MAT104

School of Humanities \ Mathematics

4

7

Compulsory

Turkish

MAT103

Departments of Economics, Management and Psychology

This course includes the following topics:
Area by integrals and applications, improper integrals, introduction to differential equations and applications, number sequences and series, convergence tests for series, power series, Taylor and Maclaurin series, multivariable functions, partial derivatives and applications, maximum-minimum problems and Lagrange multipliers, method of least squares, multiple integrals and applications.

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.

To learn integral and its applications. To understand the basic properties of sequences and series. To learn the concept of partial derivative in multivariable functions.

1. Gain basic mathematical knowledge and apply this knowledge to different disciplines.
2. Understand and use how definite and indefinite integrals are applied to area, volume and surface calculations.
3. Gain the ability to solve problems in economics and psychology by mathematical modeling with differential equations.
4. Develop the ability to choose the right methods in mathematical analysis and calculations by examining the convergence criteria of sequences and series.
5. Ability to solve optimization problems by applying partial derivatives, chain rule and extremum calculations for functions of several variables.
6. To produce solutions to scientific problems by understanding double integrals and coordinate transformations and multidimensional calculations.

Week 1: Riemann sum, the concept of definite integral, calculating area with definite integral, area between two curves
Week 2: Volume calculation with perpendicular sections-slicing method, volume calculation with cylindrical shell method, first, second and third kind of improper integrals
Week 3: First order differential equations, separable differential equation, exact differential equation, linear differential equation, some applications of differential equations
Week 4: The concept of sequence, finite sequences, increasing-decreasing sequences, arithmetic-geometric sequences, convergence of sequences
Week 5: Series concept, harmonic series, geometric series, convergence of series with positive terms, comparison, ratio and root tests, alternating series, absolute convergent and conditionally convergent series
Week 6: Power series and convergence, radius of convergence and interval of convergence, series expansion of functions, Taylor and Maclaurin series
Week 7: Orthogonal coordinate system in three dimensional space, functions of two and three variables, level curves and level surfaces, distance between two points in space
Week 8: Limit and continuity concepts in functions of two variables, partial derivatives and general properties, higher order partial derivatives, chain rule
Week 9: Maximum-minimum calculus for functions of two variables, local and absolute extrema, Lagrange method
Week 10: Least squares method and its applications
Week 11 The concept of double integral, change of order of integration in double integrals and Fubini's theorem
Week 12: Area and volume calculation with double integrals, various applications

• Midterm 40 %
• Final 60 %