Course Snapshot for MAT 201 - Calculus I
The information listed below is subject to change. Please review the course syllabus within your online course at the start of class.
Course Competencies
The competencies you will demonstrate in this course are as follows:
- Solve selected algebraic and trigonometric problems.
- Identify limits of algebraic, trigonometric, and composite functions.
- Solve for the derivatives of algebraic, trigonometry and composite functions.
- Solve for the derivatives of selected functions.
- Use the appropriate algorithm(s) (including product, quotient, and chain rules) to find derivatives of algebraic, trigonometric, and composite functions.
- Find derivatives of implicitly defined functions.
- Use the first and second derivatives of functions to find extrema, points of inflection, and sketch the graph of the function.
- Set up and solve applied problems selected by the instructor.
- Find indefinite and definite integrals of algebraic, trigonometric, and composite functions.
- Apply definite integrals.
- Read, analyze, and apply written material to new situations.
- Write and speak clearly and logically in presentations and essays.
- Demonstrate the ability to select and apply contemporary forms of technology to solve problems or compile information.
Module Outcomes Mapped to Competencies
Module 0: Before Calculus |
Mapped to Course Competencies (above) |
| Students will be able to add, subtract, multiply and divide polynomial and rational functions. | 1, 11, 14 |
| Students will be able to comfortably use their TI calculator to perform arithmetic and graphing operations. | 1, 11, 14 |
| Students will be able to find the inverse of an algebraic and trigonometric function. | 1, 11, 13, 14 |
| Students will be able to work problems and solve equations that involve exponential and logarithmic functions. | 1, 11, 12, 14 |
| Understand and be able to graph linear functions, rational functions, absolute value functions, and trigonometric functions along with corresponding translations. | 1, 11, 14 |
Module 1: Limits and Continuity |
Mapped to Course Competencies (above) |
| Students will be able to find one sided limits. | 2, 11, 12, 13, 14 |
| Students will be able to determine the relationship between one and two sided limits. | 2, 11, 12, 13, 14 |
| Students will be able to use limits to determine end behavior of a function. | 2, 11, 12, 14 |
| Students will use and apply the limit laws to calculate the limit of a function. | 2, 11, 12, 14 |
| Students will be able to apply limit techniques to find horizontal and vertical asymptotes of rational functions. | 2, 11, 12, 14 |
| Students will be able to determine if various functions are continuous or discontinuous at given locations. | 2, 11, 12, 14 |
| Students will be able to apply the squeeze thm to find the limit of a function. | 2, 11, 12, 14 |
| Students will be able to apply continuity properties to various functions. | 2, 11, 12, 14 |
Module 2: The Derivative |
Mapped to Course Competencies (above) |
| Students will be able to calculate the slopes of secant lines. | 3, 11, 12, 14 |
| Students will be able to apply the formal definition of the derivative to various problems. | 4, 11, 12, 13, 14 |
| Students will be able to use the power rule, sum and difference rule as well as constant multiple rule when calculating derivatives. | 3, 4, 5, 11, 12, 13, 14 |
| Students will be able to calculate higher order derivatives. | 3, 4, 5, 11, 12, 13, 14 |
| Students will be able to use the product and quotient rules to calculate the derivative. | 3, 4, 5, 11, 12, 13, 14 |
| Students will be able to calculate the derivative of trigonometric functions. | 3, 4, 5, 11, 12, 13, 14 |
| Students will be able to apply the chain rule to find the derivatives of composite functions. | 3, 4, 5, 11, 12, 13, 14 |
Module 3: Topics in Differentiation |
Mapped to Course Competencies (above) |
| Students will be able to calculate the derivative implicitly. | 6, 11, 12, 13, 14 |
| Students will be able to calculate the derivative of logarithmic functions. | 3, 4, 5, 6, 11, 12, 13, 14 |
| Students will be able to calculate the derivative of logarithmic functions. | 3, 4, 5, 6, 11, 12, 13, 14 |
| Students will be able to relate two or more quantities that are all changing with time. | 3, 4, 5, 6, 8, 11, 12, 13, 14 |
| Students will be able to use linear approximation techniques to estimate function values at given points. | 8, 11, 12, 13, 14 |
| Students will use L”Hopital’s Rule to calculate limits. | 8, 11, 12, 13, 14 |
Module 4: The Derivative in Graphing and Applications |
Mapped to Course Competencies (above) |
