Course Information

Course Name	Turkish	Matematik I
	English	Mathematics I
Course Code	MAT 111E	Credit	Lecture (hour/week)	Recitation (hour/week)	Laboratory (hour/week)
Semester	1	5	4	2	-
Course Language		English
Course Coordinator		İrma Hacınlıyan
Course Objectives		1. To provide the concepts of functions, limits, continuity, differentiation and integration. 2. To provide the applications of differentiation and integration 3. To give an ability to apply knowledge of mathematics on engineering problems
Course Description		Preliminaries:Real Numbers and the Real Line, Lines, Circles,and Parabolas, Functions and Their Graphs, Identifying Functions; Mathematical Models, Combining Functions; Shifting and Scaling Graphs, Trigonometric Functions. Limits and Continuity: Rates of Change and Limits, Calculating Limits Using the Limits Law, The Precise Definition of a Limit, One-Sided Limitsa and Limits at Infinity, Infinite Limits and Vertical Asymptotes, Continuity, Tangents and Derivatives. Differentiation: The Derivative as a Function, Differentiation Rules, The Derivative as a Rate of Change, Derivatives of Trigonometric Functions, The Chain Rule and Parametric Equations, Implicit Differentiation, Related Rates, Linearization and Differentials. Applications of Derivatives: Extreme Values of Functions, The Mean Value Theorem, Monotonic Functions and the First Derivative Test, Concavity and Curve Sketching, Applied Optimization Problems, Indeterminate Forms and L’Hopital’s Rule, Newton’s Method, Antiderivatives. Integration: Estimating with Finite Sums, Sigma Notation and Limits of Finite Sums, The Definite Integral, The Fundamental Theorem of Calculus, Indefinite Integrals and the Substitution Rule, Substitution and Area Between Curves. Applications of Definite Integrals: Volumes by Slicing and Rotation About an Axis, Volumes by Cylindrical Shells, Lengths of Plane Curves, Moments and Centers of Mass, Areas of Surfaces of Revolution and the Theorems of Pappus. Transcendental Functions: Inverse Functions and Their Derivatives, Natural Logarithms, The Exponential Function, Exponential Growth and Decay, Inverse Trigonometric Functions, Hyperbolic Functions.
Course Outcomes		I. Compute the limit of various functions, use the concepts of the continuity, use the rules of differentiation to differentiate functions. II. Sketch the graph of a function using asymptotes, critical points and the derivative test for increasing/decreasing and concavity properties. III. Set up max/min problems and use differentiation to solve them. IV. Evaluate integrals by using the Fundamental Theorem of Calculus and apply integration to compute areas and volumes by slicing, volumes of revolution, arclength. V. Work with transcendental functions and evaluate integrals using techniques of integration.
Pre-requisite(s)		none
Required Facilities
Other
Textbook		Thomas’ Calculus, 11th Edition, G.B Thomas, M.D.Weir, J.Hass and F.R.Giordano, Addison-Wesley, 2005.
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