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 1031 CALCULUS I COMPULSORY 4 2 0 9

Offered By

Mathematics (English)

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

ASSISTANT PROFESSOR DIDEM COŞKAN ÖZALP

Offered to

Mathematics (English)
Mathematics (Evening)

Course Objective

This aim of this course is to learn the basic concepts of calculus for real valued functions of a real variable: Limit, Continuity, Derivative and Integral. We shall use these to find the slope of a curve at a point, to graph functions, to find the maximum and minimum values of a function, to find the area of a region bounded by curves, to find the length of curves, to find the volumes of solids bounded by surfaces, etc.

Learning Outcomes of the Course Unit

1   Will be able to define the basic algebraic and transcendental functions and their inverses together with their properties and graphs.
2   Will be able to express the limit and the continuity concepts of a real-valued function of a real variable theoretically, graphically and computationally.
3   Will be able to find derivatives of functions.
4   Will be able to use derivative in applied problems.
5   Will be able to evaluate definite and indefinite integrals.
6   Will be able to use integral in applied problems.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 The set of real numbers. Real-valued functions of a real variable. Trigonometric functions, exponential functions.
2 Inverse functions. Inverse trigonometric functions, logarithm functions, hyperbolic and inverse hyperbolic functions.
3 Limit of a function: Precise definition of limits, limit laws, limits involving infinity. Continuity of a function.
4 Derivative of a function: Tangent line, rate of change, definition of derivative, differentiation rules, derivatives of trigonometric, exponential, hyperbolic functions. Chain Rule.
5 Implicit differentiation, derivatives of inverse functions, Mean Value Theorem, linearization and differentials.
6 Applications of derivatives: Finding limits of indeterminate forms using L'Hopital Rule. Extreme values of functions, monotonic functions, the First Derivative Test.
7 Applications of derivatives: Concavity of functions, the Second Derivative Test, asymptotes, curve sketching.
8 Review and problem solving. Midterm.
9 Applications of derivatives: Optimization problems.
10 Integral of a function: Area under curves, Riemann sums, definite integral, the Fundamental Theorem of Calculus, antiderivatives, indefinite integral.
11 Techniquesof integration: the Substitution Method, Integration by Parts.
12 Trigonometric integrals, trigonometric substitutions.
13 Integration of rational functions.
14 Area between curves, improper integrals.
15 Applications of integrals: Volumes using cross sections and cylindrical shells, arc length of curves.
16 Review and problem solving.

Recomended or Required Reading

Textbook: Hass , J., Weir, M. D. and Thomas , G. B., Jr., University Calculus, Early Transcendentals ,International Edition, 2nd edition, Pearson, 2012.
Supplementary Book(s): Spivak, M. Calculus. Corrected 3rd ed. Cambridge University Press, 2006.
Materials: Instructor's notes and presentations

Planned Learning Activities and Teaching Methods

Lecture Notes, Presentation, Problem Solving

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

The weighted average of the student's midterm and final grades will be taken and the letter grade will be given according to the relative scoring method. If the student's letter grade is FD or FF, or a student except given exemption from attendance does not satisfy the requirement of attendance, she/he will be assumed to be unseccessfull.

Language of Instruction

English

Course Policies and Rules

Any unethical behavior that occurs either in lessons or in exams will be dealt with as outlined in school policy. You can find the document "Fen Fakültesi Öğretim ve Sınav Uygulama Esasları" at https://fen.deu.edu.tr/tr/belge-ve-formlar/ and the document "Önlisans ve Lisans Öğretim ve Sınav Yönetmeliği" at https://ogrenci.deu.edu.tr/regulations-and-directives/

Contact Details for the Lecturer(s)

E-mail: didem.coskan@deu.edu.tr
Office: B 351-3 (Faculty of Science, Block B, Third Floor)
Phone: +90 232 301 86 06

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 14 4 56
Tutorials 14 2 28
Preparation for midterm exam 1 20 20
Preparation for final exam 1 30 30
Preparations before/after weekly lectures 14 6 84
Final 1 1 1
Midterm 1 1 1
TOTAL WORKLOAD (hours) 220

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10PO.11PO.12PO.13
LO.15555
LO.25555
LO.355555
LO.45555
LO.555554
LO.655554

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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