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Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS MAT 1010 CALCULUS II COMPULSORY 4 0 0 6

Offered By

Computer Science

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

INSTRUCTOR VOLKAN ÖĞER

Offered to

Computer Science

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, 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 understand the convergence of sequences and series of real numbers and the tests for convergence of series. 2   Will be able to estimate a function by its Taylor polynomials when its Taylor series converges to the function. 3   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. 4   Will be able to find partial derivatives of functions using the Chain Rule. 5   Will be able to find the tangent plane to a surface at a point using partial derivatives and gradients. 6   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. 7   Will be able to evaluate double and triple integrals by iterated integrals using Fubini s theorem and by change of variables. 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 Sequences of real numbers, convergent sequences. 2 Limit theorems for sequences, commonly occurring limits, divergent sequences, divergence to infinity, subsequences, series of real numbers, convergent series, geometric series, divergent series 3 Basic tests for convergence of series: integral test, comparison tests, ratio and root tests; alternating series, absolute and conditional convergence 4 Power series, Taylor and Maclaurin Series, convergence of Taylor Series, Taylor s Theorem. 5 Vector functions and their derivatives, integrals of vector functions, arc length of curves in space. 6 Functions of several variables, limits and continuity in higher dimensions, partial derivatives and differentiability, the Mixed Partial Derivative Theorem 7 The Chain Rule, implicit differentiation; Directional derivatives and gradient vectors; tangent planes and differentials, linearization 8 Midterm 9 Taylor series of functions of two variables 10 Extreme Values and Saddle Points, Second Derivative Test; absolute maxima and minima on bounded closed regions, the method of Lagrange Multipliers for constrained maxima and minima 11 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 12 Triple integrals, volume by triple integration, triple integrals in cylindrical coordinates and spherical coordinates; substitutions in multiple integrals, change of variables; moments and centers of mass 13 Line integrals; vector fields, work, circulation, and flux; path independence, potential functions and conservative fields, exact differential forms; 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 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.Spivak, M.

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 FCGR FINAL COURSE GRADE (RESIT) MTE * 0.40 + FIN * 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 13 4 52 Preparations before/after weekly lectures 12 3 36 Preparation for midterm exam 1 20 20 Preparation for final exam 1 30 30 Final 1 2 2 Midterm 1 2 2 TOTAL WORKLOAD (hours) 142

Contribution of Learning Outcomes to Programme Outcomes

PO/LO PO.1 PO.2 PO.3 PO.4 PO.5 PO.6 PO.7 PO.8 PO.9 PO.10 PO.11 PO.12 PO.13 LO.1 5 4 3 5 3 LO.2 5 4 3 5 3 LO.3 5 4 3 5 3 LO.4 5 4 3 5 3 LO.5 5 4 3 5 3 LO.6 5 4 3 5 3 LO.7 5 4 3 5 3 LO.8 5 4 3 5 3