COURSE UNIT TITLE

: MATHEMATICS I

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
MAT 1037 MATHEMATICS I COMPULSORY 4 0 0 4

Offered By

Biology

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

DOCTOR VOLKAN ÖĞER

Offered to

Biology

Course Objective

The aim of this course is to teach 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 graph the basic transcendental functions and their inverses using their properties.
2   Will be able to express the continuity and limit concepts theoretically and graphically.
3   Will be able to use calculus in applied problems by interpreting the derivative and integral concept geometrically and physically.
4   Will be able to find the derivative of the functions using the differentiation rules.
5   Will be able to draw the graph of a function using the sign of its first and second derivative by finding the local maximum and local minimum values, absolute maximum and absolute minimum values and inflection points if any.
6   Will be able to estimate the definite integral using Riemann sums.
7   Will be able to apply the Fundamental Theorem of Calculus to evaluate definite integrals using integration techniques.
8   Will be able to evaluate areas, volumes and arc lengths by definite integrals.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 Real number and functions; trigonometric functions, exponential functions, inverse functions, logarithm function, inverse trigonometric functions, hyperbolic and inverse hyperbolic functions
2 Limit of a function and limit laws, precise definition of limits
3 Continuity; limits involving infinity, asymptotes
4 Tangent line, rate of change, derivative, linearization and differentials, differentiation rules
5 Chain rule, implicit differentiation, derivative of inverse functions, Mean Value Theorem, finding limits of indeterminate forms using L Hôpital s Rule
6 Monotonic functions and the First Derivative Test, concavity and curve sketching, graphing functions using the sign of its first and second derivative
7 Extreme values of functions, maximum/minimum problems, application problems: optimization and related rates problems
8 Area under curves, Riemann sums, definite integral
9 Antiderivatives and indefinite integral, the Fundamental Theorem of Calculus
10 Techniques of integration: substitution, integration by parts, trigonometric integrals, trigonometric substitutions, integration of rational functions
11 Area between curves, definition of the logarithm as an integral and definition of the exponential function as its inverse, improper integrals
12 Volumes using cross-sections and cylindrical shells, arc length of curves
13 Parametrizations of plane curves, graphing parametric curves, graphing in polar coordinates, areas and arc length in polar coordinates
14 Physical applications of integration: Exponential change (half-life, Newton s Law of Cooling, etc.), work, moments and center of mass

Recomended or Required Reading

Textbook(s): Stewart , J. Calculus Thomson, 2003
Supplementary Book(s): Hass , J., Weir, M. D. and Thomas , G. B., Jr., University Calculus, Early Transcendentals ,International Edition, 2nd edition, Pearson, 2012.
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 VZ Vize
2 FN Final
3 BNS BNS VZ * 0.40 + FN * 0.60
4 BUT Bütünleme Notu
5 BBN Bütünleme Sonu Başarı Notu VZ * 0.40 + BUT * 0.60


Further Notes About Assessment Methods

None

Assessment Criteria

To be announced.

Language of Instruction

Turkish

Course Policies and Rules

To be announced.

Contact Details for the Lecturer(s)

e-mail : volkan.oger@deu.edu.tr
office: Faculty of Science, B251-3, phone:18580

Office Hours

Will be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 14 4 56
Preparations before/after weekly lectures 14 1 14
Preparation for midterm exam 1 15 15
Preparation for final exam 1 15 15
Midterm 1 2 2
Final 1 2 2
TOTAL WORKLOAD (hours) 104

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10PO.11PO.12PO.13PO.14
LO.13
LO.23343
LO.33
LO.433
LO.53
LO.63
LO.743
LO.833

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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