MAT102

School of Humanities \ Mathematics

4

7

Compulsory

Turkish

MAT101

Faculty of Engineering Departments

This course includes the following topics:
Methods of integration, improper integrals, hyperbolic and inverse hyperbolic functions, infinite series, geometric series, harmonic series, convergence tests for series, absolute and conditional convergence, power series, term-by-term differentiation and integration, Taylor and Maclaurin series, polar coordinates, parametric forms, graphing in the polar coordinates, functions of several variables and their domains, graphing of functions of two variables, limits and continuity, partial derivatives, the chain rule, the total differential, directional derivatives, extrema of functions, region transformations, vector field, a geometrical mean of the partial derivatives, Leibnitz’s rule, double integrals, Jacobiens, applications of double integrals.

Course Book:
Thomas’ Calculus- Early Transcendentals (14th Ed.); Joel R. Hass, Maurice D. Weir, George B. Thomas; Pearson, 2019. ISBN: 978-0-13-443902-0
References:
• Kalkülüs Kavram ve Kapsam, 2. Baskı”, James Stewart, TÜBA, ISBN 975–8593–94–3.
• Calculus with Analytic Geometry (5th Ed.)”; C. H. Edwards and D. E. Penney; Prentice Hall, 1998.

Introducing fundamental mathematical background. Devoloping mathematical thinking and modeling techniques. Learn about limits, derivatives, integrals and their applications. Obtain problem determination, identification and solving skills.

1. Acquire fundamental mathematical knowledge and applies it to various disciplines.
2. Understand the applications of integrals in engineering by calculating the volume and surface area of rotational solids.
3. Analyze infinite sequences and series, determining their behavior using convergence tests.
4. Examine multivariable functions using concepts such as polar coordinates, limits, continuity, directional derivatives, and gradients.
5. Compute multiple integrals in rectangular, polar, cylindrical, and spherical coordinates to perform area and volume calculations in engineering applications.

Week 1: Applications of Integrals. Volume calculation using the disk method. Volume calculation using the cylindrical shell method.
Week 2: Arc length. Surface area of rotational solids. Infinite sequences and series. Sequences.
Week 3: Infinite series. Integral test. Comparison test. Absolute convergence; Ratio and root tests.
Week 4: Alternating series, absolute and conditional convergence. Power series (radius and interval of convergence). Taylor and Maclaurin series.
Week 5: Convergence of Taylor series. Applications of Taylor series.
Week 6: Parametric equations and polar coordinates. Parametrization of curves in the plane. Calculus with parametric curves. Polar coordinates.
Week 7: Graphs in polar coordinates. Area and arc length in polar coordinates. Partial derivatives. Concept of multivariable functions (level curves and level surfaces).
Week 8: Limits and continuity in higher dimensions. Partial derivatives.
Week 9: Chain rule. Directional derivatives and gradient vector. Tangent planes and differentials.
Week 10: Extreme values and saddle points. Lagrange multipliers. Multiple integrals. Double integrals over rectangles.
Week 11: Double integrals over general regions. Area calculation using double integrals. Double integrals in polar coordinates.
Week 12: Triple integrals in rectangular coordinates. Triple integrals in cylindrical and spherical coordinates.

• Midterm 40 %
• Final 60 %