# Calculus III

**I. Course Prefix/Number: **
MAT 252

** Course Name: **
Calculus III

** Credits: **
4 (4 lecture; 0 lab)

**II. Prerequisite **

MAT 251 with a grade of C or better.

**III. Course (Catalog) Description **

Course surveys topics of calculus for multivariable functions. Content focus is on: vectors, functions of several variables, curves and surfaces, differentiation, partial derivatives, multiple integrals, and line integrals. Technology is integrated throughout.

**IV. Learning Objectives **

1. Perform and interpret vector operations in space, including dot and cross products.

2. Use vectors to represent and analyze lines, planes and curves in space.

3. Differentiate and integrate curves in space

4. Use tangent and normal vectors to analyze motion along curves in space.

5. Analyze, classify and evaluate multivariable functions.

6. Use differential calculus operations, including partial derivatives and gradients, to calculate tangent planes and normal lines for multivariable functions.

7. Solve applications of optimization for multivariable functions, including Lagrange multipliers.

8 .Use multiple integration to solve applications, including area, voluem, and center of mass.

9. Model and solve problems using cylindrical and spherical coordinates.

10. Evaluate line, curve and surface integrals.

11. Use technology to graph, differentiate, and integrate multivariable functions.

2. Use vectors to represent and analyze lines, planes and curves in space.

3. Differentiate and integrate curves in space

4. Use tangent and normal vectors to analyze motion along curves in space.

5. Analyze, classify and evaluate multivariable functions.

6. Use differential calculus operations, including partial derivatives and gradients, to calculate tangent planes and normal lines for multivariable functions.

7. Solve applications of optimization for multivariable functions, including Lagrange multipliers.

8 .Use multiple integration to solve applications, including area, voluem, and center of mass.

9. Model and solve problems using cylindrical and spherical coordinates.

10. Evaluate line, curve and surface integrals.

11. Use technology to graph, differentiate, and integrate multivariable functions.

**V. Academic Integrity **

Students and employees at Oakton Community College are required to demonstrate academic integrity
and follow Oakton's Code of Academic Conduct. This code prohibits:

• cheating,

• plagiarism (turning in work not written by you, or lacking proper citation),

• falsification and fabrication (lying or distorting the truth),

• helping others to cheat,

• unauthorized changes on official documents,

• pretending to be someone else or having someone else pretend to be you,

• making or accepting bribes, special favors, or threats, and

• any other behavior that violates academic integrity.

There are serious consequences to violations of the academic integrity policy. Oakton's policies and procedures provide students a fair hearing if a complaint is made against you. If you are found to have violated the policy, the minimum penalty is failure on the assignment and, a disciplinary record will be established and kept on file in the office of the Vice President for Student Affairs for a period of 3 years.

Details of the Code of Academic Conduct can be found in the Student Handbook.

• cheating,

• plagiarism (turning in work not written by you, or lacking proper citation),

• falsification and fabrication (lying or distorting the truth),

• helping others to cheat,

• unauthorized changes on official documents,

• pretending to be someone else or having someone else pretend to be you,

• making or accepting bribes, special favors, or threats, and

• any other behavior that violates academic integrity.

There are serious consequences to violations of the academic integrity policy. Oakton's policies and procedures provide students a fair hearing if a complaint is made against you. If you are found to have violated the policy, the minimum penalty is failure on the assignment and, a disciplinary record will be established and kept on file in the office of the Vice President for Student Affairs for a period of 3 years.

Details of the Code of Academic Conduct can be found in the Student Handbook.

**VI. Sequence of Topics **

1. Vectors

a. Geometric and algebraic review

b. Dot product

c. Cross product

d. Equations of lines and planes in R3

2. Calculus of curves

a. Parametric representation of curves in R3

b. Limits, continuity, and derivatives

c. Applications including motion, velocity, and acceleration

d. Integration and arc length

e. Tangent and normal vectors

f Curvature

3. Fundamentals of multivariable functions

a. Surfaces

b. Contour plots

c. Cylindrical and quadratic surfaces

4. Differential calculus of multivariable functions

a. Limits and continuity of functions

b. Partial derivatives, differentials and the chain rule

c. Directional derivatives and gradients

d. Tangent planes and normal lines

e. Second derivative test and Lagrange multipliers

f. Applications involving optimization

5. Integral calculus of multivariable functions

a. The definite integral and Fubini's theorem

b. Triple integrals in Euclidean coordinates

c. Cylindrical and spherical coordinates

d. Applications including area, volume, average value, centers of mass

e. Change in variables and the Jacobian

6. Integrals over curves and surfaces

a. Line integrals

b. The Fundamental Theorem of Line Integrals

c. Div and Curl

d. Green’s Theorem

e. Flux and Stoke’s Theorem

7. Recommended Technology

a Use of technology to manipulate vector quantities

b. Use of technology to differentiate vector functions and evaluate integrals.

