problems

1,2

1

LO - 5 :

know the concepts of integral of functions

1,2

1

LO - 6 :

apply the integration to some engineering problems and to some applications

1,2

1

CTPO : Contribution to programme outcomes, TOA :Type of assessment (1: written exam, 2: Oral exam, 3: Homework assignment, 4: Laboratory exercise/exam, 5: Seminar / presentation, 6: Term paper), LO : Learning Outcome

Contents of the Course

Functions, inverse functions, plotting the graphs of basic curves, transformation of graphs. Trigonometric functions, inverse trigonometric functions, logarithmic and exponential functions . Limit, rules of limit, continuity . Derivative of function, geometric meaning of derivative, rules of derivative, derivative of trigonometric functions, inverse trigonometric functions, logarithmic and exponential functions. Higher order derivative, chain rules, derivative of implicit functions, applications of derivative, concept of derivation. L?hospital rule, limit at infinity, Rolle Theorem and Mean Value Theorem, extrema of functions . Asymptotes, plotting graphs by observation of changes in functions . Indefinite integrals . Methods of integration, change of variable, integration by parts, integration of polynomials, algebraic and trigonometric (rational) functions . Riemann sums, definite integration and properties, fundamental theorem of analysis. Applications of definite integrals: areas of regions, length of curves, volumes of rotating objects, surface arease, calculation of mass, moment, gravitational center and work. Change of variables for definite integrals. Generalization of integration . Sequences, series, alternating series, power series, series expansion of functions (Taylor and Maclaurin series)

Course Syllabus

Week

Subject

Related Notes / Files

Week 1

Functions, inverse functions, plotting the graphs of basic curves, transformation of graphs.

Week 2

Trigonometric functions, inverse trigonometric functions, logarithmic and exponential functions.

Week 3

Limit, rules of limit, continuity.

Week 4

Derivative of a function, geometric meaning of derivative, rules of derivative, derivative of trigonometric functions, inverse trigonometric functions, logarithmic and exponential functions

Week 5

Higher order derivative, chain rules, derivative of implicit functions, applications of derivative, concept of derivation.

Week 6

L'hospital rule, limit at infinity, Rolle Theorem and Mean Value Theorem, extrema of functions.

Week 7

Asymptotes, plotting graphs by observation of changes in functions

Week 8

Asymptotes, plotting graphs by observation of changes in functions

Week 9

Mid-term exam

Week 10

Methods of integration, change of variable, integration by parts, integration of polynomials, algebraic and trigonometric (rational) functions

Week 11

Riemann sums, definite integration and properties, fundamental theorem of analysis

Week 12

Change of variables for definite integrals. Short Exam.

Week 13

Applications of definite integrals: areas of regions, length of curves, volumes of rotating objects, surface arease, calculation of mass, moment, gravitational center and work.

Week 14

Generalization of integration

Week 15

Sequences, series, alternating series, power series, series expansion of functions (Taylor and Maclaurin series)

Week 16

End-of-term exam

Textbook / Material

1

Temel Matematik, Mustafa Balcı, Balcı Yayınları, 2008, 457 s., ISBN:9756683187.

Recommended Reading

1

Temel ve Genel Matematik 1?2, Kolektif, Üniversite Kitabevi, Elazığ, 2006.

2

Temel Matematik, İrfan Ertuğrul, Ekin Kitabevi Yayınları, 2006.

3

Genel Matematik, Ahmet Dernek, Nobel Yayın Dağıtım, 2005.

4

Çözümlü ve Alıştırmalı Genel Matematik, Ali Dönmez, Üniversiteli Kitabevi, 2007.

5

Matematik Analiz ve Analitik Geometri ?1, C. Henry Edwards, çev.: Ömer Akın, Palme Yayın Dağıtım, 2008.