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.
- Identify the mathematical and/or real-world assumptions used in approaching a given problem and evaluate the reasonableness of the conclusion in this context.
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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