SANTA BARBARA CITY COLLEGE

ASSOCIATE DEGREE CREDIT COURSE OUTLINE

 

 

Department:     Mathematics

Subject Area and Course Number:     Mathematics 130

Course Title:    Calculus for Biological Sciences, Social Sciences and Business I

Discipline:         Mathematics

Units:   5

Repeatability:     None

Catalog Course Description:   Calculus of one variable, limits, continuity, differentiation, Riemann approximations, definite and indefinite integrals; introduction to integration techniques, exponential and logarithmic functions, curve-sketching, maxima/minima problems, related rates and applications.

Description for Schedule of Classes:   Calculus of one variable, limits, continuity, exponential and logarithmic functions, curve-sketching, extrema, related rates and applications; indefinite and definite integrals, including basic techniques of integration. 

Lecture Hours per Week:   5.3  (80-90 Total Semester Hours)

Laboratory Hours per Week:    None

Plus Hours:       None

Prerequisites: Math 111 or Math 120 with grade of "C" or better or qualifying score on SBCC placement exam.

Co-Requisites:    None

Skills Advisories:    Eligibility for English 100 or English 103

Course Advisories:       None

Limitation on Enrollment:       None

Course Objectives:    At the end of this course, the student will be able to:

1.             Demonstrate an understanding of the intuitive definition of a limit.

2.            Demonstrate an understanding of a single derivative as a measure of the rate of change of a function.

3.            Demonstrate a basic understanding of the definite integral as a limit of an approximating sum.

4.            Demonstrate a basic understanding of the fundamental theorem of calculus.

5.            Demonstrate an understanding of definite and indefinite integrals.

6.            Use the above concepts to solve problems in business, economics, and life sciences.

7.            Demonstrate the manipulative skills necessary for the above applications.

 

Course Content and Scope:   

I.             Preliminaries

                A.           Equations and Inequalities in One Variable

                B.           Functions and Graphs

                C.           Logarithmic and Exponential Functions

II.           Limits and the Derivative

                A.           Limits and Continuity

                B.           Increments, Tangent Lines and Rates of Change

                C.           The Derivative

                D.           Derivatives of Powers, Constants, and Sums

                E.            Derivatives of Products and Quotients

                F.            The General Power Rule

                G.           Applications of the Derivative

III.          Graphing and Optimization

                A.           First and Second Derivatives and Graphs

                B.           Optimization:  Maxima and Minima

                C.           Curve Sketching Techniques:  Unified and Extended

                D.           Differentials and Applications

IV.          Additional Derivative Topics

                A.           Derivatives of Logarithm and Exponential Functions

                B.           Chain Rule

                C.           Implicit Differentiation

                D.           Related Rates

                E.            Applications

V.           Integration

                A.           Antiderivatives and Indefinite Integrals

                B.           Integration by Substitution

                C.           Definite Integral and Applications to Area

VI.          Additional Integration Topics

                A.           Techniques of Integration

                B.           Areas and Volumes

                C.           Numerical Integration

                D.           Improper Integrals

 

Methods of Instruction:    Lecture is the primary activity in class with student problem solving. Students are also expected to work outside of class on assigned exercises, reading from the text and supplemental reading as determined by the instructor.

 

Required Assignments:   

1.              Appropriate Readings:  Students are required to read assigned chapters in texts.

2.              Writing Assignments:  Students must work assigned mathematical problems requiring the manipulation of abstract symbols.

3.              Appropriate Outside Assignments:  Students will be expected to spend a sufficient amount of time outside of class to practice techniques taught during class time, read assigned materials, and complete frequent homework assignments.

4.              Appropriate Assignments that Demonstrate Critical Thinking:  Students must demonstrate mathematical skills which involve analyzing information, recognizing concepts in new contexts, and drawing analogies. 

 

Methods of Evaluation:   A student's grade will be based on multiple measures of performance in the solving of problems, preparation and analysis of graphs, and an analysis of logical arguments.  Such measures will include at least three exams and a comprehensive final examination requiring demonstration of problem-solving skills.  In addition, instructors may make use of quizzes, written homework assignments, or other appropriate means to judge a student's dexterity with mathematical skills. Calculator (or computer use) is incorporated in the course.  Students should be able to perform differentiation and some basic integration "by hand."

 

Appropriate Texts and Supplies:  

Hoffman, Bradley, Applied Calculus, 9th Ed., 2007

TI-84 Graphing Calculator

 

 

Student Learning Outcomes:

1.                  Evaluate limits and use them to find derivatives.

2.                  Evaluate derivatives and recognize the connection between the derivative, the slope of a curve, and rates of change.

3.                  Determine the behavior of a function from its derivatives and use them to solve optimization problems and other applications.

4.                  Evaluate integrals and recognize the connection between the integral, the area bounded by curves, and total change.

 

 

CO/mej

Revised August 2006; 8/24/09

FRC (WPC)