Catalog Description: This course includes limits, continuity of functions, algebraic and trigonometric function derivative of functions with application in related-rate and optimization problems, differentials, indeterminate forms, L'Hospital's Rule, Max-Min Theorems, Mean Va
Semester Credit Hours: 4 Lecture Hours per Week: Contact Hours per Semester: 64 State Approval Code: 2701015900
Course Subject/Catalog Number: MATH2413
Course Title: Calculus I With Analytical Geometry
Core Curriculum: State Criteria
Basic Intellectual Competencies (Those marked with a √ reflect the state-mandated
competencies taught in this course.)
Perspectives (Those marked with a √ reflect the state-mandated perspectives
taught in this course.)
Establish broad and multiple perspectives
on the individual in relationship to the larger society and world in which
he/she lives, and to understand the responsibilities of living in a culturally
and ethnically diversified world.
Stimulate a capacity to discuss and
reflect upon individual, political, economic, and social aspects of life in
order to understand ways in which to be a responsible member of society.
Recognize the importance
of maintaining health and wellness.
Develop a capacity to use knowledge
of how technology and science affect their lives.
Develop personal values for ethical
behavior.
Develop the ability to make
aesthetic judgments.
Use logical reasoning in problem solving.
Integrate knowledge and understand
the interrelationships of the scholarly disciplines.
Exemplary Objectives (Those marked with a √ reflect state-mandated exemplary
objectives taught in this course.)
Mathematics: The objective of the mathematics component
of the core curriculum is to develop a quantitatively literate college graduate. Every
college graduate should be able to apply basic mathematical tools in the
solution of real-world problems.
To apply arithmetic, algebraic, geometric, higher-order thinking and
statistical methods to modeling and solving real-world situations.
To represent and evaluate basic mathematical information verbally,
numerically, graphically, and symbolically.
To expand mathematical reasoning skills and formal logic to develop
convincing mathematical arguments.
To use appropriate technology to enhance mathematical thinking and
understand and to solve mathematical problems and judge reasonableness
of the results.
To interpret mathematical models such as formulas, graphs, tables
and schematics, and draw inferences from them.
To develop the limitations of mathematical and statistical models.
To develop the view that mathematics is an evolving discipline interrelated
with human culture, and understand its connections to other disciplines.
Instructional Goals and Purposes:
Lee College's instructional goals include 1) creating an academic atmosphere
in which students may develop their intellects and skills and 2) providing
courses so students may receive a certificate/an associate degree or transfer
to a senior institution that offers baccalaureate degrees.
General Course Objectives:
Successful completion of this course will promote the general student learning
outcomes listed below. The student will be able
To apply problem-solving skills through solving application problems.
To demonstrate arithmetic and algebraic manipulation skills.
To read and understand scientific and mathematical literature by utilizing
proper vocabulary and methodology.
To construct appropriate mathematical models to solve applications.
To interpret and apply mathematical concepts.
To use multiple approaches - physical, symbolic, graphical, and verbal - to
solve application problems.
Specific Course Objectives:
Upon successful completion of the course, the student will be able
To apply the concepts of limits and continuity to functions.
To able to find derivatives by evaluating limits and by derived
formulas.
To able to show how to use derivatives to find maximum and
minimum values of functions.
To be able to predict and analyze the shapes of graphs.
To draw conclusions about the behavior of functions that satisfy
differential equations.
To analyze the Mean Value Theorem and its corollaries.
To describe how functions are changing at a given instant
and over a given interval.
To investigate the areas under the curve.
To discover the relationship between differential and integral
calculus in the Fundamental Theorem of Calculus.
To calculate with integrals the volumes of solids, lengths
of curves, work and force, and the coordinates of the points where solid
objects balance.
Course Content:
Students will be required to do the following:
Find limits graphically and numerically
Evaluate limits analytically
Determine continuity and one-sided limits
Use L'Hopital's Rule to evaluate limits involving indeterminate
forms
Determine infinite limits
Determine the derivative using the limit definition
Determine the derivative using the rules for differentiation
Solve application problems involving related rates
Use the first and second derivatives to sketch curves
Solve application problems involving maxima and minima
Determine antiderivatives and indefinite integrals
Determine area using Riemann sums
Evaluate definite integrals using the Fundamental Theorem of Calculus
Integrate by substitution and numerical methods
Solve application problems involving area of a region, volume of solid
of revolution, arc length of a curve, work, moments, center of mass, centroid,
fluid pressure, and fluid force
Methods of Instruction/Course Format/Delivery:
Faculty may choose from but are not limited to the following methods of instruction: lecture,
discussion, Internet, video, television, demonstrations, field trips, collaboration,
readings.
Assessment:
Faculty may assign both in- and out-of-class activities to evaluate students'
knowledge and abilities. Faculty may choose from the following methods:
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