MAC 2311H - Honors Calculus with Analytic Geometry I

Mathematics Department

Credit(s): 5
Contact Hours: 77
Effective Term Spring 2018 (540)

Requisites

(Prerequisite MAC 1140 and
Prerequisite MAC 1114) or
(Prerequisite MAC 1106 and
Prerequisite MAC 1114) or
Prerequisite MAC 1147 or
Prerequisite acceptance into the Honors College or
Permission of the Program

Course Description

In this first course the topics include limits and continuity, the derivative of algebraic, trigonometric, logarithmic and exponential functions, implicit differentiation, applications of the derivative, differentials, indefinite and definite integrals, and applications of exponential functions. (Note: Credit is only given for MAC 2311H or MAC 2311 or MAC 2233.)

Learning Outcomes and Objectives

  1. The student will apply knowledge of the limit and continuity concepts of real-valued functions of a single variable by:
    1. stating the definition of the limit of a function.
    2. proving that the limit of a function exists by the epsilon – delta definition.
    3. finding the limit of a function by use of appropriate limit theorems.
    4. using limits as they apply in graphing a function (horizontal and vertical asymptotes.)
    5. stating the definition of continuity at a point and on an interval for a function.
    6. determining for which values a function is continuous.
    7. using the "squeeze" theorem in order to find the limit of a function.
  2. The student will demonstrate knowledge of the derivative of a function and its applications by:
    1. stating the definition of the derivative of a function and use it or appropriate derivative theorems to find the derivative of a given algebraic, trigonometric, logarithmic, and exponential, function either explicitly or implicitly.
    2. applying the derivative to the following: slope of the tangent to a curve; rate of change; related rates; intervals on which a function is increasing or decreasing, extrema, concavity and inflection points of a function; rectilinear motion and curve sketching, the Mean Value Theorem, growth and decay problems, and Newton’s Method.
  3. The student will apply knowledge of the antiderivative of a function and its applications by:
    1. finding the differential and antiderivative of a given algebraic, trigonometric, logarithmic, and exponential function.
    2. finding an antiderivative of a given function by the method of substitution.
    3. using antiderivative formulas to solve velocity/acceleration problems and separable differential equations.
  4. The student will apply knowledge of the “Riemann sum and Riemann integral” of a function by:
    1. graphing a function on a closed interval and show the rectangles used in finding the Riemann sum with appropriate labels.
    2. stating the definition of the Riemann Integral and be able to determine it over a given interval.
    3. evaluating a definite integral of a function using the Fundamental Theorem of Integral Calculus.
  5. The student will synthesize the concepts learned in this course by:
    1. studying limits from the theoretical point of view, developing competence with epsilon-delta proofs.
    2. developing a deeper understanding of the derivative and integral by proving key theorems related to both.
    3. applying the knowledge of mathematics to identify, formulate, and solve problems.
    4. producing mathematical models representing continuous functions.
    5. understanding the applications of calculus to the sciences, social sciences, and the environment.
    6. The student will demonstrate this synthesis of the concepts through application by:
    7. developing enhanced use of graphing calculators and/or computer software capabilities to view concepts, test conjectures, and model problems.
    8. collaborating on projects that require the student to use his/her communication and technology skills to model and solve enrichment problems.
    9. The student will demonstrate his/her ability to communicate calculus effectively by:
    10. working effectively in diverse teams.
    11. writing proofs and/or derivations of various calculus theorems and formulas.
    12. presenting problems and solutions to the class .
    13. developing a portfolio which may include proofs of theorems, summaries of readings, projects and/or problems, oral presentations, or research papers.

Criteria Performance Standard

Upon successful completion of the course the student will, with a minimum of 70% accuracy, demonstrate mastery of each of the above stated objectives through classroom measures developed by individual course instructors.

History of Changes

C&I 4/27/04, BOT 5/21/04, Eff 20041 (0340 PS). 3 Year Review 2007. (additional exception added 021810) C&I Approval: 04/27/2004, BOT Approval: 05/21/2004, Effective Term: Fall 2004 (340).
C&I Approval: , BOT Approval: , Effective Term: Spring 2018 (540)