Akademik Dersler - İçerik

Define the basic concepts of mathematics.
Define the real number system.
Define the equations of straight lines, circles, parabolas, ellipses and hyperbolas in the plane.
Explain functions, the domain and range of functions.
Perform the operation connected with functions.
Define the concepts of limit and continuity.
Describe the behavior of a function at a point with the help of its limit.
Calculate the limits of functions using limit rules.
Evaluate the limits at infinity and infinite limits.
Define the continuity of a function at a point with the help of the limit concept.
Express the concept of derivative.
Find the equation of the straight line tangent to a given curve at a point.
Define the concept of derivative.
Calculate derivatives of functions using differentiation rules.
Interpret the Mean-Value Theorem geometrically.
Define the concept of inverse of a function.
Express the conditions of existence of the inverse of a function.
Find the inverse of a function if it exists.
Define the exponential and logarithmic functions.
List the properties of exponential and logarithmic functions.
Define inverse trigonometric and hyperbolic functions.
List the properties of inverse trigonometric and hyperbolic functions.
Calculate the derivative of the inverse function at a point.
Apply the concept of derivative to the related rates, extreme values and sketching the graph of a function.
Classify the extreme values of a function.
Determine the increasing and decreasing intervals of a function and its concavity with the help of its derivative.
Sketch the graph of a function.
Evaluate indeterminate forms.
Find the Taylor polynomial of a function at a point.
Define the concept of definite integral of a function.
Express the area of planar regions as a limit of an infinite sum.
Define the definite integral.
List the properties of definite integral.
Calculate integrals of certain functions using the properties of the definite integral.
Express the Fundamental Theorem of Calculus.
Compute indefinite and definite integrals using by techniques of integration.
Use the method of substitution and integration by parts to evaluate integrals.
Evaluate integrals using inverse substitution.
Calculate integrals of rational functions.
Analyze the convergence of improper integrals.