MTH 271 Syllabus
Division: Arts and Sciences Date: January, 2014
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
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. Learner Outcomes
Students, upon completion of this course, will be able to:
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. Students will use calculators only after demonstrating mastery of essential deductive skills without them.
VII. This course supports the following objectives:
DCC Educational Objectives: