COURSE UNIT TITLE

: CALCULUS I

DEGREE PROGRAMMES

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

Aerospace Engineering
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.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

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 1
14 More Volumes by Slicing Arc Length and Surface Area 2

Recomended or Required Reading

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 MTE MIDTERM EXAM
2 FIN FINAL EXAM
3 FCG FINAL COURSE GRADE MTE * 0.50 + FIN * 0.50
4 RST RESIT
5 FCGR FINAL COURSE GRADE (RESIT) MTE * 0.50 + RST * 0.50


Further Notes About Assessment Methods

None

Assessment Criteria

Percentage of mid-term exam is 50% 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.

Language of Instruction

English

Course Policies and Rules

To be announced.

Contact Details for the Lecturer(s)

Assoc.Prof.Dr. Mustafa ÖZEL

Office Hours

Monday (09.00 - 11.00)

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 14 4 56
Preparation for midterm exam 2 13 26
Preparation for final exam 1 13 13
Preparations before/after weekly lectures 14 2 28
Final 1 2 2
Midterm 1 2 2
TOTAL WORKLOAD (hours) 127

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10PO.11PO.12PO.13
LO.15412
LO.25412
LO.35412
LO.45412
LO.55412
LO.65412

CONTACT INFORMATION
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Phone: +90(232) 412 12 12 - Fax: +90 (232) 464 81 35

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