MATH& 151 - Calculus I

5 Credits

Differential Calculus. 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.

Pre-requisite(s) MATH& 142 min 2.0
Placement Eligibility Math 151
Course Note Graphing Calculator Required; TI-84 recommended.
Fees

Quarters Typically Offered
Summer Day
Fall Day, Evening
Winter Day
Spring Day

Designed to Serve Transfer students in mathematics, engineering, and the sciences.
Active Date 20190626T13:17:48

Grading System Decimal Grade
Class Limit 32
Contact Hours: Lecture 55
Total Contact Hours 55
Degree Distributions:
AA

Quantitative Skills
Science

ProfTech Related Instruction

Computation

PLA Eligible Yes

Course Outline

Limits: Limits, continuity, L’Hospital’s Rule, and indeterminant forms
Derivatives: algebraic, trigonometric, inverse trigonometric, exponential, logarithmic, and higher derivatives. Also logarithmic and implicit differentiation
Curve sketching using the techniques of calculus
Introduction to antiderivatives
Applications: finding extrema, optimization problems, and related rates
Numerical methods: differentials and Newton’s method
Important theorems: the Mean Value Theorem, Extreme Value Theorem, and Intermediate Value Theorem

Student Learning Outcomes
Evaluate limits and interpret their meaning.

Determine the continuity of functions and justify reasoning using the formal definition.

Differentiate using the definition.

Differentiate a variety of functions using rules (power, chain, product, quotient, etc.).

Construct graphs of functions using calculus, by finding local extremes, inflection points, and asymptotes.

Compute numerical approximations using Newton’s Method and differentials.

Set up and solve applications, including optimization and related rates.

Compute elementary antiderivatives.