| Students will be able to find intervals of increase and decrease by evaluating derivatives. | 7, 11, 12, 13, 14 |
| Students will be able to find local extrema from evaluating derivatives. | 7, 11, 12, 13, 14 |
| Students will be able to determine concavity of a function by using the second derivative test. | 7, 11, 12, 13, 14 |
| Students will be able to find inflection points from evaluating derivatives. | 7, 11, 12, 13, 14 |
| Students will be able to analyze information about the derivative in order to sketch a graph of the function. | 7, 11, 12, 13, 14 |
| Students will be able to optimize information in various real life application situations. | 7, 8, 11, 12, 13, 14 |
| Students will utilize the derivative to explain the movement of objects. | 8, 11, 12, 13, 14 |
| Students will be able to find the zeros of a function by using Newton’s method. | 8, 11, 12, 13, 14 |
| Students will be able to accurately apply Rolle’s Theorem and the Mean Value Theorem to better understand the relationship between secant and tangent lines. | 8, 11, 12, 13, 14 |
Module 5: Integration |
Mapped to Course Competencies (above) |
| Students will be able to calculate the anti-derivative of algebraic and trigonometric functions. | 9, 11, 12, 13, 14 |
| Students will be able to approximate the area under a curve by using any given number of rectangles. | 8, 11, 12, 13, 14 |
Students will be able to calculate the exact area under a curve by using sums and sigma notation as well as the fundamental theorem of calculus. |
9, 11, 12, 13, 14 |
| Students will be able to evaluate indefinite and definite integrals for algebraic, trigonometric and transcendental functions | 9, 11, 12, 13, 14 |
| Students will be able to use the substitution technique when evaluating integrals. | 9, 11, 12, 13, 14 |
| Students will understand and apply the Fundamental Theorem of Calculus. | 9, 11, 12, 13, 14 |
| Students will use integration techniques to explore the motion of an object. | 9, 11, 12, 13, 14 |
| Students will calculate the average value of a function. | 9, 11, 12, 13, 14 |
| . Students will integrate various logarithmic and exponential functions. | 9, 11, 12, 13, 14 |
Module 6: Applications of the Definite Integral in Geometry, Science, and Engineering |
Mapped to Course Competencies (above) |
| Students will be able to find the area between two curves. | 9, 10, 11, 12, 13, 14 |
| Students will be able to find the volume created by rotating a curve by either the disk or shell method. | 8, 9, 10, 11, 12, 13, 14 |
| Students will be able to calculate arc length and surface area. | 8, 9, 10, 11, 12, 13, 14 |
| Students will be able to calculate the area of a surface of revolution. | 8, 9, 10, 11, 12, 13, 14 |
| Students will be able to apply integration techniques to physics and engineering applications. | 8, 9, 10, 11, 2, 13, 14 |
Module 7: Final Exam |
Mapped to Course Competencies (above) |
| Students will be able to exhibit all of the competencies above at a satisfactory level before leaving the course. | 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 |
Course Time Commitment and Expectations
For every credit hour, students should plan to spend an average of 2-3 hours per week for course-related activities in a 15-week course. For example, a 3 credit hour course would average an average 6-9 hours per week to read/listen to the online content, participate in discussion forums, complete assignments, and study the course material. For 10 and 6-week courses, the amount of time per week will be higher so all course competencies, module outcomes, and assignments will be covered.
Aside from typical reading assignments, this course has the following (Please Note: This list is subject to change based on the discretion of the instructor facilitating this course.):
Assignment | Points |
|---|---|
| oduction | 5 |
| Scavenger Hunt | 10 |
| Discussions (Best 6 out of 7 @ 10 points each) | 60 |
| Homework (Best 13 out of 14 @ 5 points each) | 65 |
| Quizzes (Best 13 out of 14 @ 5 points each) | 65 |
| Exams (Best 6 out of 7 Module 0 - 6 exam scores @ 100 points each) | 600 |
| Group Project | 45 |
| Module 7 (Final) Exam | 150 |
| TOTAL |
1,000 |
CCCOnline Course Quality Commitment
CCCOnline goes to great lengths to assure the quality of your online learning experience. You can expect the following from our courses:
- All CCCOnline courses are developed by content experts and a professional team of instructional designers.
- CCCOnline courses are built with a template that assures accessibility and Quality Matters Design Standards.
- There is navigation consistency across all CCCOnline courses.
- Most of our courses come with illustrative models and videos to enhance learning concepts.