MATH 1325:
Prerequisites
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When an instructor feels that a student has been absent to such a degree as to invalidate the learning experience, the instructor may recommend to the Vice President of Instruction that the student be withdrawn from the course. Instructors may seek to withdraw students for non-attendance after they have accumulated the following number of absences:
Fall or spring semesters:
3 or more class meeting times per week - 5 absences
2 class meeting times per week - 3 absences
1 class meeting per week - 2 absences
The student is responsible for seeing that he or she has been officially withdrawn from a class. A student who stops attendance in a class without officially withdrawing from that class will be given a failing grade; consequently, the student must follow official withdrawal procedures in the Admissions/Records Office.
Please note: Health Science and Cosmetology courses may require more stringent attendance policies based on their accreditation agencies. Please see the addendum and/or program handbook for further information concerning attendance.
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There are situations throughout the course where you may be permitted to use artificial intelligence (AI) tools to aide in further understanding of mathematical concepts. However, AI tools may not be used for any graded assignments including but not limited to exams, quizzes, and projects. Use of any AI-generated content in this course without the instructor’s consent qualifies as academic dishonesty and violates Panola College’s standards of academic integrity.
Communication Skills – to include effective development, interpretation, and expression of ideas through written, oral, and visual communication
Empirical and Quantitative Skills – to include the manipulation and analysis of numerical data or observable facts resulting in informed conclusions
Upon completion of MATH 1325, the student will be able to demonstrate:
- Competence in finding limits for function, if they exist, at a point and approaching infinity and in applying these concepts to continuity and asymptotes.
- Competence in finding derivatives for functions using the definition of the derivative.
- Competence in applying the rules for finding derivatives of functions.
- Competence in finding higher order derivatives.
- Competence in using the first and second derivatives, asymptotes, x- and y-intercepts have points of inflection, extrema, and symmetry to graph functions.
- Competence in finding first and second derivatives implicitly.
- Competence in applying derivatives to optimization (applied max/min) problems.
- Competence in finding the indefinite integral for a variety of functions.
- Competence in finding the definite integral.
- Competence in finding the areas under and between curves.
- Competence in evaluating improper integrals.
Upon successful completion of this course, students will:
- Apply calculus to solve business, economics, and social sciences problems.
- Apply appropriate differentiation techniques to obtain derivatives of various functions have including logarithmic and exponential functions.
- Solve application problems involving implicit differentiation and related rates.
- Solve optimization problems with emphasis on business and social sciences applications.
- Determine appropriate technique(s) of integration.
- Integrate functions using the method of integration by parts or substitution, as appropriate.
- Solve business, economics, and social sciences applications problems using integration techniques
A general description of lecture/discussion topics included in this course are listed in the Learning Objectives / Specific Course Objectives sections of this syllabus.
Students in all sections of this course will learn the following content:
After studying the material presented in the text(s), lecture, laboratory, computer tutorials, and other resources, the student should be able to complete all behavioral/learning objectives listed below with a minimum competency of 70%.
Algebra Concepts and Functions
Upon completion of this section, the student will be able to correctly:
- Apply (identify) the above terms in applied problems.
- Sketch the graph of a relation and determine by using the function vertical line test if it is the graph of a function.
- Determine the domain and range of a relation that is specified via a graph.
- Determine the slope of a line given two ordered pairs.
- Determine the slope of any given horizontal line.
- Identify the slope of any given vertical line as undefined.
- Given two sets of ordered pairs, determine if the indicated line segments are parallel have perpendicular, or neither.
- Graph an equation of the form y = c or x = c, where c is a constant.
- Graph an equation of the form y = mx +b.
- Write the equation of a line when given a point and the slope.
- Write the equation of a line when given a point and the equation of a line parallel or perpendicular to the desired line.
- Write the equation of a line when given two points on that line.
- Write the equation of a line when given the x- and y-intercepts of that line.
- Write a linear cost function when given the variable cost and the fixed costs.
- Write a cost function when given that (i) the function is linear and (ii) ordered pairs (q,p) (quantity, price).
- Solve a system of equations using the addition/elimination method.
- Translate word problems into systems of equations and solve.
- Find the break-even point when given a linear cost function and a linear revenue function.
- Find the market equilibrium point given the supply equation and the demand equation.
- Determine if a relation is a function.
- State the domain and range of certain specified functions.
- Use functional notation.
- Graph linear functions.
- Find slopes of parallel and perpendicular lines.
- Write equations of lines given certain data.
- Formulate, graph, and evaluate total cost, total revenue, and profit functions.
- Find break-even points
- Evaluate and graph supply and demand functions.
- Find market equilibrium.
- Determine if a vertex of a parabola is a maximum point or a minimum point.
- Find the vertex of the graph of a quadratic function.
- Find the zeros (x-intercepts) of a quadratic function.
- Graph quadratic functions.
Derivatives
Upon completion of this section, the student will be able to correctly:
- Evaluate the limit of a given function at a point using the properties of limits.
- Evaluate one-sided limits of a function at a point using the properties of limits.
- State the definition of continuity at a point for a function.
- Determine if a function is continuous in its domain by using the definition referenced above.
