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 | | MATH120 syllabus




COURSE NUMBER: MATH120
COURSE TITLE:Calculus & Analytic Geometry I
DIVISION:Sciences
IAI CODE(S): M1 900 MTH 901
SEMESTER CREDIT HOURS:5
CONTACT HOURS:75
STUDENT ENGAGEMENT HOURS:225
DELIVERY MODE:In-Person

COURSE DESCRIPTION:
The course is the first of a three semester sequence of integrated calculus and analytic geometry. Both understanding of theoretical concepts and the ability to use manipulative techniques are considered of prime importance. The approach is intuitive and after the student has attained a conceptual understanding, the theorems are advanced and proved. Time is spent in applications as they arise throughout the course. The course presumes algebraic and trigonometric competency at the 70% level or higher. Graphing calculator recommended.

The following description is for the full Calculus sequence (M1900-1, M1900-2, M1900-3): Topics include (but are not limited to) the following: limits and continuity; definition of derivative, rate of change, slope; derivatives of polynomial and rational functions; the chain rule; implicit differentiation; approximation by differentials; higher-order derivatives; Rolle's Theorem and mean value theorem; applications of the derivative; antiderivatives; the definite integral; the fundamental theorem of calculus; area, volume, other applications of the integral; the calculus of the trigonometric functions; logarithmic and exponential functions; techniques of integration, including numerical methods, substitution, integration by parts, trigonometric substitution, and partial fractions; indeterminate forms and L'Hôpital's rule; improper integrals; sequences and series, convergence tests, Taylor series; parametric equations; polar coordinates and equations; vectors in 2 and 3 dimensions, vector operations; lines and planes in space; surfaces, quadric surfaces; functions of more than one variable, partial derivatives; the differential, directional derivatives, gradients; double and triple integrals, evaluation and applications; cylindrical and spherical coordinates.
PREREQUISITES:
Place into MATH120 with approved and documented math placement test scores or by completing both MATH111 (College Algebra) and MATH114 (Trigonometry) with a grade of C or better, or Precalculus with a grade of C or better.

NOTES:

STUDENT LEARNING OUTCOMES:
Upon completion of this course, students will be able to:
  • Clearly write interpretation of solutions to standard calculus application problems.
  • Translate/explain statements made in symbolic form
  • Clearly state each of the following component to a solution
    1. All given values and formulas
    2. the primary unknown for which a solution is desired
    3. any secondary unknowns or relationships that may be required
    4. the technique(s) required to move toward solution
    5. interpretation of the solution
  • Explain/write the step-by-step logical process by which a solution will be attained in calculus application problems
  • Graph functions on graphing calculators for the purpose of solving solve numeric analysis problems
  • check work through graphing technique using graphing calculators
  • Use, understand and write all required algebraic symbols and abbreviations
  • Calculate the limit algebraically to derive the slope formula of a function
  • Calculate the limit of a function to identify functions as either continuous or discontinuous
  • calculate the limit of functions to identify function behavior as either finite or infinite
  • Calculate the limit of functions to determine the exact area beneath a curve
  • Calculate the limit of a function using L’Hopital’s Rule
  • Classify the types of indeterminant function
  • Generate the slope predictor of a function to determine the equation of a tangent line
  • Generate the slope predictor of a function to distinguish between tangent lines that are horizontal, vertical, or neither
  • Solve the slope function set equal to zero to identify function points as maximums, minimums, or neither
  • Identify points at which functions have nonexistent value
  • Use function domain to identify potential maximum or minimum function values
  • Differentiate basic algebraic and trigonometric functions to create slope-functions
  • Identify objective and constraint functions in application problems
  • Identify independent function and differentiation variable in applied rate problems
  • write interpretations of answers to application problems
  • Use Newton’s Method to numerically calculate the solution to equations
  • Distinguish between explicit and implicit differentiation
  • Simplify derivative functions according to the laws of algebra and trigonometry
  • Predict a function’s slope-graph from the function’s graph
  • Partition a function domain into a set of contiguous sub-domain. Via Riemann Sums
  • Determine the Riemann Sum simple standard geometric mathematical model for area on an infinitesimal interval for a non-standard geometrical problem, over a finite domain
  • Integrate a slope function to determine the parent function
  • Solve basic separable differential equations
  • Calculate the area between two functions from integration techniques
  • Calculate the volume, surface area and arc length of solids of revolution from integration techniques
  • Calculate the total amount of work done in moving forces from integration techniques

TOPICAL OUTLINE:
  • Real numbers, coordinate systems in two dimensions, lines, functions, combination of functions. 6%
  • Definition of limit, theorems on limits, one-sided limits, continuous functions.12%
  • The derivative of a function, rules for finding derivatives, increments and differentials,12%
  • The chain rule, implicit differentiation, derivatives involving powers of functions, derivatives of trigonometric functions, higher order derivatives, Newton’s method. 14%
  • Local extrema of functions, Rolles' Theorem and the Mean Value Theorem, the first derivative test, concavity and the second derivative test, horizontal and vertical asymptotes, applications of extrema, the derivative as a rate of change, related rates, anti- derivatives, application to economics. 14%
  • Area, definition of definite integral, properties of the definite integral, the Mean Value Theorem for definite integrals, the Fundamental Theorem of Calculus, indefinite integrals and change of variables, numerical integration. 16%
  • Area, solids of revolution, volumes using cylindrical shells, volumes by slicing. 14%
  • Separable differential equations, Force and Work applications, Moments and Moment Applications. 12%

TEXTBOOK / SPECIAL MATERIALS:

Calculus, Early Transcendentals, 7th Edition, Edwards, Penney, Pearson/Prentice-Hall, 2008.

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

EVALUATION:

6-7 hourly exams are given during the semester, 100 points each. A comprehensive final exam, which accounts for 200 points of the grade, and homework and/or projects using computer software account for 100 points.

Determination of grade based upon all work completed is as follows:
90%-100%
80%-89%
70%-79%
60%-69%
below 60%
A
B
C
D
F

BIBLIOGRAPHY:

Current internet resources.

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:
Fall 2019

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