Math Courses

MAT 170

Brief  Calculus & Its Applications

3 credit hours

Description:

Provides an introduction to differential and integral calculus with applications in biological sciences, social sciences, physical sciences, or business. Analyzes algebraic, exponential, and logarithmic functions.  Students may not receive credit for MAT 170 if they have already received credit in either MAT 175

*Topics may include:

  • limits
  • differential and integration of algebraic functions
  • differential and integration of trigonometric functions
  • differential and integration of exponential functions
  • differential and integration of hyperbolic functions
  • inverse trigonometric functions with applications

*topics are not specifically listed in the catalog

Pre-requisites:  MAT 150 College Algebra (with or without MAT 100)  or placement

Testing Placement:

ACT 27 +

Compass 83-99

Competencies:

Upon completion of this course, the student can:

1.             Approximate limits graphically and numerically and evaluate limits analytically.

2.             List the conditions for the continuity of a function at a point and determine if a function is continuous or discontinuous at a point.

3.             Determine the intervals of continuity of a function.

4.             Evaluate infinite limits and limits at infinity.

5.             Define the derivative of a function and evaluate the derivative of a function using the definition.

6.             Evaluate the derivative of a function using differentiation rules for algebraic functions as well as product, quotient, and chain rules.

7.             Use the derivative of a function to find the equation of the line tangent to the graph of the function at a given point.

8.             Sketch the graph of a function using the first and second derivatives to determine the critical points, intervals on which the function is either increasing or decreasing, relative extrema, intervals on which the graph is either concave up or concave down, and inflection points of the graph.

9.             Perform implicit differentiation.

10.          Use derivatives to solve application problems including problems involving related rates and optimization for biological sciences, social sciences, physical sciences, or business.

11.          Define the differential and use differentials to approximate function values.

12.          Find indefinite and definite integrals of a function using integration rules for algebraic functions.

13.          Find definite and indefinite integrals using substitution.

14.          Find the average value of a function on an interval.

15.          Use definite integrals to find the area under a curve and the area between two curves.

16.          Determine if a function is differentiable or nondifferentiable at a point.

17.          Find the derivative and integral of functions including polynomial, rational, root, exponential, and logarithmic functions.

18.          Solve application problems using integrals for biological sciences, social sciences, physical sciences, or business.

 

Outline:

I.             Limits

                A.            Finding limits graphically

                B.            Approximating limits numerically

                C.            Finding limits analytically 

                D.            One-sided limits  

                E.            Continuity            

                F.             Infinite limits (f(x)→∞)   

                G.            Limits as x→∞  

                H.            Horizontal asymptotes

                I.             Vertical asymptotes

II.            Differentiation

                A.            Definition of the derivative              

                B.            Finding derivatives using the definition          

                C.            Finding the tangent line to the graph of a function      

                D.            Basic differentiation rules for algebraic functions, product and quotient rules, chain rule  

                E.            Finding the tangent line to a graph

                F.             Implicit Differentiation     

III.          Applications of Differentiation

                A.            Related rate applications  

                B.            Finding critical numbers    

                C.            First derivative test/increasing/decreasing     

                D.            Finding relative maxima and minima            

                E.            Concavity and inflection points      

                F.             Second derivative test       

                G.            Curve sketching  

                H.            Optimization applications

                I.             Differentials         

IV.          Integration           

                A.            Fundamental theorem of calculus  

                B.            Finding the average value of a function        

                C.            Properties of definite integrals          

                D.            Integration using substitution

V.            Applications of Integration

                A.            Area under curve

                B.            Area between two curves