The course aims to provide basic mathematical tools for engineering students.

Learning Outcomes

CTPO

TOA

Upon successful completion of the course, the students will be able to :

LO - 1 :

Analyse problems requiring vector and matrix algebra, including eigenvalue and eigenvector problems

1,2

LO - 2 :

Solve linear system of qquations

1,2

LO - 3 :

Analize convergence of sequences and series.

1,2

LO - 4 :

understand functions of two and three variables and their properties

1,2

LO - 5 :

know the concepts of limit and continuity of functions of two and three variables

1,2

LO - 6 :

know the concepts of derivative and apply it to engineering problems

1,2

LO - 7 :

know the concepts of integration and apply it to engineering problems

1,2

CTPO : Contribution to programme outcomes, TOA :Type of assessment (1: written exam, 2: Oral exam, 3: Homework assignment, 4: Laboratory exercise/exam, 5: Seminar / presentation, 6: Term paper), LO : Learning Outcome

Contents of the Course

Vektors, vektor algebra, lines and planes in space, matrices, system of linear equations, matrix algebra, Gauss elimination, eigenvalues and eigenvectors. Sequences, convergence of squences, series, convergence tests(integral ,comparision, ratio, and root tests). Power series and their convergence, Taylor series. Polar coordinates. Vector valued functions, curvature and acceleration. Multi-valued functions, limit, continuity, partial derivatives, chain rule, directional derivative, extreme values for functions of two variables, Lagrange multipliers. Double integrals, transformation of domains in double integrals, integration in polar coorrdinates, appli,cation of double integrals(mass, moment). Line integrals.

Course Syllabus

Week

Subject

Related Notes / Files

Week 1

Vectors and vector algebra, lines ann planes in space.

Week 2

Linear system of equations, matrices and matrix algebra.

Week 3

Gauss elimination method, eigenvalues and eigenfunctions.

Week 4

Squences and their convergence, series and their convergence.

Week 5

Convergence tests for series and power series.

Week 6

Taylor and Maclaurin series

Week 7

Conics, polar coordinate system

Week 8

Calculus of vector-valued functions

Week 9

Mid-term exam

Week 10

Multivariable functions, limit, continuity and partial derivatives.

Week 11

Chain rule, directional derivatives and gradient vectors

Week 12

Extreme values, absolute maxima and minima,Lagrange multipliers (Single constraint case)

Week 13

Double integrals and their applications (Area)

Week 14

Substitutions in Double Integrals, Double integrals in Polar Coordinates and polar curves and their applications (mass and density, center of mass ).

Week 15

General assessment

Week 16

Final exam

Textbook / Material

1

Dennis G. Zill, Warren S. Wright, Matematik Cilt II(Calculus Early Transcendentals, 4. basımdan çeviri) Çeviri Editörü: Prof. Dr. İsmail Naci Cangül, Nobel Yayınevi, 2011.

2

C. Henry Edwards, David E. Penney: Calculus, Matrix Version (6th Edition), Prentice Hall, 2003.