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

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.  Learner Outcomes


Students, upon completion of this course, will be able to:

VI.  Evaluation

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:

Critical Thinking

Information Literacy

Quantitative Reasoning