- State the definition for slope of a tangent line to the graph of the function y = f(x).
- Find the slope of a tangent line to a point using the definition referenced above.
- State the definition of the derivative of y= f(x) at a point.
- Find the equation of the tangent line to the graph of y = f(x) at a given point.
- Find the point(s), if any, at which the derivative is nonexistent.
- List the different symbols for the derivative.
- Find a derivative using the power rule.
- Find a derivative using the "constant times a function" rule.
- Find a derivative using the sum and/or difference rules.
- Find a derivative using the Product Rule.
- Find a derivative using the Quotient Rule.
- Find a derivative using the Chain Rule.
- Find the derivative of a function using implicit differentiation.
- Find higher order derivatives.
- Find the second derivative using implicit differentiation.
- State the definition of the differentials dx and dy.
- Approximate quantities using differentials.
Applications of Derivatives
Upon completion of this section, the student will be able to correctly:
- Find the derivative of a function using implicit differentiation.
- Evaluate the derivative at a given point of and implicitly defined function and find the equation of the tangent line at the point.
- Find limits at infinity.
- Indicate if a function has an infinite limit at a point.
- Indicate if a function possesses a vertical asymptote.
- Indicate if a function possesses a horizontal asymptote.
- Find on what intervals a function is increasing and on what intervals it is decreasing.
- Find the critical values of a function.
- Find and classify the local extrema of a function.
- Discuss the concavity of a function.
- Find the points of inflection of a function.
- Use the Second Derivative Test to classify local extrema.
- Analyze a function using the first and second derivatives to find (i) intervals where the function is increasing/decreasing/constant have (ii) intervals where the function is concave upward/downward, and (iii) and classify all local extrema and points of inflection.
- Find and classify the absolute (global) extrema of a function on an interval.
- Solve selected applied optimization (max/min) problems.
Exponential and Logarithmic Functions
Upon completion of this section, the student will be able to correctly:
- Graph an exponential function.
- Recognize the typical types of exponential graphs.
- Graph functions involving the irrational number e.
- Solve exponential equations.
- Define a logarithmic function.
- Change from a logarithmic to exponential form and vice versa.
- State and apply the properties of logarithms.
- Find the derivative of logarithmic functions.
- Graph y = ln (x).
- Find the derivative of exponential functions.
- Graph y = ex and y = e-x.
Indefinite Integrals
Upon completion of this section, the student will be able to correctly
- State the specified basic indefinite integral (anti-derivative) formulae.
- State the properties of the indefinite integral.
- Integral a function using the general power rule.
Definite Integrals
Upon completion of this section, the student will be able to correctly:
- Identify the integrand and the upper and lower limits of integration for a definite integral.
- Evaluate the definite integral using the Fundamental Theorem of Integral Calculus.
- Find the area under a curve, area between two curves, and signed areas, all using the definite integral.
- Use the rectangular rule for approximating the definite integral.
- State the definition of the definite integral.
- State the Fundamental Theorem of Calculus.
- Find the average value of a continuous function over a given interval.
- Perform integration by the substitution (change of variable) technique.
- Perform integration by the integration by parts technique.
Methods of Instruction/Course Format/Delivery: Methods employed will include Lecture/demonstration have discussion, problem solving, analysis, and reading assignments. Homework will be assigned. Faculty may choose from, but are not limited to, the following methods of instruction:
- Lecture
- Discussion
- Internet
- Video
- Television
- Demonstrations
- Field trips
- Collaboration
- Readings
Assignments
Faculty may assign both in- and out-of-class activities to evaluate students' knowledge and abilities. Faculty may choose from – but are not limited to -- the following methods: attendance, class preparedness and participation, collaborative learning projects, exams/tests/quizzes, homework, internet, library assignments, readings, research papers, scientific observations, student-teacher conferences, and written assignments.
The Mathematics Department does not accept late work.
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Assignment Weights |
- Daily Grades 25%
- Major Exams 50%
- Comprehensive Final Exam 25%
Letter Grades for the Course will be assigned as follows:
A: 90 < Average < 100
B: 80 < Average < 90
C: 70 < Average < 80
D: 60 < Average < 70
F: 00 < Average < 60
- Textbook: Applied Calculus by Shana Calaway, Dale Hoffman and David Lippman by Lumen Learning (No Purchase Necessary)
- Lumen OHM (No Purchase Necessary)
- Canvas Access
- Scientific Calculator
- Courses conducted via video conferencing may be recorded and shared for instructional purposes by the instructor.
- For current texts and materials, use the following link to access bookstore listings: https://www.panolacollegestore.com.
- For testing services, use the following link: https://www.panola.edu/student-services/studentsupport/academic-testing-center.
- If any student in this class has special classroom or testing needs because of a physical learning or emotional condition, please contact the ADA Student Coordinator in Support Services located in the Charles C. Matthews Student Center or go to https://www.panola.edu/studentservices/student-support/disability-support-services for more information.
- Withdrawing from a course is the student’s responsibility. Students who do not attend class and who do not withdraw will receive the grade earned for the course.
- Student Handbook: https://www.panola.edu/ (located on at the bottom under student)