Courses

Course Syllabus

MATH1425 - Calculus with Business Applications

Catalog Description: Includes such topics as limits and continuity, rates of change, slope, differentiation, the derivative, maxima and minima techniques, integration: definite and indefinite integration techniques. Lecture Hrs = 4, Lab Hrs = 0

Semester Credit Hours: 4
Lecture Hours per Week:
Contact Hours per Semester: 64
State Approval Code: 2703015200

Course Subject/Catalog Number: MATH 1425
Course Title: Calculus with Business Applications

Instructional Goals and Purposes:

Lee College's instructional goals include 1) creating an academic atmosphere in which students may develop their intellects and skills and 2) providing courses so students may receive a certificate/an associate degree or transfer to a senior institution that offers baccalaureate degrees.  

General Course Objectives:

Successful completion of this course will promote the general student learning outcomes listed below. The student will be able

1. To apply problem-solving skills through solving application problems.
2. To demonstrate arithmetic and algebraic manipulation skills.
3. To read and understand scientific and mathematical literature by utilizing proper vocabulary and methodology.
4. To construct appropriate mathematical models to solve applications.
5. To interpret and apply mathematical concepts.
6. To use multiple approaches – physical, symbolic, graphical, and verbal – to solve application problems.

Specific Course Objectives:

Upon successful completion of the course, the student will be able

1. To evaluate limits of functions.
2. To determine the derivative of functions.
3. To use the derivative to solve for relative maxima and minima of functions.
4. To use the first and second derivatives as a tool for graphing functions.
5. To solve related rate applications with the technique of implicit differentiation.
6. To evaluate indefinite and definite integrals and apply their use to solve applied problems.
7. To solve differential equations and apply their use to solve applied problems.
8. To determine the area between curves
9. To solve a variety of problems from management and social sciences using the area between curves.
10. To evaluate improper integrals.
11. To solve applied problems involving functions of two or more variables.
12. To use partial differentiation to solve applied problems.

Course Content:

Students will be required to do the following:

1. Limits and Discontinuity
   1. Find limits of functions, when they exist.
   2. List and use the properties of limits.
   3. Determine if a function is continuous or discontinuous.
   4. Find vertical and horizontal asymptotes of a graph using the concept of continuity.
2. Derivatives
   1. Define the derivative as a rate of change.
   2. Use the definition of derivative to find the derivative of a function.
   3. Use the derivative to find the slope of a tangent to a curve.
   4. Find the derivatives of constant functions and powers of x.
   5. Find the derivatives of sums and differences of functions.
   6. Use the product rule and the quotient rule to find the derivative of appropriate functions.
   7. Use the chain rule and the power rule to differentiate functions.
   8. Find the derivative of exponential and logarithmic functions.
   9. Find derivatives by using implicit differentiation.
3. Applications of Derivatives
   1. Use derivative formulas separately and in combination with each other to solve a variety of problems from management and social sciences.
   2. Use derivatives to determine relative maxima, minima, and horizontal points of inflection of functions and then use this information to sketch the curve.
   3. Find absolute maxima and minima of functions.
   4. Apply the procedures for finding maxima and minima to solve a variety of problems from management and social sciences.
   5. Determine maximum profit given the average cost and price in a competitive market.
   6. Find the maximum profit given the demand function and average cost function in a monopoly.
   7. Determine elasticity of demand and predict its effect on revenue.
4. Indefinite Integrals
   1. Determine indefinite integrals of the form and .
   2. Evaluate indefinite integrals involving exponential and logarithmic functions.
   3. Use integration to find total cost functions from information involving marginal cost.
   4. Use integration to find national consumption functions from information about marginal propensity to consume and marginal propensity to save.
   5. Find general solutions of separable differential equations.
   6. Find particular solutions of separable differential equations.
   7. Evaluate integrals using the method of integration by parts.
   8. Evaluate improper integrals.
5. Definite Integrals
   1. Use the sum of areas of rectangles to approximate the area under a curve.
   2. Evaluate definite integrals using the Fundamental Theorem of Calculus.
   3. Find the area between two curves.
   4. Find the average value of a function.
   5. Use definite integrals to find consumer's surplus, producer's surplus total income and present value of continuous income streams.
   6. Use tables of integrals to evaluate appropriate integrals.
   7. Evaluate integrals using the method of integration by parts.
   8. Evaluate improper integrals.    
6. Functions Of Two Or More Variables
   1. Find the domain and range of two or more variables.
   2. Evaluate a function of two or more variables given values for the independent variables.
   3. Find partial derivatives of functions of two or more variables.
   4. Evaluate partial derivatives of function of two or more variables at given points.
   5. Use partial derivatives to find slopes of tangents to surfaces.
   6. Evaluate cost functions at given levels of production for functions of two variables.
   7. Find marginal costs from total cost and joint cost function.
   8. Find marginal productivity for given production functions.
   9. Find marginal demand functions for a pair of related products.
   10. Find and evaluate second and higher-order partial derivatives of functions of two variables.
   11. Find relative maxima, minima, and saddle points of functions of two variables.

Methods of Instruction/Course Format/Delivery:

Faculty may choose from but are not limited to the following methods of instruction:   lecture, discussion, Internet, video, television, demonstrations, field trips, collaboration, readings.

Assessment:

Faculty may assign both in- and out-of-class activities to evaluate students' knowledge and abilities.   Faculty may choose from the following methods:  

• Attendance
• Book reviews
• Class preparedness and participation
• Collaborative learning projects
• Compositions
• Exams/tests/quizzes
• Homework
• Internet  
• Journals
• Library assignments
• Readings
• Research papers
• Scientific observations
• Student-teacher conferences
• Written assignments

Course Grade:

Students' final grades are determined by:

100-90	A
89-80	B
79-70	C
69-60	D
59 or below	F

Texts, Materials, and Supplies:

For current texts and materials, use the following link to access bookstore listings:   http://www.leecollegebooks.com

Other:

• Faculty Vitae
• Faculty Course Material
• Department Budget
• Six-hour Rule
• Class Attendance
• The Academic Honesty Code
• Students with Disabilities