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MAT141 - Calculus 1
Catalog Description: Studies functions of a single variable with regard to limits, continuity, differentiation, anti-differentiation, and applications of these topics. Concludes with a study of the definite integral and the fundamental theorem of calculus. Four class hours. Prerequisite: MAT 140 (with a minimum grade of C) or equivalent by placement.
Lecture: 4 hrs.
Course Learning Outcomes (CLOs):
Upon successful completion of this course as documented through writing, objective testing, case studies, laboratory practice, and/or classroom discussion, the student will be able to:
1.Given a polynomial or rational function, find the limit of the function as x approaches some constant value (if it exists) or state why it does not exist.
2.Given a polynomial, rational, or trigonometric function, show that it is continuous at a point or over a stated interval.
3.Given a simple polynomial function, apply the definition of derivative to find the derivative of the function.
4.Apply any of the appropriate rules (constant rule, sum and difference rule, product rule, quotient rule, chain rule) to find the derivative of a function involving factors or components that are polynomial, rational, or trigonometric.*
5.Given the curve of any of the above functions and a point on the curve, find the equation of the line tangent to the curve.
6.Given a polynomial function, sketch the graph by using derivatives to locate intervals of increase/decrease and intervals of positive concavity/negative concavity.
7.Given a function defined implicitly, find its derivative and/or apply this concept to related rate problems.
8.Given a function of the types describe in (4), find any optimal values of the function.
9.Given any of the fundamental integrable functions, find the anti-derivative of the function using the appropriate rule.
10.Apply a u-substitution to integrate functions of the form f(g(x)) g(x).
11.Given any function of the forms described in (9) or (10), find the area under the curve of the function using a definite integral.
* This course objective has been identified as a student learning outcome that must be formally assessed as part of the Comprehensive Assessment Plan of the college. All faculty teaching this course must collect the required data and submit the required analysis and documentation at the conclusion of the semester to the Office of Institutional Research and Assessment.
I. The Cartesian plane and functions
1.1 The real line
1.2 The Cartesian plane, the Distance Formula, and circles
1.3 Graphs of equations
1.4 Lines in the plane
1.6 Review of trigonometric functions
II. Limits and their properties
2.1 An introduction to limits
2.2 Properties of limits
2.3 Techniques for evaluating limits
2.4 Continuity and one-sided limits
2.5 Infinite limits
3.1 The derivative and the tangent line problem
3.2 Velocity, acceleration, and other rates of change
3.3 Differentiation rules for sums, constant multiples, powers, sines, and cosines
3.4 Differentiation rules for products, quotients, secants, and tangents
3.5 The Chain Rule
3.6 Implicit differentiation
3.7 Related rates
IV. Applications of differentiation
4.1 Extrema on an interval
4.2 The Mean Value Theorem
4.3 Increasing and decreasing functions and the First Derivative Test
4.4 Concavity and the Second Derivative Test
4.5 Limits at infinity
4.6 A summary of curve sketching
4.7 Optimization problems
4.8 Business and economics applications
4.9 Newton's Method
5.1 Antiderivatives and indefinite integration
5.2 Integration by substitution
5.3 Sigma notation and the limit of a sequence
5.5 Riemann sums and the definite integral
5.6 The Fundamental Theorem of Calculus
5.7 Variable bounds of integration and the natural logarithmic function
5.8 The natural logarithmic function and differentiation
5.9 The natural logarithmic function and integration
Effective Term: Fall 2012