COURSE UNIT TITLE

: CALCULUS II

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
MAT 1002 CALCULUS II COMPULSORY 4 0 0 5

Offered By

Faculty of Engineering

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

DOCTOR MELTEM ALTUNKAYNAK

Offered to

Aerospace Engineering
Electrical and Electronics Engineering (English)
Computer Engineering (English)

Course Objective

The aim of this course to learn sequences and series of real numbers for Taylor series of functions and to learn multivariable calculus, that is, 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 understand the convergence of sequences and series of real numbers and the tests for convergence of series.
2   Will be able to find the interval and radius of convergence for a given power series.
3   Will be able to find the partial derivatives of a functions of several variables.
4   Will be able to find the tangent plane to a surface at a point using partial derivatives and gradients.
5   Will be able to analyze and solve constrained and unconstrained optimization problems.
6   Will be able to evaluate multiple integrals either by using iterated integrals.
7   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 Sequences of real numbers, convergent sequences. Series of real numbers. Basic tests for convergence of series.
2 Alternating series, absolute and conditional convergence.
3 Power series, Taylor and Maclaurin Series.
4 Planes, lines, and quadratic surfaces. Functions of several variables. Limits and continuity
5 Partial derivatives, Higher-order derivatives.
6 The Chain Rule, implicit differentiation.
7 Directional derivatives and gradient vectors; tangent planes and differentials, linearization.
8 Extreme values. Extreme values of functions defined on restricted domains.
9 The method of Lagrange Multipliers for constrained maxima and minima.
10 Calculating double integrals over rectangles and over general regions, area by double integration.
11 Double integrals in Polar Coordinates
12 Triple integrals, volume by triple integration, triple integrals in cylindrical coordinates and spherical coordinates
13 Line integrals, path independence, potential functions and conservative fields, Green s Theorem in the plane.
14 Surface integrals, Stokes Theorem, Divergence Theorem.

Recomended or Required Reading

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. Percentage of final exam is 50% to the course grade.

Language of Instruction

English

Course Policies and Rules

To be announced.

Contact Details for the Lecturer(s)

will be announced later

Office Hours

will be announced later

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 13 13
Preparation for final exam 1 25 25
Final 1 5 5
Midterm 1 2 2
TOTAL WORKLOAD (hours) 129

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10
LO.15434
LO.25353
LO.34453
LO.444533
LO.53335
LO.632243
LO.732243

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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