By their efforts in this course, students should improve in the following course-specific content areas: informal and formal definition of a limit, calculating limits, continuity, vertical and horizontal asymptotes, derivative as a limit, tangent lines, derivative rules for basic functions (power function, polynomial, exponential, logarithm, trigonometric, inverse trigonometric, hyperbolic), derivative rules for combinations of functions (sum, difference, product, quotient, chain), implicit differentiation, logarithmic differentiation, related rates, linear approximation, Mean Value Theorem, using derivatives to understand the graph of a function (increasing, decreasing, concavity, maxima, minima, inflection points), L'Hospital's rule, optimization, antiderivatives, area under a curve, definite integral as the limit of a sum, Fundamental Theorem of Calculus, indefinite integrals, integration by u-substitution.
Furthermore, Math 1210 satisfies the Quantitative Literacy requirement for General Education: Upon successful completion of the General Education Quantitative Literacy requirement, students will be able to:
- Communicate: Use correct terminology and proper notation to explain quantitative or mathematical relationships (equations, graphs, diagrams, tables, data) and to support an argument, assertion, or purpose using quantitative or mathematical evidence;
- Mathematization: Convert quantitative or mathematical information into appropriate mathematical representations and/or models such as equations, graphs, diagrams, or tables, including making and evaluating important assumptions as needed;
- Calculation: Use algebraic skills and techniques to solve problems, including the ability to identify and correct errors in calculations and understanding the role and proper use of technology in assisting with calculations;
- Analysis: Draw appropriate conclusions through quantitative or mathematical analysis of data or models, including understanding and evaluating important assumptions in order to recognize the limits of the analysis; and
- Application / Creation: Solve concrete and abstract problems across multiple disciplines.
MATH 1210 Calculus I requires students to convert mathematical information into various representations (equations, graphs) and use precise notation to explain relationships and support arguments. Students master algebraic skills and computational techniques to solve problems and apply these tools in concrete science and engineering contexts, which is the core of the application/creation outcome.