# MATH 2315

# Calculus III

### Math 2415

**State Approval Code:**2701015919**Semester Credit Hours:**4**Lecture Hours per Week:**3**Contact Hours per Semester:**64

### Catalog Description

Conic sections, polar equations, and their graphs, parametric equations, vector calculus,
multivariable calculus, partial differentiation, double and triple integrals and applications
of “Green’s Theorem” and “Stoke’s Theorem.” Lab fee (2701015919) 4-3-3

### Prerequisites

TSIP complete and Math 2414

### 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 2415, the student will be able to demonstrate:

1)Competence in solving problems related to vectors in 2- and 3- dimensions and their applications

2)Competence in determining and writing equations of surfaces in space

3)Competence in solving problems related to functions in several variables

4)Competence in problems related to limits and continuity

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

6)Competence in determining single, double, and triple integrals of various functions and using these to solve problems in area, volume work, fluid pressure and mass moments

7)Competence in solving problems related to vector fields

8)Competence in determining line integrals and using these to solve problems related to work and mass

9)Competence in applying Green’s and Stoke’s theorems

Essential Competencies

Upon completion of MATH 2415, the student will be able to demonstrate:

1)Competence in solving problems related to vectors in 2- and 3- dimensions and their applications

2)Competence in determining and writing equations of surfaces in space

3)Competence in solving problems related to functions in several variables

4)Competence in problems related to limits and continuity

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

6)Competence in determining single, double, and triple integrals of various functions and using these to solve problems in area, volume work, fluid pressure and mass moments

7)Competence in solving problems related to vector fields

8)Competence in determining line integrals and using these to solve problems related to work and mass

9)Competence in applying Green’s and Stoke’s theorems

### 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)Find the component form of a vector.

2)Use the properties of vector operations.

3)Identify the direction cosines and angles for a vector.

4)Calculate the projection of one vector onto another.

5)Solve application problems using the dot and cross products.

6)Determine the standard, parametric, and symmetric equations for a line in space.

7)Determine the distance between a point and a line in space.

8)Identify and sketch quadric surfaces.

9)Convert equations and points between rectangular, cylindrical, and spherical coordinate forms.

10)Determine derivatives and integrals of vector-valued functions.

11)Solve application problems involving velocity and acceleration using vector-valued functions.

12)Solve application problems involving arc length and curvature using vector-valued functions.

13)Determine tangent and normal vectors to a surface in space.

14)Calculate limits and continuity for functions of several variables.

15)Determine partial derivative and differentials.

16)Use the chain rule for functions of several variables.

17)Calculate directional derivatives and gradients.

18)Determine tangent planes and normal lines.

19)Determine extrema and saddle point for functions of several variables.

20)Determine Lagrange multipliers.

21)Solve application problems involving area and volume using iterated integrals.

22)Solve application problems involving center of mass, moments of inertia, and surface area.

23)Solve application problems using triple integrals.

24)Determine triple integral using cylindrical and spherical coordinates.

25)Determine double integrals using a change of variables and the Jacobian.

26)Use the properties of vector fields.

27)Determine the curl of a vector field.

28)Determine line integrals.

29)Solve application problems for line integrals using independence of path.

30)Determine surface integrals.

31)Apply Green’s theorem and Stokes’ theorem to certain line and surface integrals.

1)Find the component form of a vector.

2)Use the properties of vector operations.

3)Identify the direction cosines and angles for a vector.

4)Calculate the projection of one vector onto another.

5)Solve application problems using the dot and cross products.

6)Determine the standard, parametric, and symmetric equations for a line in space.

7)Determine the distance between a point and a line in space.

8)Identify and sketch quadric surfaces.

9)Convert equations and points between rectangular, cylindrical, and spherical coordinate forms.

10)Determine derivatives and integrals of vector-valued functions.

11)Solve application problems involving velocity and acceleration using vector-valued functions.

12)Solve application problems involving arc length and curvature using vector-valued functions.

13)Determine tangent and normal vectors to a surface in space.

14)Calculate limits and continuity for functions of several variables.

15)Determine partial derivative and differentials.

16)Use the chain rule for functions of several variables.

17)Calculate directional derivatives and gradients.

18)Determine tangent planes and normal lines.

19)Determine extrema and saddle point for functions of several variables.

20)Determine Lagrange multipliers.

21)Solve application problems involving area and volume using iterated integrals.

22)Solve application problems involving center of mass, moments of inertia, and surface area.

23)Solve application problems using triple integrals.

24)Determine triple integral using cylindrical and spherical coordinates.

25)Determine double integrals using a change of variables and the Jacobian.

26)Use the properties of vector fields.

27)Determine the curl of a vector field.

28)Determine line integrals.

29)Solve application problems for line integrals using independence of path.

30)Determine surface integrals.

31)Apply Green’s theorem and Stokes’ theorem to certain line and surface integrals.

### 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:
http://www.panola.edu/collegestore.htm