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 :

apply the integration to some engineering problems and to some applications

2,4,5

1

LO - 2 :

analize convergence of improper integrals.

2,4,5

1

LO - 3 :

analize convergence of sequences and series.

2,4,5

1

LO - 4 :

understand functions of two and three variables and their properties

2,4,5

1

LO - 5 :

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

2,4,5

1

LO - 6 :

know the concepts of derivative of functions of two variables and apply it to engineering problems

2,4,5

1

LO - 7 :

know the concepts of integration of functions of two variables and apply it to engineering problems

2,4,5

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

Riemann sums, definite integrals and their properties, Fundamental Theorem of Calculus.Change of variables in definite integrals
Applications of definite integrals: areas of plane regions,Applications of definite integrals: Volume computations (disk and cross-section methods) length of parametric curves, areas of surfaces of revolution.Improper integrals (Type 1 and Type 2).Sequences and infinite series, (definitions of convergence and divergence, geometric series, n-th term test, p-series, alternating series).Series(absolute convergence, ratio and root tests) Power series and their convergence, Taylor and Maclaurin series.
Multivariable functions, limit, continuity and partial derivatives.Chain rule, directional derivatives,
Maximum and minimum, Lagrange Multipliers (Single constraint case) Double integrals and their applications (Area). Polar Coordinates ,Double integrals in Polar Coordinates and their applications (mass and density, center of mass ).

Course Syllabus

Week

Subject

Related Notes / Files

Week 1

Riemann sums, definite integrals and their properties, Fundamental Theorem of Calculus

Week 2

Change of variables in definite integrals and Area Between Curves

Week 3

Applications of definite integrals: Volume computations (disk, cross-section, the washer, the shell methods)

Week 4

Length of parametric curves, areas of surfaces of revolution

Week 5

Improper integrals (Type 1 and Type 2)

Week 6

Sequences and infinite series, (definitions of convergence and divergence, geometric series, n-th term test, integral test, ratio and root tests)

Week 7

Alternating series, absolute and conditional convergence, power series

Week 8

Taylor and Maclaurin series

Week 9

Mid-term exam

Week 10

Multivariable functions, limit, continuity and partial derivatives.

Week 11

Chain rule, directional derivatives and gradient

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

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

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