MAT 265 is a primary course for incoming freshmen in their first semester. It is a course required for the other maths courses throughout your journey at ASU. MAT 265 is considered to be a course that’s not too difficult but not too easy either. It has few concepts that will blow your mind and few that will please your mind. It is basically Calculus one. The concepts in MAT 265 are listed below:
1) Functions and Limits
The limit of a function is defined as the fundamental concept of calculus and analyzing the behavior of that function near a particular input. Functions and limit primarily include :
a) Approximate a limit at a point numerically with a calculator.
b) Find a limit at a point rigorously through common algebraic processes or with the Squeeze Theorem.
c) Continuity of a function at a point.
d) Be able to determine when a limit does not exist, including going to plus or minus infinity and find the limit at infinity
The concept of derivative is at the core of Calculus and modern mathematics. The definition of the derivative can be approached in two different ways. One is geometrical (as a slope of a curve) and the other one is physical (as a rate of change).
a) Derivatives and Rates of Change.
b) Find the derivative of a function using the limit definition.
c) Compute the derivative of a function at a point using the limit definition. d) Find the derivative of all of the basic functions.
e) Use the rules of differentiation (sum/difference, constant multiplier, product, quotient, and chain rule) to differentiate combinations of functions.
f) Find an equation of the line tangent to a curve, whether the curve is given explicitly or implicitly.
g) Related Rates and linear approximations and differentials.
3) Exponential, Logarithmic, and Inverse Trigonometric Functions
In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are functions of an angle. They relate the angles of a triangle to the lengths of its sides.
a) Exponential, Logarithmic, Inverse Functions.
b) Derivative of Logarithmic and Exponential Functions.
c) Find the value of the derivative of the inverse of a function at a point.
d) Find the value of a limit using L’Hôpital’s rule.
4) Applications of Derivatives
The two main applications of derivatives are using derivatives to determine information about graphs of functions and optimization problems.
a) Use the derivative to graph a function, labeling local extrema and inflection points.
b) Mean value theorem.
c) Solve optimization problems.
d) Find antiderivatives of basic functions.
Integral is a function of which a given function is the derivative, i.e. which yields that function when differentiated, and which may express the area under the curve of a graph of the function.
a) Approximate the area or distance traveled of a function (velocity) using a small Riemann sum.
b) Evaluate definite integrals using the fundamental theorem of calculus.
c) Find antiderivatives of functions using the fundamental theorem of calculus.
Concepts involved in MAT 265 are written above. Making the most out of lectures can be very important to the overall college experience so you should not miss any MAT classes. Follow these five keys to make the most before finalizing MAT 265 as your course.