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 1032 CALCULUS II 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

The aim of this course is to learn sequences and series of real numbers,Taylor series of functions and to learn basic concepts of multivariable calculus, that is, limit, continuity, derivative, integral of vector-valued functions, limit, continuity, partial derivatives, double and triple integrals of real-valued functions of several real variables and line integrals, surface integrals.

Learning Outcomes of the Course Unit

1   Will be able to understand theoretically and compututationally the convergence of sequences and series of real numbers by their precise definitions and the tests for convergence of series.
2   Will be able to find power series and Taylor series by their intervals of convergence.
3   Will be able to find the limit, continuity, derivative and integral of vector-valued functions.
4   Will be able to find the limit and continuity of a real-valued function of several variables.
5   Will be able to evaluate partial derivatives and directional derivatives.
6   Will be able to evaluate double and triple integrals.
7   Will be able to use partial derivatives, double and triple integrals in applied problems.
8   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 Completeness of the real number system, the least upper bound property, sequences of real numbers, convergent sequences, Monotone Convergence Theorem
2 Limit theorems for sequences, commonly occurring limits, divergent sequences, divergence to infinity, subsequences
3 Series of real numbers, convergent series, geometric series, divergent series
4 Basic tests for convergence of series: integral test, comparison tests, ratio and root tests; alternating series, absolute and conditional convergence
5 Power series, Taylor and Maclaurin Series, convergence of Taylor Series, Taylor's Theorem, Maclaurin series of basic transcendental functions and the binomial series
6 Vector functions, limit, continuity, derivative and integral of vector functions
7 Functions of several variables, limits and continuity in higher dimensions, partial derivatives, the Increment Theorem and differentiability, the Mixed Partial Derivative Theorem
8 The Chain Rule, implicit differentiation; Directional derivatives and gradient vectors; tangent planes and differentials, linearization
9 Review of the topics
10 Midterm
11 Extreme Values and Saddle Points, Second Derivative Test; absolute maxima and minima on bounded closed regions
12 The method of Lagrange Multipliers for constrained maxima and minima
13 Fubin's Theorem for calculating double integrals by iterated integrals over rectangles and over general regions, area by double integration, double integrals in polar coordinates
14 Triple integrals, volume by triple integration, triple integrals in cylindrical coordinates and spherical coordinates; substitutions in multiple integrals
15 Line integrals; vector fields, work, circulation, and flux; path independence, potential functions and conservative fields, exact differential forms; Green's Theorem in the plane
16 Surfaces and area of surfaces, surface integrals and flux, Stokes' Theorem, Divergence Theorem
17 Review of the topics

Recomended or Required Reading

Textbook(s): Hass , J., Weir, M. D. and Thomas , G. B., Jr., University Calculus, Early Transcendentals ,International Edition, 2nd edition, Pearson, 2012.

Supplementary Book(s):
a) Spivak, M. Calculus. Corrected third ed. Cambridge University Press, 2006.
b) Hubbard, J. and Burke Hubbard, B. Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach. Fourth edition. Matrix Editions, 2009.

References:
1) Callahan, James J. Advanced Calculus, A Geometric View. Springer, 2010.
2) Bressoud, D. M. Second Year Calculus, From Celestial Mechanics to Special Relativity, Springer 1991.
3) Edwards, H. M. Advanced calculus. A differential forms approach. Corrected reprint of the 1969 original. With an introduction by R. Creighton Buck. Birkhuser Boston, Inc., Boston, MA, 1994.
4) Bressoud, D. M. A Radical Approach to Real Analysis, Second edition. Mathematical Association of America, 2007.

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)

Asst.Prof.Dr. Didem COŞKAN ÖZALP
E-mail: didem.coskan@deu.edu.tr

Office Hours

Will be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 14 4 56
Tutorials 14 2 28
Preparations before/after weekly lectures 14 6 84
Preparation for midterm exam 1 20 20
Preparation for final exam 1 30 30
Midterm 1 1 1
Final 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
LO.75555
LO.855555

CONTACT INFORMATION
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Phone: +90(232) 412 12 12 - Fax: +90 (232) 464 81 35

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