SANTA BARBARA CITY COLLEGE

ASSOCIATE DEGREE CREDIT COURSE OUTLINE

 

Department:    Mathematics

Subject Area and Course Number:   Mathematics 150

Course Title:   Calculus with Analytic Geometry I

Discipline:         Mathematics

Units:   5

Repeatability:   None

 

Catalog Course Description:  Limits, derivatives and integrals of algebraic, trigonometric, exponential and logarithmic functions. Differentials and applications of the derivative.  Introduction to Differential equations.

 

Description for Schedule of Classes: Limits, derivatives and integrals of algebraic, trigonometric, exponential and logarithmic functions. Differentials and applications of the derivative.  Introduction to Differential equations.

Lecture Hours per Week:   5. 3            (80-90 Total Semester Hours)

Laboratory Hours per Week:   None

Plus Hours:       None

Prerequisites:  Math 138 with a 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:   

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

2.            Demonstrate an understanding of the definite integral as the limit of an approximating sum.

3.            Calculate derivatives and definite integrals graphically and algebraically.

4.            Use derivatives and definite integrals to solve problems in science and other areas.

5.            Demonstrate an understanding of the Fundamental Theorem of Calculus.

6.            Develop graphical, numerical, and analytical techniques to analyze and solve separable differential equations.

 

Course Content and Scope:   

1.        Limits

a.        Intuitive and geometric idea of a limit

b.        Calculation of limits

c.        One- and two- sided limits and limits at infinity

d.        Continuity

e.        L'Hopital's Rule

2.        Derivatives

a.        Definition of the derivative

b.        Interpretation as slope and rate of change

c.        Computation of derivatives; sum, product, quotient and chain rules and implicit differentiation

d.        Differentials

3.         Applications of the derivative

a.         Motion of a particle

b.         Related Rates

c.         Maximizing and minimizing

d.         Curve sketching

e.         Economic Applications (optional)

f.          Newton's Method

4.         The definite integral

a.         Riemann sums and the definition of the integral

b.         Properties of the integral

c.         The Fundamental Theorem of Calculus and evaluation of integrals

d.         Indefinite integrals

e.         Areas under and between curves

5.         Inverse functions

a.         The logarithm as an integral and the exponential as its inverse

b.         Exponential growth and decay

c.         The inverse trigonometric functions

6.         Differential Equations

a.         Slope Fields

b.         Euler's Method

c.         Separation of Variables

 

Methods of Instruction:    Lecture is the primary activity, along with student problem-solving.  Students are expected to work outside of class on supplemental reading from the text and on assigned exercises.

 

Required Assignments:   

1.              Appropriate Readings:  Students are required to read assigned chapters in texts.  Outside readings are generally not required.

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.  They must also analyze logical arguments for validity and write proofs of their own using both inductive and deductive reasoning within a logical system.

 

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 analysis of logical arguments.  Such measures will include at least three exams and a comprehensive final examination requiring demonstrations 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 and familiarity with mathematical vocabulary. Calculator (or computer use) is incorporated in the course.  Students are expected be able to perform differentiation and integration "by hand."

Appropriate Texts and Supplies:  

Stewart, Calculus with Early Transcendentals, 6th Ed., Cengage Publishing, 2008

Rogawski, Calculus with Early Transcendentals, 1st Ed., Freeman Publishing, 2008

TI-84 Graphing Calculator, Maple, or equivalent computer algebra system

 

Student Learning Outcomes:

1.                  Evaluate limits and use them to find derivatives and integrals.

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.

5.                  Solve elementary first-order differential equations.

 

 

 

 

 

CO/mej

Revised August 2006; 8/24/09

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