COURSE UNIT TITLE

: CALCULUS III

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
MAT 2025 CALCULUS III COMPULSORY 3 2 0 6

Offered By

Statistics

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

PROFESSOR HALIL ORUÇ

Offered to

Statistics
Statistics(Evening)

Course Objective

The aim of this course to learn multivariable calculus, that is, vector-valued functions, geometry of curves in space, partial derivatives, surfaces and tangent planes, double and triple integrals, line integrals and surface integrals.

Learning Outcomes of the Course Unit

1   Will be able to investigate the geometry of a curve traced by a particle in space by finding its tangents, velocity, acceleration and arc length
2   Will be able to find partial derivatives of functions using the Chain Rule
3   Will be able to find the tangent plane to a surface at a point using partial derivatives and gradients
4   Will be able to find the local or absolute, or constrained, maxima and minima of functions of several variables using multivariable methods like Second Derivative Test and Lagrange Multipliers
5   Will be able to evaluate double and triple integrals by iterated integrals using Fubini s theorem and by change of variables
6   Will be able to evaluate line integrals and surface integrals

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 Vector functions and their derivatives, integrals of vector functions, arc length of curves in space.
2 Functions of several variables, limits and continuity in higher dimensions.
3 Partial derivatives and differentiability, the Mixed Partial Derivative Theorem
4 The Chain Rule, implicit differentiation; Directional derivatives and gradient vectors; tangent planes and differentials, linearization
5 Taylor series of functions of two variables
6 Extreme Values and Saddle Points, Second Derivative Test; absolute maxima and minima on bounded closed regions
7 The method of Lagrange Multipliers for constrained maxima and minima
8 Fubini s Theorem for calculating double integrals by iterated integrals over rectangles and over general regions, area by double integration, double integrals in polar form
9 Midterm
10 Triple integrals, volume by triple integration, triple integrals in cylindrical coordinates and spherical coordinates
11 Substitutions in multiple integrals, change of variables; moments and centers of mass
12 Line integrals; vector fields, work, circulation, and flux; path independence, potential functions and conservative fields, exact differential forms
13 Green s Theorem in the plane
14 Surfaces and area of surfaces, surface integrals and flux, Stokes Theorem, Divergence Theorem

Recomended or Required Reading

Textbook(s):
Stewart, J., Calculus: Concepts and Contexts, 2nd edition, Brooks/Cole.
Supplementary Book(s):
1. Hass , J., Weir, M. D. and Thomas , G. B., Jr., University Calculus, Early Transcendentals ,International Edition, 2nd edition, Pearson, 2012.Spivak, M.
References:
Materials: None

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 * 0.40 + FIN * 0.60
4 RST RESIT
5 FCG FINAL COURSE GRADE MTE * 0.40 + RST * 0.60

Further Notes About Assessment Methods

None

Assessment Criteria

To be announced.

Language of Instruction

English

Course Policies and Rules

Attendance to at least 70% for the lectures is an essential requirement of this course and is the responsibility of the student. It is necessary that attendance to the lecture and homework delivery must be on time. Any unethical behavior that occurs either in presentations or in exams will be dealt with as outlined in school policy. You can find the undergraduate policy at http://web.deu.edu.tr/fen

Contact Details for the Lecturer(s)

DEU Fen Fakültesi Matematik Bölümü
e-posta: ali.sevimlican@deu.edu.tr
Tel: 0232 301 85 84

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 13 3 39
Tutorials 13 2 26
Preparations before/after weekly lectures 12 4 48
Preparation for midterm exam 1 15 15
Preparation for final exam 1 30 30
Final 1 2 2
Midterm 1 2 2
TOTAL WORKLOAD (hours) 162

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10PO.11PO.12PO.13PO.14
LO.144
LO.2344
LO.33
LO.4355
LO.5555
LO.6555

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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