MATH& 151 Calculus I (5 credits)

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.

Degree Outcomes
Quantitative & Symbolic Reasoning: Graduates utilize mathematical, symbolic, logical, graphical, geometric, or statistical analysis for the interpretation and solution of problems in the natural world and human society.

Critical, Creative and Reflective Thinking: Graduates will evaluate, analyze, synthesize, and generate ideas; construct informed, meaningful, and justifiable conclusions; and process feelings, beliefs, biases, strengths, and weaknesses as they relate to their thinking, decisions, and creations.

Effective Communication: Graduates will be able to exchange messages in a variety of contexts using multiple methods.

Intercultural Engagement: Graduates demonstrate self-efficacy in intercultural engagement to advance equity, diversity, and inclusion through reflections and expressions of cultural humility, empathy, and social and civic engagement and action. Further, graduates examine how identities/positionalities such as races, social classes, genders, sexual orientations, disabilities, and cultures impact perceptions, actions, and the distribution of power and privilege in communities, systems, and institutions.

Lecture Contact Hours 50
Lab Contact Hours 0
Clinical Contact Hours 0
Total Contact Hours 50