The aim of the course is to teach the basic mathematical techniques. Analyzing the two and three dimensional problems in engineering sciencies and introducing a number of mathematical skills which can be used for the analysis of problems. The emphasis is on the practical usability of mathematics; this goal is mainly pursued via a large variety of examples and applications from these disciplines.

Learning Outcomes

CTPO

TOA

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

LO - 1 :

knows the concepts of matrix and determinant and enable to solve system of equations

1,2

1

LO - 2 :

knows the concepts of conic sections and express in polar coordinates.

1,2

1

LO - 3 :

know vectors in two and three dimensional spaces.

1,2

1

LO - 4 :

understand functions of two and three variables and their properties

1,2

1

LO - 5 :

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

1,2

1

LO - 6 :

know the concepts of derivative and apply it to engineering problems

1,2

1

LO - 7 :

know the concepts of integration and apply it to engineering problems

1,2

1

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

Matrices, determinants, eigenvalues and eigenvectors, inverse matrix. Systems of lineer equations and solutions by reduction to echelon form and Crammer rule. Conic sections and quadratic equations, polar coordinates and plotting graphs, parameterization of curves on plane. Three dimensional space and Cartesian coordinates. Vectors on the plane and space. Dot, cross and scalar triple product. Lines and planes on three dimensional space. Cylinders, conics and sphere. Cylindrical and spherical coordinates. Vector valued functions, and curves on the space, curvature, torsion and TNB frame. Multi variable functions, limit, continuity and partial derivative. Chain rule, directional derivative, gradient, divergence, rotational and tangent planes. Ekstremum values and saddle points, Lagrange multipliers, Taylor and Maclaurin series. Double integration, areas, moment and gravitational center. Double integrals in polar coordinates. Triple integrals in cartesian coordinates. Mass, moment and gravitational center in three dimensional space. Triple integrals in cylindrical and spherical coordinates. Change of variables in multiple integrals. Line integrals, vector fields, work, flux. Green's theorem on plane. Areas of surface and surface integrals. Stokes theorem, divergence theorem and applications.

Course Syllabus

Week

Subject

Related Notes / Files

Week 1

Matrices, determinants, eigenvalues and eigenvectors, inverse matrix.

Week 2

Systems of lineer equations and solutions by reduction to echelon form and Crammer rule.

Week 3

Conic sections and quadratic equations, polar coordinates and plotting graphs, parameterization of curves on plane

Week 4

Three dimensional space and Cartesian coordinates. Vectors on the plane and space. Dot, cross and scalar triple product.

Week 5

Lines and planes on three dimensional space. Cylinders, conics and sphere. Cylindrical and spherical coordinates.

Week 6

Vector valued functions, and curves on the space, curvature, torsion and TNB frame.

Week 7

Multi variable functions, limit, continuity and partial derivative.

Week 8

Chain rule, directional derivative, gradient, divergence, rotational and tangent planes.

Week 9

Mid-term exam

Week 10

Ekstremum values and saddle points, Lagrange multipliers, Taylor and Maclaurin series.

Week 11

Double integration, areas, moment and gravitational center. Double integrals in polar coordinates. Triple integrals in cartesian coordinates.

Week 12

Mass, moment and gravitational center in three dimensional space. Triple integrals in cylindrical and spherical coordinates. Change of variables in multiple integrals.

Week 13

Line integrals, vector fields, work, flux. Green's theorem on plane.

Week 14

Areas of surface and surface integrals.

Week 15

Stokes theorem, divergence theorem and applications.

Week 16

End-of-term exam

Textbook / Material

1

Thomas, G.B., Finney, R.L.. (Çev: Korkmaz, R.), 2001. Calculus ve Analitik Geometri, Cilt II, Beta Yayınları, İstanbul.

2

Balcı, M. 2009. Genel Matematik 2, Balcı Yayınları, Ankara