Course Descriptions & Syllabi

Course Descriptions & Syllabi

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Note: some or all of the courses in the subjects marked as "Transfer" can be used towards a transfer degree: Associate of Science and Arts or Associate of Engineering Science at DACC. Transferability for specific institutions and majors varies. Consult a counselor for this information.

Areas of Study | | MATH125 syllabus




COURSE NUMBER: MATH125
COURSE TITLE:Introductory Analysis I (Calculus for Business & Sciences)
DIVISION:Sciences
IAI CODE(S): M1 900B
SEMESTER CREDIT HOURS:4
CONTACT HOURS:60
STUDENT ENGAGEMENT HOURS:180
DELIVERY MODE:In-Person

COURSE DESCRIPTION:
A freshman level calculus class intended for transfer students pursuing degrees in the fields of agricultural science, business/accounting, engineering/industrial technology and psychology. This course may also serve as a math elective for various other transfer programs. The course covers a broad range of topics that include limits and continuity, the definition of the derivative, techniques for differentiation, applications of the derivative, single and multivariable calculus, higher order derivatives, implicit differentiation, the antiderivative and indefinite integral, techniques of integration including integration by parts, numerical integration and the Riemann sum, the fundamental theorem of calculus, the definite integral and double integrals. Other topics covered may include but would not be restricted to differentials and approximation, improper integrals, functions of several variables, partial derivatives and multiple integrals. The class meets four hours per week.

PREREQUISITES:
The student must place into MATH125 with approved and documented math placement test score or complete MATH111 with a grade of C or better.

NOTES:

Credit will not be given for both MATH125 and MATH120.
This course is not for Math and Science Majors.



STUDENT LEARNING OUTCOMES:
Upon completion of this course, students will be able to:
  • Able to use, understand and write all limit, differentiation and integration symbolic forms and algebraic terminology.
  • Clearly relate interpretations and solutions of limit problems to graphs as well as application problems.
  • Clearly demonstrate the organized, logical steps taken to arrive at the solution. Master the use of relevant technology for calculus.
  • Achieve strong critical thinking/problem solving skills as applied to calculus problems.
  • Demonstrate comprehension of limits by calculating limits for functions at fixed values (including from the left and from the right) and at plus and negative infinity using:
    • Tables of values
    • Various rules and/or theorems for limits
    • Algebraic techniques
  • Clearly relate interpretations and solutions of limit problems to graphs as well as application problems.
  • Demonstrate understanding of continuity by locating all points of discontinuity and applying the definition in determining reasons for the discontinuity.
  • Apply the definition of the derivative in calculating the derivative of basic functions, including but not limited to:
    • Linear, quadratic and cubic functions
    • Square root functions with linear radicands
    • Rational functions
  • Apply rules of differentiation in calculating the derivative of functions, including but not limited to:
    • Polynomial functions
    • Radical functions
    • Rational functions
    • Exponential and logarithmic functions
  • Apply the definition of the derivative/rules of differentiation in:
    • Determining and interpreting marginal profit, revenue and cost
    • Locating values that will optimize various functions, including but not limited to:
      • Profit, revenue and cost
      • Area and volume
      • Material use and energy expenditure
    • Utilize the first/second derivative of a function in:
      • Determining intervals of increasing and decreasing
      • Locating and labeling all relative extrema
      • Determining intervals of concavity and convexity
      • Locating and labeling all absolute extrema
      • Performing curve sketching
    • Utilize implicit differentiation in determining rates of change between various related variables, including but not limited to:
      • Demand, revenue, cost and profit
      • Dimensions of two and three dimensional shapes, area and volume
      • Distance and velocity
    • Utilize functions of multiple variables and rules of differentiation to find:
      • Partial derivatives
      • Relative extrema and saddle points in three-dimensional space
    • Calculate indefinite integrals using:
      • Basic rules of integration
      • Integration by parts
    • Approximate area in the Cartesian coordinate system through numerical integration using:
      • The left endpoint, right endpoint and midpoint methods
      • The trapezoidal rule and Simpson’s rule
    • Calculate the definite integral and use it to determine the area on a closed interval between:
      • A function and the x-axis
      • Two functions
  • Correctly use and understand all limit, differentiation and integration symbolic forms and algebraic terminology
  • Clearly demonstrate organized, local steps taken to arrive at the solution. Master the use of relevant technology for calculus
  • Demonstrate strong critical thinking and problem solving skills as applied to calculus problems

