Course Description: Mth251 introduces concepts of differential and integral calculus for Science, Mathematics, and Engineering students. Topics include limits and continuity; rates of change; the derivative of polynomial, rational, trigonometric, log and exponential functions; antiderivatives, and definite integrals. Topic presentation includes group activities, writing assignments and laboratory projects to emphasize concepts. The instructor and student will communicate concepts verbally, analytically, numerically, and/or geometrically (the “Rule of Four”).
Mth 251 has the competencies from Mth 111: College Algebra, Mth 112: Trigonometry, and Mth 113: Analytic Geometry; the course is college-transferable. Mth 251 is a 4 credit hour (quarter system) course and is the first course in the Calculus sequence.
Performance Based Outcomes in Mathematics
Students who successfully complete any mathematics course at Central Oregon Community College will be able to:
1. Work independently to explore mathematical applications and models, and to develop algebraic/symbolic, graphical, numerical, and narrative skills in solving mathematics problems.
2. Work as a member of a group/team on projects or activities that are designed to explore mathematical applications and models.
3. Use both written and oral skills to communicate about mathematical concepts, processes, complete mathematical solutions and their implications.
4. Use a variety of problem solving tools including symbolic/algebraic notation, graphs, tables, and narratives to identify, analyze, and solve mathematical problems.
5. Develop mathematical conjectures and use examples and counterexamples to examine the validity and reasonableness of those conjectures.
6. Create and analyze mathematical models of real world and theoretical situations, including the implications and limitations of those models.
7. Use appropriate technologies to analyze and solve mathematics problems, and verify the appropriateness and reasonableness of the solution(s).
Specifically, students who complete Math 251: Calculus I will be able to:
• understand and apply limits
• apply the basic techniques of differentiation and integration on polynomial, rational, trigonometric, exponential, and logarithmic functions to investigate the behavior of mathematical models
• understand, apply, and interpret the relationships between applied or theoretical
models and their derivatives or antiderivatives. Emphasis will given to applications of rates of change
• determine and analyze the rate of change of functions given function data from a graph, table of values, or formula
• use the topics from calculus in conjunction with the graphing calculator to obtain precise graphs of models, including a graphical analysis of rates of change, concavity, and extrema for the model
• write significant mathematics in at least one of the following formats:
Determine the solution or lack of solution to a multiple-step problem and develop the solution in a formal laboratory report.
Analyze, discuss in a team, and develop the solution to an open-ended problem and present that solution in the form of a formal technical report.