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 2.0 or better; satisfactory placement test score; or instructor permission.
Course Description
This is the first of four courses in the calculus sequence. Topics include limits and derivatives, with an emphasis on the calculation and application of derivatives for algebraic, trigonometric, exponential, and logarithmic functions. Concludes with an introduction to antiderivatives.
Course Content
Limits Finding Limits Numerically, Graphically, and Algebraically Indeterminate Forms Limits at Infinity Limits and Continuity Derivatives Continuity And Differentiability Limit Definition of Derivative Derivative Rules Derivatives of Exponential, Logarithmic, Trigonometric and Inverse Trig Functions Derivatives of Inverse Functions Implicit Differentiation Higher Order Derivatives Applications of Derivatives Rates of Change Equation of the Tangent Line Related Rates Linear approximations and differentials Bernoulli’s (L’Hopital’s) Rule Extrema, Concavity, and Curve Sketching Optimization Antiderivatives
Student Outcomes
- Determine the continuity, differentiability, and end behavior of functions, algebraically and graphically using limits at real numbers and infinity.
- Compute derivatives and simple antiderivatives of algebraic and transcendental functions using rules of differentiation or implicit differentiation as appropriate.
- Use the first and second derivatives of a function to determine rates of change, intervals of increasing and decreasing, extrema, concavity, and other graphical features.
- Apply and transition between various meanings of the derivative, such as the local slope of a curve, the slope of a tangent line, a limit of a difference quotient, a rate of change, and a symbolic process that produces a new function.
- Use context to develop viable calculus-related problem-solving strategies, including the choice of appropriate representations of the derivative.
- Solve applied problems using techniques of differential calculus and communicate strategies and solutions in the context of the problem.
- Evaluate the reasonableness of a problem solution in the context of its mathematical and/or real-world assumptions.
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 craft and exchange ideas and information in a variety of situations, in response to audience, context, purpose, and motivation.
Lecture Contact Hours 50
Lab Contact Hours 0
Clinical Contact Hours 0
Total Contact Hours 50
Potential Methods
Discussions Written Assignments Projects Case Studies Presentations Homework Quizzes Objective Tests
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