Santa Barbara City College Course Outline

MATH 130 - Calculus for Biological Sciences, Social Sciences and Business I

MATH 130
Calculus for Biological Sciences, Social Sciences and Business I
Disciplines
Mathematics (Masters Required)
5.000
0 - May not be repeated
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, and related rates and applications.
80.000-90.000 Total Hours
Total Hours
160.000-180.000 Total Hours
80.000-90.000 Total Hours
Prerequisite: MATH 137 or equivalent based on SBCC's Assessment Center placement via multiple measures
Prerequisite or Corequisite: None
Concurrent Corequisite: None
Course Advisories: None
Limitation on Enrollment: None
Course Objectives:
Demonstrate an understanding of the intuitive definition of a limit.
Demonstrate an understanding of a single derivative as a measure of the rate of change of a function.
Demonstrate a basic understanding of the definite integral as a limit of an approximating sum.
Demonstrate a basic understanding of the fundamental theorem of calculus.
Demonstrate an understanding of definite and indefinite integrals.
Use the above concepts to solve problems in business, economics, and life sciences.
Demonstrate the manipulative skills necessary for the above applications.
Student Learning Outcomes
MATH130 SLO1 - Evaluate limits and use them to find derivatives.
MATH130 SLO2 - Evaluate derivatives and recognize the connection between the derivative, the slope of a curve, and rates of change.
MATH130 SLO3 - Determine the behavior of a function from its derivatives and use them to solve optimization problems and other applications.
MATH130 SLO4 - Evaluate integrals and recognize the connection between the integral, the area bounded by curves, and total change.
  1. Preliminaries
    1. Equations and Inequalities in One Variable
    2. Functions and Graphs
    3. Logarithmic and Exponential Functions
  2. Limits and the Derivative
    1. Limits and Continuity
    2. Increments, Tangent Lines and Rates of Change
    3. The Derivative
    4. Derivatives of Powers, Constants, and Sums
    5. Derivatives of Products and Quotients
    6. The General Power Rule
    7. Applications of the Derivative
  3. Graphing and Optimization
    1. First and Second Derivatives and Graphs
    2. Optimization:  Maxima and Minima
    3. Curve Sketching Techniques:  Unified and Extended
    4. Differentials and Applications
  4. Additional Derivative Topics
    1. Derivatives of Logarithm and Exponential Functions
    2. Chain Rule
    3. Implicit Differentiation
    4. Related Rates
    5. Applications
  5. Integration
    1. Antiderivatives and Indefinite Integrals
    2. Integration by Substitution
    3. Definite Integral and Applications to Area
  6. Additional Integration Topics
    1. Techniques of Integration
    2. Areas and Volumes
    3. Numerical Integration
    4. Improper Integrals
Methods of Instruction
Directed Study
Discussion
Lecture
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
The volume of a cylinder is 48 pi cubic inches. The cost of the top and bottom is 3 cents per square inch and the cylindrical side is 5 cents a square inch. Represent the cost of the cylinder in terms of the radius.
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.
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."
    Applied CalculusHoffman, Bradley, -McGraw Hill, 2012
  • TI-84 Graphing Calculator
01/07/2019
Board of Trustees: 01/24/2019
CAC Approval: 01/14/2019