# MATH 2413

# Calculus I

### Math 2413

**State Approval Code:**2701015937**Semester Credit Hours:**4**Lecture Hours per Week:**3**Contact Hours per Semester:**64

### Catalog Description

Review of analytic geometry, limits, derivatives of functions, applications of derivatives,
integration, areas and volumes by integration. (Lab fee) (2701015937)

4-3-3

4-3-3

### Prerequisites

TSIP completed & high school precalculus or Math 2312 or permission of instructor

### Course Curriculum

### Basic Intellectual Compentencies in the Core Curriculum

- Reading
- Writing
- Speaking
- Listening
- Critical thinking
- Computer literacy

### Perspectives in the Core Curriculum

- 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.

### Core Components and Related Exemplary Educational Objectives

### Communication (composition, speech, modern language)

- To participate effectively in groups with emphasis on listening, critical and reflective thinking, and responding.

### Mathematics

- 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 understanding and to solve mathematical problems and judge the reasonableness of the results.
- To interpret mathematical models such as formulas, graphs, tables and schematics, and draw inferences from them.
- To recognize 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

Panola 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:

1.To apply problem-solving skills through solving application problems.

2.To demonstrate arithmetic and algebraic manipulation skills.

3.To read and understand scientific and mathematical literature by utilizing proper vocabulary and methodology.

4.To construct appropriate mathematical models to solve applications.

5.To interpret and apply mathematical concepts.

6.To use multiple approaches - physical, symbolic, graphical, and verbal - to solve application problems

1.To apply problem-solving skills through solving application problems.

2.To demonstrate arithmetic and algebraic manipulation skills.

3.To read and understand scientific and mathematical literature by utilizing proper vocabulary and methodology.

4.To construct appropriate mathematical models to solve applications.

5.To interpret and apply mathematical concepts.

6.To use multiple approaches - physical, symbolic, graphical, and verbal - to solve application problems

### Specific Course Objectives

Major Learning Objectives

Essential Competencies

Upon completion of MATH 2413, the student will be able to demonstrate:

1)Competence in solving problems related to lines.

2)Competence in solving problems related to limits and continuity.

3)Competence in determining the derivatives of various functions and using derivatives to solve problems in maxima and minima, curvature, graphics, velocity and acceleration.

4)Competence in finding the integral of various functions and using integration to solve problems in area, volume, work, fluid pressure, mass, moments, centroids, moment of inertia, growth and decay.

Essential Competencies

Upon completion of MATH 2413, the student will be able to demonstrate:

1)Competence in solving problems related to lines.

2)Competence in solving problems related to limits and continuity.

3)Competence in determining the derivatives of various functions and using derivatives to solve problems in maxima and minima, curvature, graphics, velocity and acceleration.

4)Competence in finding the integral of various functions and using integration to solve problems in area, volume, work, fluid pressure, mass, moments, centroids, moment of inertia, growth and decay.

### General Description of Each Lecture or Discussion

After studying the material presented in the text(s), lecture, laboratory, computer
tutorials, and other resources, the student should be able to complete all behavioral/learning
objectives listed below with a minimum competency of 70%.

1)Solve linear, quadratic, rational, radical and absolute value equations and inequalities, using appropriate interval notation to state answer.

2)Write the equations of circles given pertinent information.

3)Identify the center and radius of a circle whose equation is given in standard form or general form.

4)Find the midpoint of a segment, and find the distance between two points in the Cartesian plane.

5)Write the equation of a line given the slope and a point, or two points.

6)Define and identify a function, its domain and range.

7)Evaluate and graph functions, including piecewise and step functions.

8)Perform basic operations with functions, including composition of functions.

9)Given a basic graph of a function, transform it by shifting, reflecting or stretching it.

10)Find the limits of functions using tables and graphing calculators.

11)Find the limits of functions using the strategies for finding limits.

12)Apply the rules of differentiation to find the derivative of a function: the constant rule, power rule, constant multiple rule, sum and difference rules, product and quotient rules, chain rule, and general power rule.

13)Determine whether a function is continuous or discontinuous; determine whether the discontinuities are removable or nonremovable.

14)Apply the properties of infinite limits when determining the limit of functions.

15)State and apply the definition of limit.

16)Find the derivative of a function using the definition of derivative (the 4-step limit process).

17)Find the average rate of change, the instantaneous rate of change and the acceleration of the position function.

18)Differentiate a function using implicit differentiation.

19)Solve problems involving related rates.

20)Define extrema and critical number and use the Mean Value Theorem to find the extrema on [a,b].

21)State and apply Rolle’s Theorem and the Mean Value Theorem.

22)Define increasing and decreasing functions and use the first derivative test to find relative extrema.

23)Define concavity and point of inflection and use the second derivative test to find the relative extrema and points of inflection.

24)Find the limits of functions as x approaches infinity.

25)Define horizontal asymptote and determine the horizontal asymptotes of a function.

26)Sketch the graph of a function given the first or second derivative; sketch the graph of the first or second derivative given a function.

27)Solve optimization problems by applying unit theorems and definitions regarding extrema.

28)Define anti-derivative and apply basic integration rules to evaluate indefinite integrals.

29)Use sigma notation to write the sum of a finite sequence.

30)Find the area of a region using the limit of the upper and lower sums.

31)Evaluate definite integrals applying appropriate properties.

