Understand and Use Derivatives - Learning Outcomes Calculus I | MAT 201 | Exams Calculus

MAT 201 CALCULUS I

Learning Outcomes

Demonstrate a knowledge and usage of Limits:

Understand the tangent line and area problems

State an informal definition of a limit

Estimate a limit graphically and numerically

Demonstrate how a limit fails to exist

Evaluate limits using properties of limits, analytically, and the Squeeze Theorem

Define and determine continuity at a point or on an open interval

Evaluate one-sided limits

Understand and use the Intermediate Value Theorem

Determine infinite limits

Find vertical asymptotes of a graph using limits

Understand and use derivatives

Find the slope of a tangent line to a curve at a point

Define a derivative using limits

Discuss the relationship between differentiability and continuity

Evaluate a derivative using basic rules including trigonometric functions

Find rates of change

Evaluate derivatives using the Product and/or Quotient rules

Find higher-order derivatives

Evaluate derivatives using the Chain Rule

Determine implicit and explicit functions

Find derivatives of implicit functions

Use related rates to solve application problems

Use derivatives to solve application situations:

Understand the concept of extrema of a function

Locate relative extrema and extrema on a closed interval

Utilize Rolle’s Theorem and the Mean Value Theorem

Determine intervals of increase and decrease using calculus techniques

Verify relative extrema using the First Derivative Test

Determine intervals of concavity and locate points of inflection

Verify relative extrema using the Second Derivative Test

Determine limits at infinity

Identify horizontal asymptotes using limits

Sketch and analyze a graph using calculus techniques

Solve optimization problems

Approximate a zero using Newton’s Method

Distinguish between dy and the actual change in y

Estimate propagated error and find differentials for a function

Understand and evaluate Integrals:

Define an antiderivative

Find antiderivatives using indefinite integrals

Find general and particular solutions to differential equations

Use sigma notation to write and evaluate a sum

Approximate and evaluate the area of a plane region

Define a Riemann sum

Evaluate definite integrals using limits

Use the Fundamental Theorem of Calculus to evaluate definite integrals

Understand and use the Mean Value Theorem for Integrals and the Second Fundamental Theorem of Calculus

Evaluate an indefinite integral using pattern recognition

Evaluate indefinite and definite integrals using a change of variable (Substitution)

Approximate a definite integral using the Trapezoidal Rule and Simpson’s Rule

Calculus techniques with transcendental functions:

Define and use natural logarithmic functions

Define the number e

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MAT 201 CALCULUS I

Learning Outcomes

Demonstrate a knowledge and usage of Limits:  Understand the tangent line and area problems  State an informal definition of a limit  Estimate a limit graphically and numerically  Demonstrate how a limit fails to exist  Evaluate limits using properties of limits, analytically, and the Squeeze Theorem  Define and determine continuity at a point or on an open interval  Evaluate one-sided limits  Understand and use the Intermediate Value Theorem  Determine infinite limits  Find vertical asymptotes of a graph using limits Understand and use derivatives  Find the slope of a tangent line to a curve at a point  Define a derivative using limits  Discuss the relationship between differentiability and continuity  Evaluate a derivative using basic rules including trigonometric functions  Find rates of change  Evaluate derivatives using the Product and/or Quotient rules  Find higher-order derivatives  Evaluate derivatives using the Chain Rule  Determine implicit and explicit functions  Find derivatives of implicit functions  Use related rates to solve application problems Use derivatives to solve application situations:  Understand the concept of extrema of a function  Locate relative extrema and extrema on a closed interval  Utilize Rolle’s Theorem and the Mean Value Theorem  Determine intervals of increase and decrease using calculus techniques  Verify relative extrema using the First Derivative Test  Determine intervals of concavity and locate points of inflection  Verify relative extrema using the Second Derivative Test  Determine limits at infinity  Identify horizontal asymptotes using limits  Sketch and analyze a graph using calculus techniques  Solve optimization problems  Approximate a zero using Newton’s Method  Distinguish between dy and the actual change in y  Estimate propagated error and find differentials for a function Understand and evaluate Integrals:  Define an antiderivative  Find antiderivatives using indefinite integrals  Find general and particular solutions to differential equations  Use sigma notation to write and evaluate a sum  Approximate and evaluate the area of a plane region  Define a Riemann sum  Evaluate definite integrals using limits  Use the Fundamental Theorem of Calculus to evaluate definite integrals  Understand and use the Mean Value Theorem for Integrals and the Second Fundamental Theorem of Calculus  Evaluate an indefinite integral using pattern recognition  Evaluate indefinite and definite integrals using a change of variable (Substitution)  Approximate a definite integral using the Trapezoidal Rule and Simpson’s Rule Calculus techniques with transcendental functions:  Define and use natural logarithmic functions  Define the number e

 Find derivatives and integrals involving the natural logarithmic function  Integrate rational and trigonometric functions  Identify one-to-one functions and the existence of an inverse  Find the derivative of an inverse function  Use properties of natural exponential functions  Differentiate and integrate natural exponential functions  Differentiate and integrate all exponential functions  Model compound interest and exponential growth problems  Use separation of variables to solve differential equations  Model growth and decay problems Use integration in applications:  Find the area of a closed region between two curves  Find the volume of a solid of revolution using the method of disks, washers, or shells  Find the volume of a solid with known cross-sections  Find the arc length of a smooth curve  Find the area of a surface of revolution General Education Demonstrate the ability to select and apply contemporary forms of technology to solve problems or compile information in the study of math. Read, analyze, and apply to new situations, written material related to the study of math. Write and speak clearly and logically in presentations and essays about topics in math. All written reports are expected to demonstrate the following competencies: Identify the problem to be discussed and state a position or hypothesis Select research material appropriate to the topic Research, interpret, and convey the topic using suitable resources and technologies, including Internet Use correct vocabulary, formats, and documentation of sources

Understand and Use Derivatives - Learning Outcomes Calculus I | MAT 201, Exams of Calculus

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Partial preview of the text

Download Understand and Use Derivatives - Learning Outcomes Calculus I | MAT 201 and more Exams Calculus in PDF only on Docsity!

MAT 201 CALCULUS I

Learning Outcomes