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MTH 251 - Calculus 1 (Differential Calculus) |
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Associated Term:
Summer 2022
Learning Objectives: Upon successful completion of this course, the student should be able to: 1. Understand the definition of the derivative as the limit of the difference quotient for a function. 2. Be able to use the definition of the derivative to find derivatives of certain elementary functions. 3. Find derivatives numerically utilizing technology. 4. Visualize and interpret derivatives graphically. 5. Understand and use the derivative of a function as a function in its own right. 6. Understand the development and use of procedures for differentiating polynomial, exponential, logarithmic, and trigonometric functions, including the inverse sine & inverse tangent functions. 7. Use the power, product, quotient, and chain rules to find derivatives of functions. 8. Use the technique of implicit differentiation to find derivatives of implicitly defined functions. 9. Find equations of tangent lines to the graphs of functions at specific points. 10. Understand local linearity and that the tangent line to the graph of a function at a specific point is the best linear approximation for the function at that point. 11. Use linear approximation to estimate function values. 12. Use the methods and techniques of differential calculus to solve a variety of application problems, including optimization and related rate problems. 13. Use a programmable graphing calculator as an effective tool in confirming analytical work and obtaining numerical and graphical results related to differential calculus. Required Materials: Technical Requirements: |

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