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Dec 06, 2024
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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 real-valued 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 non-removable
- State and apply the Intermediate Value Theorem
- Apply the basic rules of differentiation
- Define the derivative for real-valued 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 real-world problems
- Write models for real-world 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 real-valued 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 anti-derivatives 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 anti-derivatives 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 anti-derivatives 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 anti-derivatives of the hyperbolic functions
- Calculate derivatives and anti-derivatives of the inverse hyperbolic functions
- Solve simple differential equations
- Solve differential equations using separation of variables and anti-differentiation
- Solve differential equations involving exponential growth or decay
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