
MAT 211  Calculus I Credits: 5 Lecture Hours: 5 Lab Hours: 0 Practicum Hours: 0 Work Experience: 0 Course Type: Core Introduction to limits, continuity, differentiation, applications of the derivative, the definite and indefinite integral, numerical integration, exponential and logarithmic functions, other transcendental functions and introduction to differential equations. Prerequisite: Minimum ALEKS scores of 76% or MAT 121 and MAT 130 with a C or better, or MAT 129 with a C or better Competencies
 Establish the limit of a function
 Associate the proper limit symbolism with a given graphical situation
 Calculate limits of certain elementary functions
 Define the concept of limit for realvalued functions of one real variable
 Prove that a given limit statement is valid
 Compute limits involving the trigonometric functions
 Determine the continuity of functions
 State the conditions for the continuity of a function at a point
 Define continuity on an open interval and on a closed interval
 Identify intervals of continuity from a given graph
 Determine points of discontinuity
 Identify points of discontinuity as removable or nonremovable
 State and apply the Intermediate Value Theorem
 Apply the basic rules of differentiation
 Define the derivative for realvalued functions of one real variable
 Calculate the derivative of certain elementary functions directly from the definition
 Calculate derivatives using the appropriate rules for sums, products, and quotients
 State the connection between differentiability and continuity
 Calculate higher order derivatives
 Differentiate composite functions
 Calculate derivatives using the chain rule
 Compute derivatives by the method of implicit differentiation
 Set up and solve related rate problems
 Use the derivative to identify extrema
 Define relative maximums and minimums of a function
 Define and find critical values of a function
 Find the relative extrama of a function using the first and second derivative tests
 State and apply the Extreme Value Theorem
 Identify increasing and decreasing functions
 Define an increasing (and decreasing) function on an open interval
 Use the first derivative to determine if a function is increasing (or decreasing) on an interval
 Determine the open intervals on which a function is increasing and on which it is decreasing
 Identify the concavity of a function on an interval
 Define concave up (and concave down) on an open interval
 Use the second derivative to determine if a function is concave up (or concave down) on an interval
 Determine the open intervals on which a function is concave up and on which it is concave down
 Find vertical, horizontal and slant asymptotes of a function
 Define and locate the vertical asymptotes of a function
 Evaluate infinite limits of a function
 Use limits at infinity to determine the ?end behavior? of a function
 Use the end behavior of a function to identify any horizontal or slant asymptotes
 Apply the derivative to realworld problems
 Write models for realworld problems
 Set up and solve applied min/max problems
 Use the first and second derivative to graph certain elementary functions
 State the geometrical significance of the first and second derivatives
 State the physical significance for the first and second derivatives for rectilinear motion
 State and apply the mean Value Theorem for derivatives
 Calculate indefinite and definite integrals
 Calculate indefinite integrals for elementary functions
 Calculate Riemann sums in simple cases
 Define the concept of the definite integral for realvalued functions of one real variable
 Calculate the definite integral in simple cases directly from the definition
 State the first and Second Fundamental theorems of calculus
 Apply the fundamental Theorem of calculus to evaluate definite integrals
 State the mean Value Theorem for integrals
 Find inverse functions
 Determine whether a function is one to one
 Define the inverse of a function
 State the graphical relationship of inverse functions
 Find the derivative of an inverse function a specified point
 Calculate the logarithmic and exponential functions
 Define the logarithm function in the natural base e
 Demonstrate the basic properties of logarithms using the definition in 6.1
 Define logarithms in bases other than e.
 Calculate derivatives and antiderivatives of the logarithmic functions
 Define the exponential function in the natural base e.
 Define the exponential functions in based other than e
 Calculate derivatives and antiderivatives that are inverse trigonometric functions
 Calculate the inverse trigonometric functions
 Define the inverse trigonometric functions
 State the domain and range of the inverse trigonometric functions
 Calculate derivatives of the inverse trigonometric functions
 Recognize and calculate antiderivatives that are inverse trigonometric functions
 Calculate the hyperbolic trigonometric functions
 Define the hyperbolic trigonometric functions
 State the geometrical interpretation of the hyperbolic functions
 Calculate derivatives and antiderivatives of the hyperbolic functions
 Calculate derivatives and antiderivatives of the inverse hyperbolic functions
 Solve simple differential equations
 Solve differential equations using separation of variables and antidifferentiation
 Solve differential equations involving exponential growth or decay
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