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Nov 21, 2024
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MATH& 151 Calculus I (5 credits)
Distribution Area Fulfilled Natural Sciences; Quantitative and Symbolic Reasoning; General Transfer Elective
Formerly MATH 124 - CCN
Prerequisite MATH& 142 with a grade of at least 2.0, satisfactory placement test score, or instructor permission.
Course Description
Families of algebraic and transcendental functions and their derivatives. Limits, including indeterminate forms. Applications of differential calculus, anti-derivatives.
Student Outcomes
Limits and Continuity
1. Determine limits of functions at real numbers and at infinity using graphical, algebraic, and numerical techniques.
2. Use the definition of continuity to graphically and analytically determine whether a function is continuous.
3. Determine the differentiability of a function graphically and/or analytically.
4. Use the limit definition of the derivative to find the derivatives of polynomial functions.
Derivatives of Algebraic and Transcendental Functions
5. Calculate the derivatives of polynomial, rational, exponential, logarithmic, trigonometric, and inverse trigonometric functions by use of the basic rules of differentiation including the product, quotient, and chain rules, without use of technology.
6. Calculate derivatives of functions defined implicitly.
Applications of Derivatives
7. Determine average and instantaneous rates of change algebraically, graphically, and numerically, and interpret the rate of change in the context of the problem.
8. Determine the equations of tangent lines.
9. Sketch the graph of the first and second derivatives when given the graph of a function. Interpret the graph in the context of the problem.
10. Find global and local extrema, inflection points, intervals of increase/decrease, and intervals of concavity, and use these to sketch the graph of a function.
11. Apply differentiation to solve applications, including optimization and related rates, in a variety of fields such as physics, chemistry, biology, or economics.
12. Calculate linear approximations and/or differentials, and use them to solve problems such as approximating function values and/or calculating uncertainties.
13. Apply L’Hospital’s Rule to calculate limits of indeterminate forms, including 0/0, inf/inf, and 0*inf.
Anti-derivatives
14. Calculate anti-derivatives of power functions, polynomials, basic exponentials, and basic trigonometric functions.
General Content
15. Write clear, correct, and complete solutions to mathematical problems utilizing proper mathematical notation, units, and appropriate language.
16. Solve and analyze application problems that involve concepts covered in this course and in previous courses.
17. Use technology appropriately as a tool to solve problems.
18. Link graphical, numeric, and symbolic representations of derivatives when interpreting situations and analyzing problems.
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