# COURSE UNIT TITLE

: CALCULUS I

#### Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
MAT 1001 CALCULUS I COMPULSORY 4 0 0 5

#### Offered By

Faculty of Engineering

#### Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

#### Course Coordinator

ASSOCIATE PROFESSOR MUSTAFA ÖZEL

#### Offered to

Electrical and Electronics Engineering
Computer Engineering

#### Course Objective

The sequence Math 1001-1002 is the standard complete introduction to the concepts and methods of calculus. It is taken by all engineering students. The emphasis is on concepts, solving problems, theory and proofs. Students will develop their reading, writing and questioning skills in Mathematics.

#### Learning Outcomes of the Course Unit

 1 Interpret a function from an algebraic, numerical, graphical and verbal perspective and extract information relevant to the phenomenon modelled by the function. 2 Verify the value of the limit of a function at a point using the definition of the limit. 3 Find points of discontinuity for functions and classify them. 4 Show whether a function is differentiable at a point. 5 Find the derivative of elementary polynomials, exponential, logarithm and trigonometric functions. 6 Interpret the definite integral geometrically as the area under a curve and the volumes of solids using the areas of their cross-sections.

Face -to- Face

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#### Course Contents

 Week Subject Description 1 Preliminaries, Functions Limits and Continuity Limit ve Süreklilik 2 Differentiation, Tangent Lines and Their slopes 3 The Derivative Differentiation Rules The Chain Rule 4 Derivatives of Trigonometric Functions Higher Order Derivatives The Mean Value Theorem Implicit Differentiation Transcendental Function Inverse Functions, Exponential and Logarithmic Functions 5 The Natural Logarithm and Exponential The inverse Trigonometric Functions Hyperbolic Functions More Applications in Differentiation, Related Rates 6 1. Midterm 7 Indeterminate Forms Extreme Values Concavity and Inflections Içbükeylik ve Bükümler 8 Sketching the Graph of a Function Extreme-Value Problems Linear Approximations 9 Integration Sums and Sigma Notation Areas as Limits of Sums The Definite Integral Properties of the Definite Integral The Fundamental Theorem of Calculus 10 The Method of Substitution Areas of Plane Regions 11 Integration by Parts Integrals of Rational Functions Inverse Substitutions 12 Improper Integrals Applications of Integration 13 More Volumes by Slicing Arc Length and Surface Area 14 2. Midterm

Textbook(s): Thomas Calculus (12th Edition) , George B. Thomas, Maurice D. Weir,
Joel Hass, 2010.
Supplementary Book(s): Calculus, Robert A. Adams & Christopher Essex, 2008.

#### Planned Learning Activities and Teaching Methods

Teaching should combine basic education and training with the development of creative thinking and application.

#### Assessment Methods

 SORTING NUMBER SHORT CODE LONG CODE FORMULA 1 MTE1 MIDTERM EXAM 1 2 MTE2 MIDTERM EXAM 2 3 FIN FINAL EXAM 4 FCG FINAL COURSE GRADE MTE1 * 0.25 + MTE2 * 0.25 + FIN * 0.50 5 RST RESIT 6 FCG FINAL COURSE GRADE MTE 1 * 0.25 + MTE 2 * 0.25 + RST * 0.50

*** Resit Exam is Not Administered in Institutions Where Resit is not Applicable.

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#### Assessment Criteria

Percentage of mid-term exams is 25% to the course grade. L1-2-3-4 will be examined
Percentage of final exam is 50% to the course grade. All learning targets (L1-2-3-4-5-6) will be examined.

English

To be announced.

#### Contact Details for the Lecturer(s)

Asst.Prof.Dr. Mustafa ÖZEL

#### Office Hours

Monday (09.00 - 11.00)

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