MATH 131 - Calculus For Biological Sciences, Social Sciences And Business II
MATH 131
Calculus For Biological Sciences, Social Sciences And Business II
Disciplines
Mathematics - Basic Skills: noncredit
3.000
0 - May not be repeated
Techniques of integration for single and multivariable calculus, functions of several variables, partial differentiation, maxima/minima problems, differential equations, and probability. Optional topics: infinite series, Taylor's Theorem and the calculus of trigonometric functions.
48.000-54.000 Total Hours
Total Hours
96.000-108.000 Total Hours
48.000-54.000 Total Hours
Prerequisite: MATH 130 Prerequisite or Corequisite: None Concurrent Corequisite: None Course Advisories: ENG 098 or ENG 103 Limitation on Enrollment: None
Course Objectives:
Evaluate and apply multivariable functions to business, economics, and life sciences applications.
Evaluate partial derivatives and apply them to analyze phenomena in economics, business, and life sciences.
Evaluate single and multiple definite integrals and apply them to analyze phenomena in business, economics, and life sciences.
Model physical phenomena with differential equations.
Find exact solutions to differential equations using analytical methods.
Estimate solutions to differential equations using numerical approximation techniques.
Solve discrete probability problems with finite random variables.
Set up, evaluate, and interpret integrals of continuous probability density functions.
Student Learning Outcomes
MATH131 SLO1 - Differentiate and integrate functions of several variables.
MATH131 SLO2 - Solve separable and linear differential equations.
MATH131 SLO3 - Set up, evaluate, and interpret integrals of probability density functions.
Multivariable Calculus
Functions of Several Variables
Level Curves and Contour Diagrams
Partial Derivatives
Maxima and Minima
The Method of Least Squares (Optional)
Double Integrals
Applications
Calculus and Probability
Basic Concepts: Finite Random Variables
Continuous Random Variables
Exponential and Normal Random Variables
Differential Equations
Separable Differential Equations
Applications of Differential Equations
Slope Fields and Euler's Method
Other Topics
Taylor Series (Optional)
Newton’s Method (Optional)
Triogonometric Functions (Optional)
Methods of Instruction
Directed Study
Discussion
Individualized Instruction
Lecture
Mediated Learning
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.
-Newton's law of cooling states that the rate at which the temperature of an object changes is directly proportional to the difference in the temperature between the object and the temperature of the surrounding medium. A cup of coffee is prepared with boiling water (212 degrees F) and left to cool on the counter in a room where the temperature is 72 degrees F.
(a) Set up a differential equation and initial condition describing this scenario.
(b) Solve the initial value problem in part (a).
(c) If the temperature of the coffee is 140 degrees F after 2 minutes, determine when the coffee will be cool enough to drink (say 110 degrees F).
A. Appropriate Readings: Students are required to read assigned sections in text or supplements. Outside readings are generally not required.
B. Writing Assignments: Students must work assigned mathematical problems requiring the manipulation of abstract symbols.
C. Appropriate Outside Assignments: Students are expected to spend a sufficient amount of time outside of class to practice techniques presented during class time, read assigned materials, and complete frequent homework assignments.
D. 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 algebraic problems, preparation and analysis of graphs, and analysis of logical arguments. Such measures may 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 algebra skills, and familiarity with mathematical vocabulary. Calculator (or computer use) is incorporated in the courses. Students should be able to perform differentiation and some basic integration "by hand."
Applied CalculusHoffman, Bradley, -McGraw Hill, 2013