MTH 271
Syllabus

**Division**: Arts
and Sciences

**Curricula
in Which Course is Taught**:

**Course
Number and Title**: MTH
271, Applied Calculus I

**Credit
Hours**: 3 **Hours/Wk Lecture**: 3 **Hours/Wk Lab**: **Lec****/Lab Comb**:

I.
**Catalog
Description: **Presents limits, continuity,
differentiation of algebraic and transcendental functions with applications,
and an introduction to integration. Prerequisite: MTH 163 or MTH 166 or
equivalent. (Credit will not be awarded for both MTH 270 and MTH 271.) Lecture
3 hours per week.

II.
**Relationship
of the course to curricula objectives in which it is taught**:

This
course is required in the business transfer program and will count as a math
elective in other transfer programs.
Applications focus on topics in business and economics.

III.
**Required
background**:

MTH
163 or equivalent

IV.
**Course
Content**:

1. Precalculus Review

2. Cartesian Coordinates

3. Algebra of Functions

4. Functions and Mathematical Models

5. Limits, One Sided Limits and Continuity

6. The Derivative

7. Basic Rules of Differentiation

8. Product and Quotient Rules

9. Chain Rule

10. Marginal Functions in Economics

11. Higher Order Derivatives

12. Implicit Differentiation: Related Rates

13. Differentials and Applications of
First and Second Derivatives

14. Curve Sketching

15. Optimization

16. Exponential Functions

17. Logarithmic Functions

18. Compound Interest

19. Differentiation of Exponents

20. Differentiation of Logarithmic

21. Exponential Functions as Models

22. Anti Derivatives and Rules of Integration.

V. Students, upon completion
of this course, will be able to: |
VI. |

A.
Demonstrate their enhanced knowledge
of functions and mathematical models. B.
Evaluate limits and continuity. C.
Find derivatives of algebraic,
exponential, and logarithmic functions. D.
Use derivatives to find equations of
tangent lines, to sketch curves, and to solve maximum and minimum problems. E.
Apply derivatives to solve real world
problems. F.
Perform implicit differentiation and
solve related rates problems. G.
Find antiderivatives
(indefinite integrals) of algebraic and exponential functions. H.
Evaluate definite integrals. |
Students
will be evaluated by some combination of quizzes, tests, homework and exams
as defined by faculty |

VII.
**This course supports the following
objectives:**

**DCC Educational
Objectives:**

Critical
Thinking

Information
Literacy

Quantitative
Reasoning