TOPICAL OUTLINE:
  • Functions (student review) [5%]
    • Their domains and graphs
    • Algebra of functions
    • Difference / Quotient
    • Zeroes of functions
    • Transformations
  • Limits [15%]
    • One-sided limits
    • Limits at a fixed value
    • Rules for limits
    • Limits at plus or negative infinity
    • Limits and Continuity
    • Limits and the definition of the derivative
    • Continuity and Differentiability
  • The Derivative [20%]
    • Interpretations
      • Slope of a tangent line
      • Instantaneous rate of change
    • Rules for differentiation
      • Constant
      • Sum or difference
      • Scalar multiple
      • Power rule
      • Product
      • Quotient
      • Chain rule and the general power rule
    • Higher order derivatives
  • Exponential Functions [5%]
    • Properties
    • Graphs
    • Exponential base e
    • Applications
    • Differentiation of exponential functions
  • Logarithmic Functions [5%]
    • Properties
    • Graphs
    • Common and natural logarithms
    • Applications
    • Change-of-base formulas
    • Differentiation of logarithmic functions
  • Applications of Derivatives [30%]
    • Describing graphs of functions and curve sketching
      • First derivative: increasing and decreasing
      • Relative extrema and the first derivative test
      • Second derivative: points of inflection and intervals of concavity
      • Relative extrema and the second derivative test
    • Absolute extrema
      • Optimization
      • Applications to Business and Economics
    • Implicit differentiation
      • Related rates
      • Differentials (optional)
    • Multivariable Calculus
      • Functions of several variable
      • Partial derivatives
      • Saddle points and relative extrema
  • Integration [20%]
    • Antiderivatives and the indefinite integral
    • Techniques for integration
      • Basic rules
      • Substitution
      • Integration by parts
    • Areas in the Cartesian coordinate system and the definite integral
    • Numerical integration and the Riemann sum
      • Left and right endpoint
      • Midpoint
      • Trapezoidal rule
      • Simpson's rule
    • Double integrals (single variable)
  • Optional Material
    • Improper integrals
    • Multivariable calculus (continued)
      • Constrained optimization
      • Total differentials and their applications
      • Double and triple integrals

TEXTBOOK / SPECIAL MATERIALS:

Finite Mathematics and Calculus with Applications, 10th edition; Lial, Greenwell, and Richey, Pearson, 2016

See bookstore website for current book(s) at https://www.dacc.edu/bookstore

EVALUATION:

The student's grade for the course is based on a cumulative percent with overall grade divisions occurring at 90, 80, 70 and 60 percent. The cumulative percent will be obtained from a combination of four categories: five or more hourly exams accounting for fifty percent of the course grade, five or more quizzes accounting for fifteen percent of the course grade, classroom work / project(s) accounting for ten percent of the course grade, a midterm accounting for ten percent of the course grade and a final accounting for fifteen percent of the course grade. Attendance is required and a student may be withdrawn from the class roster due to excessive absences. Such students may avoid withdrawal by being responsible for missed material and by making prior arrangements with the instructor for missed, in-class evaluations.

Notes:
The project(s) will be a group effort with a group consisting of at least two students. The project will consist of an oral presentation with work demonstrated on the board and a written copy to be turned in to the instructor. The presentation/demonstration will be evaluated by a rubric, assigning points for clarity, organization, accuracy and originality. The written copy will be evaluated according to correct use of notation, punctuation, grammar, organization and accuracy. Projects assigned will not be restricted to but may be one or more of the following:
Proof of a rule of differentiation using the definition of the derivative
Graph of a function using algebraic concepts, limits and derivatives
Application problem using diagrams and derivatives


BIBLIOGRAPHY:

STUDENT CONDUCT CODE:
Membership in the DACC community brings both rights and responsibility. As a student at DACC, you are expected to exhibit conduct compatible with the educational mission of the College. Academic dishonesty, including but not limited to, cheating and plagiarism, is not tolerated. A DACC student is also required to abide by the acceptable use policies of copyright and peer-to-peer file sharing. It is the student’s responsibility to become familiar with and adhere to the Student Code of Conduct as contained in the DACC Student Handbook. The Student Handbook is available in the Information Office in Vermilion Hall and online at: https://www.dacc.edu/student-handbook

DISABILITY SERVICES:
Any student who feels s/he may need an accommodation based on the impact of a disability should contact the Testing & Academic Services Center at 217-443-8708 (TTY 217-443-8701) or stop by Cannon Hall Room 103. Please speak with your instructor privately to discuss your specific accommodation needs in this course.

REVISION:
Spring 2019

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