# COURSE UNIT TITLE

: CALCULUS II

#### 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

ASSOCIATE PROFESSOR MUSTAFA ÖZEL

#### Offered to

Electrical and Electronics Engineering
Computer Engineering

#### Course Objective

The sequence Math 1001-1002 is the standard complete introduction to the concepts and methods of calculus. It is taken by all engineering students. The emphasis is on concepts, solving problems, theory and proofs. Students will develop their reading, writing and questioning skills in Mathematics.

#### Learning Outcomes of the Course Unit

 1 Define the sequence of partial sum for an infinite series and relate the convergence of this sequence to the convergence of the series. Then find or estimate the sum. 2 Find the interval and radius of convergence for a given power series. 3 Understand and identify vectors in the plane and in the three dimensional space. 4 Find the total differential of a function of several variables and use it to approximate incremental change in the function. 5 Do simple manipulations involving gradient, divergence, and curl, and understand their geometrical/physical meaning. 6 Analyze and solve constrained and unconstrained optimization problems. 7 Evaluate multiple integrals either by using iterated integrals. 8 Understand vector fields, line integrals, and Green s theorem. Conservative Vector fields, and independence path. Surface integrals, divergence theorem and Stokes s theorem. 9 Understand vector fields, line integrals, and Green s theorem. Conservative Vector fields, and independence path. Surface integrals, divergence theorem and Stokes s theorem.

Face -to- Face

None

None

#### Course Contents

 Week Subject Description 1 Infinite series; Convergence tests for positive series; Power series, Taylor and Maclaurin series 2 Quadratic forms(Conic Sections) 3 Vectors and coordinate geometry in three dimensional space Analytic geometry in three dimensions, Plane, lines, and quadratic surfaces 4 Functions of several variables; Limits and continuitylı 5 Partial derivatives; Higher-order derivatives, The chain rule 6 1. Midterm 7 Linear approximation; Gradients and directional derivatives, Implicit functions 8 Applications of partial derivatives; Extreme values; Extreme values of functions defined on restricted domains 9 Lagrange multipliers; Multiple integration; Double integrals, iteration of double integrals in Cartesian- Coordinates 10 Surface area using by double integrals; Double integrals in Polar Coordinates 11 Vector and scalar fields; Line integrals 12 Conservative fields 13 Surface integrals; Green s theorem, divergence theorem, and Stokes s theorem. 14 Midterm Exam 2

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 MTE1 MIDTERM EXAM 1 2 MTE2 MIDTERM EXAM 2 3 FIN FINAL EXAM 4 FCG FINAL COURSE GRADE MTE1 * 0.25 + MTE2 * 0.25 + FIN * 0.50 5 RST RESIT 6 FCG FINAL COURSE GRADE MTE 1 * 0.25 + MTE 2 * 0.25 + RST * 0.50

*** Resit Exam is Not Administered in Institutions Where Resit is not Applicable.

None

#### Assessment Criteria

Percentage of mid-term exams is 25% to the course grade. L1-2-3-4-5-6 will be examined Percentage of final exam is 50% to the course grade. All learning targets (L1-2-3-4-5-6-7-8-9) will be examined.

English

To be announced.

#### Contact Details for the Lecturer(s)

Asst.Prof.Dr. Mustafa ÖZEL

#### Office Hours

Mondayi 9.00 - 11.00

#### Work Placement(s)

None

 Activities Number Time (hours) Total Work Load (hours) Lectures 14 4 56 Preparations before/after weekly lectures 14 2 28 Preparation for midterm exam 2 13 26 Preparation for final exam 1 13 13 Final 1 2 2 Midterm 2 2 4 TOTAL WORKLOAD (hours) 129

#### Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10PO.11PO.12PO.13
LO.154131
LO.254131
LO.354131
LO.454131
LO.554131
LO.654131
LO.754131
LO.854131
LO.954131