**Semester:** **2019-2020 Spring**

**Instructor: Ekin UÄŸurlu**

** R-219 ****e-mail: ekinugurlu****@cankaya.edu.tr**

**Office Hours: **

**Catalog Description:**

Improper Integrals, Sequences and infinite series. Convergence tests for positive series. Alternating series test. Power series. Taylor and Maclaurin series. Applications of Taylor series. Functions of several variables. Limit and continuity, partial derivatives, the chain rule. Gradients and directional derivatives. Extreme values. Lagrange multipliers. Double integrals. Double integrals in polar coordinates. Triple integrals. Conservative fields. Line integrals. Path independence. Connected and simply connected domains. Green’s theorem in the plane.

Announcement

In order to have make-up

exams , students who missed

online exams because of

technical, health-related or

other problems have to write

petitions addressing their own

departments and specifying

their excuses.

**1. Midterm (%25): 13.03.2020**

**Quiz (%10): 6 May 17:30-18:30**

(The content of quiz: Improper integrals, Volumes by slicing, Solids of revolution, arc length, area of surfaces, polar coordinates)

**2. Midterm (%25): 20 May 17:30-19:30**

The content of second midterm: Sequences and Convergence; Infinite Series; Convergence Tests for Positive Series; Absolute and Conditional Convergence, Power Series, Taylor and Maclaurin Series, Applications of Taylor and Maclaurin Series, The Binomial Theorem and Binomial Series, Infinite products, Analytic Geometry in Three Dimensions, Vectors, The Cross Product in 3-Space, Planes and Lines, Vector Functions of One Variable, Curves and Parametrizations, Functions of Several Variables, Limits and Continuity

webonline: 30 March-26 April

**Final (%40): 17 June 11:00-13:00**

The content of Final exam:

The Riemann Integral

Fundamental Theorem of Caluculus, Mean Value Theorem for Integrals

Integration by Substitutions, Integration by Parts

Integrals of Rational Functions, Inverse Substitutions

Other Integration Techniques

Improper Integrals, Volumes by Slicing, Solids of Revolution

Arc length, Surface Area, Polar Coordinates and Polar Curves, Arc Lengths for Polar Curves

Sequences and Convergence, Cauchy Sequence, Infinite series, Convergence Tests for Positive series

Absolute and Conditional Convergence, Power Series, Taylor and Maclaurin Series The Binomial Theorem, Infinite Products, Convergence of Infinite Product

Analytic Geometry in Three Dimensions, Vectors, The Cross Product, Planes and Lines, Vector Functions of One Variable, Curves and Parametrization

Functions of Several Variables, Limits and Continuity

Partial Derivatives, Higher order Derivatives, The Chain Rule, Differentiability and Differentials

Gradients and Directional Derivatives, Implicit Functions, Taylor Series

Extreme Values, Extreme Values of Functions Defined on Restricted Domains, Lagrange Multipliers

__Make-up Exam:__ 29.06.2020 13:00-14:00

**Textbook:**

Calculus: A Complete Course, 8th ed., R. A. Adams and C. Essex, Pearson, 2010

**Reference Books:**

Calculus, Early Transcendental Functions, 3rd ed., R. Smith and R. Minton, McGraw-Hill, 2007

Thomas’ Calculus, 12th ed., G. B. Thomas, Jr. and M. D. Weir and J. Hass, Addison-Wesley, 2009

** Evaluation Criteria: ** 2 midterms %25 each, Final %40, Quiz %10