32)Sketch the region whose area is indicated by a given definite integral.

33)State and apply the first and second Fundamental Theorems of Calculus and the Mean Value Theorem for integrals.

34)Use the Trapezoidal Rule and Simpson’s Rule to approximate definite integrals.

35)Find the area of a region between two plane curves.

36)Find the volume of a solid of revolution using the disc and shell methods (and washer method).

37)Find the arc length of a function on a closed interval.

38)Find the area of the surface of revolution.

39)Calculate the work done by a constant and a variable force.

40)Find the moment(s) and center of mass of a linear system and a two-dimensional system.

41)Find the moments and centroid of a planar lamina.

1)Solve linear, quadratic, rational, radical and absolute value equations and inequalities, using appropriate interval notation to state answer.

2)Write the equations of circles given pertinent information.

3)Identify the center and radius of a circle whose equation is given in standard form or general form.

4)Find the midpoint of a segment, and find the distance between two points in the Cartesian plane.

5)Write the equation of a line given the slope and a point, or two points.

6)Define and identify a function, its domain and range.

7)Evaluate and graph functions, including piecewise and step functions.

8)Perform basic operations with functions, including composition of functions.

9)Given a basic graph of a function, transform it by shifting, reflecting or stretching it.

10)Find the limits of functions using tables and graphing calculators.

11)Find the limits of functions using the strategies for finding limits.

12)Apply the rules of differentiation to find the derivative of a function: the constant rule, power rule, constant multiple rule, sum and difference rules, product and quotient rules, chain rule, and general power rule.

13)Determine whether a function is continuous or discontinuous; determine whether the discontinuities are removable or nonremovable.

14)Apply the properties of infinite limits when determining the limit of functions.

15)State and apply the definition of limit.

16)Find the derivative of a function using the definition of derivative (the 4-step limit process).

17)Find the average rate of change, the instantaneous rate of change and the acceleration of the position function.

18)Differentiate a function using implicit differentiation.

19)Solve problems involving related rates.

20)Define extrema and critical number and use the Mean Value Theorem to find the extrema on [a,b].

21)State and apply Rolle’s Theorem and the Mean Value Theorem.

22)Define increasing and decreasing functions and use the first derivative test to find relative extrema.

23)Define concavity and point of inflection and use the second derivative test to find the relative extrema and points of inflection.

24)Find the limits of functions as x approaches infinity.

25)Define horizontal asymptote and determine the horizontal asymptotes of a function.

26)Sketch the graph of a function given the first or second derivative; sketch the graph of the first or second derivative given a function.

27)Solve optimization problems by applying unit theorems and definitions regarding extrema.

28)Define anti-derivative and apply basic integration rules to evaluate indefinite integrals.

29)Use sigma notation to write the sum of a finite sequence.

30)Find the area of a region using the limit of the upper and lower sums.

31)Evaluate definite integrals applying appropriate properties.

32)Sketch the region whose area is indicated by a given definite integral.

33)State and apply the first and second Fundamental Theorems of Calculus and the Mean Value Theorem for integrals.

34)Use the Trapezoidal Rule and Simpson’s Rule to approximate definite integrals.

35)Find the area of a region between two plane curves.

36)Find the volume of a solid of revolution using the disc and shell methods (and washer method).

37)Find the arc length of a function on a closed interval.

38)Find the area of the surface of revolution.

39)Calculate the work done by a constant and a variable force.

40)Find the moment(s) and center of mass of a linear system and a two-dimensional system.

41)Find the moments and centroid of a planar lamina.

### Methods of Instruction/Course Format/Delivery

Methods employed will include lecture/demonstration, discussion, problem solving,
analysis, and reading assignments. Homework will be assigned.

Faculty may choose from, but are not limited to, the following methods of instruction:

(1) Lecture

(2) Discussion

(3) Internet

(4) Video

(5) Television

(6) Demonstrations

(7) Field trips

(8) Collaboration

(9) Readings

Faculty may choose from, but are not limited to, the following methods of instruction:

(1) Lecture

(2) Discussion

(3) Internet

(4) Video

(5) Television

(6) Demonstrations

(7) Field trips

(8) Collaboration

(9) Readings

### Assessment

Faculty may assign both in- and out-of-class activities to evaluate students' knowledge
and abilities. Faculty may choose from – but are not limited to -- the following methods

•Attendance

•Book reviews

•Class preparedness and participation

•Collaborative learning projects

•Compositions

•Exams/tests/quizzes

•Homework

•Internet

•Journals

•Library assignments

•Readings

•Research papers

•Scientific observations

•Student-teacher conferences

•Written assignments

•Attendance

•Book reviews

•Class preparedness and participation

•Collaborative learning projects

•Compositions

•Exams/tests/quizzes

•Homework

•Internet

•Journals

•Library assignments

•Readings

•Research papers

•Scientific observations

•Student-teacher conferences

•Written assignments

Letter Grades for the Course will be assigned as follows:

A: 90 < Average < 100

B: 80 < Average < 90

C: 70 < Average < 80

D: 60 < Average < 70

F: 00 < Average < 60

A: 90 < Average < 100

B: 80 < Average < 90

C: 70 < Average < 80

D: 60 < Average < 70

F: 00 < Average < 60

### Text, Required Readings, Materials, and Supplies

For current texts and materials, use the following link to access bookstore listings.