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 1009 CALCULUS I COMPULSORY 4 0 0 4

Offered By

Faculty of Engineering

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

PROFESSOR DOCTOR MUSTAFA ÖZEL

Offered to

Geophysical Engineering
Mechanical Engineering (Evening)
Textile Engineering
Mechanical Engineering
Civil Engineering
Environmental Engineering
Mining Engineering
Geological Engineering
Metallurgical and Materials Engineering
Civil Engineering (Evening)
Industrial Engineering
Geological Engineering (Evening)
Mining Engineering (Evening)

Course Objective

The aim of this course is to provide students with the ability to calculate, perform algebraic operations, and think critically about difficult problems using the basic concepts of calculus such as limits, derivatives, and integrals.

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 FUNCTIONS: Domain and Range of Functions, Function Types and Graphs, Limits and Continuity
2 LIMIT AND CONTINUITY: The Concept of Limit, One-Sided Limits: Right- hand Left-hand Limits
3 CONTINUITY: Limits at Infinity, Asymptotes - Horizontal, Vertical, Slant(oblique), and Curved Asymptotes, Continuity
4 DERIVATIVE: Rates of Change and Tangent Lines, Derivative Derivative Rules
5 Trigonometric and Hyperbolic Functions and Their Derivatives, Chain Rule, Higher Order Derivatives
6 Implicit Derivatives, Related Ratios Inverse Function Derivatives, Natural Logarithm Function and Exponential Function, Linear Approximations, Differentials
7 APPLICATIONS OF DERIVATIVES: Extreme Values of Functions, Mean Value Theorem and Applications, Concavity and Curve Sketching, Optimization Problems, Indefinite Forms and L'Hospital's Rule
8 INTEGRATION: Sigma Notation and Limits of Finite Sums, Areas as Limits of Finite Sums,
9 THE DEFINITE INTEGRAL: The Definite Integral and Its Properties, Fundamental Theorem of Calculus
10 TECHNIQUES OF INTEGRATION: Indefinite Integral and Substitution Method, Integration by Parts, Integration of Rational Functions by Partial Fractions, Trigonometric Integrals and Substitutions
11 APPLICATIONS OF THE DEFINITE INTEGRAL: Areas Between Curves
12 Volumes Using Cross-Sections, Volume Using the Cylindrical Shells
13 Lengths of Plane Curves, Arc Lengths, Areas of Surfaces of Revolution
14 Improper Integrals

Recomended or Required Reading

Textbook(s): Thomas' Calculus, Joel R.Hass, Christopher E.Heil, Maurice D.Weir, Przemyslaw Bogacki, 15th Edition, Pearson, 2023
Supplementary Book(s):
1. Calculus: Early Transcendantals , James Stewart , Saleem Watson , Daniel K. Clegg, 9th Edition, Pearson Edu., 2020
2. Calculus: A Complete Course, R. Adams & C. Essex, Addison Wesley, 10th Edition, 2023.
3. Schaum's Outline of Calculus, E. Mendolson, 7th Edition, Mc Grawn Hill, 2021.
4. Kalkülüs , Kavram ve Kapsam, James Stewart, 2. Baskı,TÜBA çevirisi Kasım 2010.
5. Kalkülüs - Robert A. Adams & Christopher Essex, Çev. M. Terziler & T. Öner, Palme Yayıncılık, 2023.
6. Thomas Kalkülüs 12. Baskı, Joel R.Hass, Christopher E.Heil & Maurice D.Weir, Pearson, Çev. M. Bayram, 2023.

Planned Learning Activities and Teaching Methods

The development of creative thinking should be combined with basic education through
lesson presentations, problem solutions and applications.

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

Midterm Exam (%50)+Final Exam (%50)+Condition Exam

Language of Instruction

Turkish

Course Policies and Rules

Attendance at 70% of classes is mandatory.

Contact Details for the Lecturer(s)

Prof.Dr. Mustafa ÖZEL - mustafa.ozel@deu.edu.tr

Office Hours

Wednesday (08.30 / 10.30)

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 14 4 56
Preparations before/after weekly lectures 14 2 28
Preparation for midterm exam 1 5 5
Preparation for final exam 1 7 7
Midterm 1 2 2
Final 1 2 2
TOTAL WORKLOAD (hours) 100

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10PO.11PO.12
LO.1544342333
LO.2544342444
LO.3544443433
LO.4544342423
LO.5544342434
LO.6444444444444

CONTACT INFORMATION
Dokuz Eylül Üniversitesi Cumhuriyet Bulvarı No: 144 35210 Alsancak / İZMİR
Phone: +90(232) 412 12 12 - Fax: +90 (232) 464 81 35

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