MAT103

School of Humanities \ Mathematics

4

7

Compulsory

Turkish

-

Departments of Economics, Management and Psychology

This course includes the following topics:
Linear equations, inequalities, functions and graphs, limit and continuity of functions, the concept of derivative, differentiation techniques, chain rule, implicit derivatives, derivatives of trigonometric functions, derivatives of exponential and logarithmic functions, the concept of differential, indeterminate forms in limits, the concept of asymptote, local extremum, first and second derivative tests, curve sketching, absolute extrema, optimization problems, anti-derivatives, indefinite integrals, integration methods, substitution technique, rational functions and simple fractions, integrals of trigonometric function, integration by parts.

Course Book:
• Calculus for Business, Economics, Life Sciences, and Social Sciences (12th Edition); Raymond A. Barnett, Michael R. Ziegler and Karl E. Byleen; Pearson International Edition
• İşletme, İktisat, Yaşam Bilimleri ve Sosyal Bilimler İçin Genel Matematik (12. Basımdan Çeviri), Nobel Yayıncılık (Türkçe Çeviri Editörü: Arif Sabuncuoğlu).
References:
• Kalkülüs Kavram ve Kapsam (2. Baskı); James Stewart, TÜBA (çeviri).
• Thomas’ Calculus-Early Transcendentals (11th Ed.-Media Upgrade); G.B. Thomas, M.D. Weir, J. Hass, F.R. Giordano; Pearson, 2008.

Gaining basic mathematical knowledge. To develop mathematical thinking and modeling techniques. Giving information about limits, derivatives and integrals of functions and their applications. Ability to identify, define and solve problems.

1. Gains basic mathematical knowledge and applies this knowledge to different disciplines.
2. Analyze the concept of functions, their graphs, limits and continuity properties.
3. Learn the rules of differentiation and use them in maximum-minimum problems and optimization applications.
4. Apply mathematical concepts to economic problems.
5. Draw graphs of functions using their derivatives and determine asymptotes.
6. Learn the concept of indefinite integral and apply various integration techniques.

Week 1: Set concept, real number system, ordering in real numbers, absolute value and its properties, number axis and intervals, orthogonal coordinate system in the plane, mathematical modeling
Week 2: The concept and types of functions, composite function, inverse function, operations on the set of functions, even and odd functions, partially defined functions, functions in economics: price-demand, income, expense and profit functions
Week 3: Curve drawing with elementary transformations, linear functions and lines in the plane, quadratic functions, polynomials, rational functions
Week 4 Exponential function, logarithm function, trigonometric and inverse trigonometric functions
Week 5: Limit concept and properties, infinite limits and limits at infinity, continuity concept and properties, types of discontinuity
Week 6: The concept of derivative and differentiation rules, the concept of differential, derivative of the composite function and chain rule, derivatives of trigonometric and inverse trigonometric functions, higher order derivatives
Week 7: Derivatives of implicit functions, derivatives of logarithm and exponential functions, indefinite states and limits, L'Hopital rule
Week 8: Increasing-decreasing functions, local maxima and minima, first and second derivative tests
Week 9: Horizontal, vertical and oblique asymptotes, graph drawings
Week 10: Absolute maximum and absolute minimum calculation, optimization problems, relative proportion problems
Week 11: Indefinite integral concept, basic integral formulas, method of changing variables, partial integration method
Week 12: Simple fractionation method, integration of trigonometric and inverse trigonometric functions

• Midterm 40 %
• Final 60 %