Department Mathematics
Subject Area and Course Number
MATH 130
Title Calculus for Biological Sciences, Social Sciences and Business I
Disciplines
Mathematics (Masters Required)
Units
5.000

Repeatability 0 - May not be repeated
Catalog Course Description
A first course in Calculus, the study of change–how to measure, model, and predict changes in quantities we observe in our universe. An investigation of functions, relations, and mathematical models arising in business, biological sciences, and social sciences, through the concepts of limit, differentiation, and integration. Applications of the derivative such as linear approximation, related rates, and optimization. Applications of integration such as area, and total change. Understanding the connection between differential calculus/rate of change and integral calculus/accumulation through the Fundamental Theorem of Calculus. This course is intended for Business and/or Biology majors who have successfully completed precalculus in high school, or SBCC’s Math 137:College Algebra, or the equivalent. Students enrolling in Math 130 are eligible to concurrently enroll in Math 130C: Support for Calculus for the Biological Sciences, Social Sciences, and Business I; students with limited experience with college algebra/precalculus are especially encouraged, or may be required to do so. Students in Math 130 will demonstrate their learning of course outcomes through multiple methods of assessment, including at least 5 hours of controlled assessments in the form of in-person proctored exams/project presentations and a cumulative in-person proctored final exam.
Lecture Hours
80.000-90.000 Total Hours
Lab Hours
Total Hours
Out-of-Class-Hours
160.000-180.000 Total Hours
Total Contact Hours
80.000-90.000 Total Hours

Prerequisite: College algebra or equivalent or SBCC's Assessment Center placement via multiple measures
Prerequisite or Corequisite: None
Concurrent Corequisite: MATH 130C based on SBCC's Assessment Center placement via multiple measures
Course Advisories: None
Limitation on Enrollment: None

Course Objectives:
Express in words, visuals and/or computation, an understanding of the intuitive definition of a limit.
Calculate and apply derivatives as a measure of the rate of change of a function.
Express in words, visuals and/or computation an understanding of the definite integral as a limit of an approximating sum.
Compute definite and indefinite integrals.
Restate and apply the fundamental theorem of calculus.
Use the above concepts to solve problems in business, economics, and life sciences.

Student Learning Outcomes
MATH130 SLO1- Describe the behavior of a function through limits and utilize the limit definition of the derivative and integral.
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.

Course Content and Scope
  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
Distance Education
Lecture
Projects
Other Methods
Central instructional techniques of the course include live or recorded lectures with guided discussion and practice, problem-solving, contextualized examples, and readings of relevant text material. Print or digital lecture and discussion materials will be provided. To support student learning, students may be asked to apply concepts from instruction to written problem sets, projects, structured group activities, CAS problem sets, exam review materials, as well as to spend time reviewing and incorporating their individual student feedback from the instructor. These activities may take place either in or outside of class sessions, or both. Clearly defined expectations for all learning activities, due dates for assignments, and dates of exams will be available with advanced notice through the college's learning management system, the section syllabus, and in-class announcements.

Examples of assignments and/or activities (required reading and writing):

The volume of a cylinder is 48pi 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. Compute the dimensions of the cylinder to minimize the cost of making it. Does your answer make sense? Turn to your neighbor and discuss how you might check your result.

 

A biomass is growing at the rate of M’(t) = 0.5exp(0.2t) grams per hour. By how much does the mass change during the second hour? How would you describe in words the growth of this biomass? 

 

Suppose you have a job with a starting salary of $60,000 per year and can expect (through raises or bonuses) an additional $4,000 per year increase in subsequent years. On top of a company 401(k) or pension, we will save an additional 6% of our income for 40 years. Suppose we can invest this savings such that we earn 5% compounded continuously. How much will we have at the end of this 40-year period? Does your answer make sense? Turn to your neighbor and discuss how you might check your result.

 

Representative of the types of assignments/outside-of-class assignments:

1. Readings/Viewings: Students will be directed to read chapters of the textbook, review digital or printed lecture materials, or view closed-captioned video recordings.

2. Discussion: Students will engage in class discussions with the instructor and their peers. Students are encouraged to question, respond, and work collaboratively toward achieving the learning goals of class sessions.

3. Written Assignments and Reflection: Students will spend a sufficient amount of time to work on mathematical problem sets requiring the understanding of abstract ideas and to practice techniques learned in lectures, as well as read or view and review course materials, assignments, assessments, and feedback to reflect upon their learning.  

4. Assignments that Demonstrate Critical Thinking: Students will demonstrate critical thinking skills in a variety of ways, such as analyzing mathematical information and visuals, critically examining logical arguments, recognizing concepts in various contexts, applying abstract knowledge to their own fields of study, solving problems in various disciplines, and/or utilizing technology (computer software/graphing calculator) within the context of the course concepts.

5. In-person Proctored Exams: Students will participate in multiple in-person proctored exams, including a cumulative final exam. Students will demonstrate their individual mastery of the course’s core concepts, dexterity with the mathematical techniques, and critical thinking and mathematical writing skills developed over the course of the semester.   

Method Of Evaluation
A student's grade will be based on multiple methods of assessment that incorporate mathematical modeling, preparation and analysis of visuals and graphs, dexterity with arithmetic skills, course specific computational skills, familiarity with mathematical vocabulary, problem-solving, critical thinking, and analysis of logical arguments. Included in such assessments are in-person proctored exams/projects, and a 2 hour, in-person proctored, cumulative final exam, each linked to the learning outcomes and objectives of the course and, combined, comprise at least 50% of the course grade. In addition, instructors may make use of frequent low-stakes assessments such as quizzing, written homework assignments, CAS/technology assignments, study guides and reviews, collaborative group work, discussion, and self-reflection.

Appropriate Texts and Supplies:
  • Applied Calculus Hoffman, Bradley, -McGraw Hill, 2012.
Course Fees and Other Materials:
  • TI-84 Graphing Calculator; digital or printed lecture materials are provided

Created On 10/03/2023
Board of Trustees: 03/21/2024
CAC Approval: 03/04/2024