Akademik Dersler - İçerik

Will be able to explain the fundamental concepts related to real numbers, sequences, and series.
States the algebraic, order, and completeness properties of real numbers.
Determines whether a sequence is convergent.
Explains the concepts of subsequences, accumulation points, limit inferior, and limit superior.
Analyzes the convergence of a series.
Explains series with positive terms, alternating series, and absolute convergence.
Will be able to analyze the concepts of limits and continuity.
States the definitions of the limit and continuity of a function at a point.
Characterizes limits and continuity by means of sequences.
Explains the relationship between limits and continuity.
Explains the fundamental properties of continuous functions on compact intervals.
Will be able to use the concept of derivative and fundamental theorems.
Defines and interprets the concept of derivative.
States Fermat's theorem, Rolle's theorem, and the mean value theorem.
Determines the intervals where a function is increasing or decreasing.
Determines local and absolute maximum and minimum points.
Applies the concept of derivative to practical problems.
Will be able to explain different types of differentiable functions.
Explains functions that are continuously differentiable up to a certain order.
Explains functions that are infinitely differentiable.
Will be able to analyze function sequences and series.
Explains the concepts of pointwise and uniform convergence.
Computes the radius of convergence of power series.
Explains binomial series.
Will be able to explain Taylor theorem and the concept of analytic functions.
States Taylor theorem.
Explains the condition for a function to be analytic.
Will be able to define elementary functions via series.
Defines exponential and logarithmic functions via series.
Defines trigonometric and inverse trigonometric functions via series.
Explains the fundamental properties of these functions.
Will be able to perform operations on function sequences and series.
Computes the derivative of function sequences and series.