c. Use of technology to graph R3 surfaces

d. Use of technology to evaluate partial derivatives

f. Use of technology to evaluate multiple integrals

g. Use of technology to evaluate vector quantities and integrals

a. Geometric and algebraic review

b. Dot product

c. Cross product

d. Equations of lines and planes in R3

2. Calculus of curves

a. Parametric representation of curves in R3

b. Limits, continuity, and derivatives

c. Applications including motion, velocity, and acceleration

d. Integration and arc length

e. Tangent and normal vectors

f Curvature

3. Fundamentals of multivariable functions

a. Surfaces

b. Contour plots

c. Cylindrical and quadratic surfaces

4. Differential calculus of multivariable functions

a. Limits and continuity of functions

b. Partial derivatives, differentials and the chain rule

c. Directional derivatives and gradients

d. Tangent planes and normal lines

e. Second derivative test and Lagrange multipliers

f. Applications involving optimization

5. Integral calculus of multivariable functions

a. The definite integral and Fubini's theorem

b. Triple integrals in Euclidean coordinates

c. Cylindrical and spherical coordinates

d. Applications including area, volume, average value, centers of mass

e. Change in variables and the Jacobian

6. Integrals over curves and surfaces

a. Line integrals

b. The Fundamental Theorem of Line Integrals

c. Div and Curl

d. Green’s Theorem

e. Flux and Stoke’s Theorem

7. Recommended Technology

a Use of technology to manipulate vector quantities

b. Use of technology to differentiate vector functions and evaluate integrals.

c. Use of technology to graph R3 surfaces

d. Use of technology to evaluate partial derivatives

f. Use of technology to evaluate multiple integrals

g. Use of technology to evaluate vector quantities and integrals

**VII. Methods of Instruction **

(To be completed by instructor)

Methods of presentation can include lectures, discussion, experimentation, audio-visual aids, small-group work and regularly assigned homework. Calculators/computers will be used when appropriate. Use of a computer algebra system is also recommended.

Course may be taught as face-to-face, media-based, hybrid or online course.

Methods of presentation can include lectures, discussion, experimentation, audio-visual aids, small-group work and regularly assigned homework. Calculators/computers will be used when appropriate. Use of a computer algebra system is also recommended.

*Mathematica, Derive*, and TI-92 calculators are available for use at the College at no charge.Course may be taught as face-to-face, media-based, hybrid or online course.

**VIII. Course Practices Required **

(To be completed by instructor)

Course may be taught as face-to-face, media-based, hybrid or online course.

Course may be taught as face-to-face, media-based, hybrid or online course.

**IX. Instructional Materials **

**Note:**Current textbook information for each course and section is available on Oakton's Schedule of Classes.

Note: Current textbook information for each course and section is available on Oakton's Schedule of Classes. Within the Schedule of Classes, textbooks can be found by clicking on an individual course section and looking for the words "View Book Information".

Textbooks can also be found at our Mathematics Textbooks page.

A graphics calculator is required. A

*TI-83*or higher numbered model will be used for instructional purposes.

**X. Methods of Evaluating Student Progress **

(To be determined and announced by the instructor)

Evaluation methods can include graded homework, chapter or major tests, quizzes, individual or group projects, calculator/computer projects and a final examination.

Evaluation methods can include graded homework, chapter or major tests, quizzes, individual or group projects, calculator/computer projects and a final examination.

**XI. Other Course Information **

If you have a documented learning, psychological, or physical disability you may be entitled to reasonable academic accommodations or services. To request accommodations or services, contact the Access and Disability Resource Center at the Des Plaines or Skokie campus. All students are expected to fulfill essential course requirements. The College will not waive any essential skill or requirement of a course or degree program.