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Course Information

Course Information

Course Title	Code	Semester	L+U Hour	Credits	ECTS
ADVANCED CALCULUS I	UMAT257	3. Semester	4 + 0	4.0	6.0

Prerequisites

None

Language of Instruction	Turkish
Course Level	Bachelor's Degree
Course Type	Compulsory
Mode of delivery
Course Coordinator
Instructors
Assistants
Goals	To teach notions of convergence of sequences and series of functions, the radius and interval of convergence of power series, Taylor series, Fourier series and orthogonal functions, Complex Fourier series, Fourier series in general intervals, expansions on half intervals, to give the Dirichlet integral formula, Bessel inequality and Parseval equality.
Course Content	Pointwise and uniform convergence of sequences of functions, Relationship between uniform convergence, integral and derivative, Uniform convergence of series of functions and its relationship between integral and derivative, Derivative and the integral of the power series, Taylor series, Taylor's expansion of functions, Fourier series and orthogonal functions, Complex Fourier series, Fourier series in general intervals, expansions on the half intervals, Dirichlet integral formula, Bessel inequality and Parseval equality.
Learning Outcomes	1) Knows the notions of the sequences of functions searches the pointwise and uniform convergences 2) Knows the notions of the series of functions searches the pointwise and uniform convergences 3) Obtains the Taylor expansion of a function at a given point 4) Searches the radius and interval of the convergence of the power series 5) Understand the Fourier series and ortogonal functions 6) Learn the Complex Fourier series and Fourier expansions on the half intervals 7) Understand the Drichlet integral formula 8) Learn the Bessel inequality and Parseval equality