Course Number and Title: MAT 281 Calculus I
This course provides students with a study of limits and continuity and differential and integral calculus of single variable functions with applications.
- Apply the concepts of limits and continuity. (CCC 2, 6)
- Compute the derivative of a function. (CCC 2, 6)
- Use derivatives to solve application problems. (CCC 2, 6)
- Use integrals to solve application problems. (CCC 2, 6)
See Core Curriculum Competencies and Program Graduate Competencies at the end of the syllabus. CCPOs are linked to every competency they develop.
Upon completion of this course, the student will:
- Apply the concepts of limits and continuity.
- Define and evaluate the limit of algebraic, trigonometric, and piece-wise functions (including one-sided limits and infinite limits) using algebraic, numeric, and graphical methods.
- Demonstrate the geometric concept of a tangent line.
- Use graphical, algebraic, and numeric techniques to evaluate limits and the slope of a tangent line.
- Calculate limits using the limit laws of sum, difference, multiplication, division, and power.
- Calculate limits using the squeeze theorem.
- Determine equations of asymptotes using limits.
- Determine the set on which a function is continuous.
- Identify the types of discontinuities in a function.
- Use the concept of a continuity when applying the intermediate value theorem.
- Relate the concept of the limit of a quotient and slope of a tangent line to velocity and average rate of change problems.
- Compute the derivative of a function.
- Determine the derivative of an algebraic function using the definition of a derivative.
- Determine the derivative of algebraic, trigonometric, exponential, logarithmic, inverse trigonometric, and hyperbolic functions and their combinations.
- Determine the derivative of a function using the laws for product, quotient, sum, difference, chain rule, and logarithmic differentiation.
- Use the relationship of differentiability and continuity.
- Use the graph of a function to construct the graph of its derivative.
- Perform implicit differentiation.
- Compute higher order derivatives.
- Use derivatives to solve application problems.
- Apply the derivative to the slope of the tangent line and instantaneous rate of change.
- Apply the derivative to solve problems involving position, velocity, and acceleration.
- Solve related rate problems.
- Apply the derivative to solve problems involving linear approximation and differentials.
- Use the derivative to determine local and absolute extrema of a function.
- Sketch the graph of a function using the first and second derivative to determine the intervals of increasing/decreasing, extrema, concavity, points of inflection, and asymptotes.
- Apply the derivative to solve problems using the mean value theorem.
- Use derivatives to solve optimization problems.
- Use Newton’s method to determine the roots of an equation on a given interval.
- Use integrals to solve application problems.
- Determine the antiderivative of a function.
- Estimate the area under a curve using Riemann sums.
- Estimate distance traveled from a velocity graph.
- Define and compute the definite integral using the limit of a Riemann sum.
- Solve problems using the properties of integrals.
- Apply the fundamental theorem of calculus to the integration process and the net change theorem.
- Apply the substitution rule and symmetry in the evaluation of integrals.
- Identify differential equations and their solution, including models for population growth.
- Solve first order separable differential equations.
Students must demonstrate proficiency on all CCPOs at a minimal 75 percent level to successfully complete the course. The grade will be determined using the Delaware Tech grading system:
Students should refer to the Student Handbook for information on the Academic Standing Policy, the Academic Integrity Policy, Student Rights and Responsibilities, and other policies relevant to their academic progress.
- Apply clear and effective communication skills.
- Use critical thinking to solve problems.
- Collaborate to achieve a common goal.
- Demonstrate professional and ethical conduct.
- Use information literacy for effective vocational and/or academic research.
- Apply quantitative reasoning and/or scientific inquiry to solve practical problems.
The College is committed to providing reasonable accommodations for students with disabilities. Students are encouraged to schedule an appointment with the campus Disabilities Support Counselor to request an accommodation needed due to a disability. A listing of campus Disabilities Support Counselors and contact information can be found at the disabilities services web page or visit the campus Advising Center.