##### Calculus II

**I. Course Prefix/Number: **MAT 251

** Course Name: **Calculus II

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

**II. Prerequisite **

MAT 250 with a minimum grade of C.

**III. Course (Catalog) Description **

Course is second in calculus and analytic geometry. Content focuses on differentiation and integration of transcendental functions such as inverse trigonometric functions hyperbolic functions and inverse hyperbolic functionsapplications of the definite integral polar coordinates techniques of integration and improper integral vectors operations and vectors functions. Calculators/computers used when appropriate.

**IV. Learning Objectives **

1. Evaluating definite integrals by using substitution, integration by parts, and tables.

2. Evaluate improper integrals.

3. Use integrals to find area, volume and arc length; application to physics and engineering.

4. Evaluating differential equations by Euler’s method and the separation of variables.

5. Evaluating infinite sequences and series.

6. Using convergence tests and estimating series.

7. Using power series and representing functions by power series.

8. Using Taylor and Maclaurin series.

9. Understand two-dimensional vector functions and their applications.

10. Understand polar equations and their application to differentiation and integration.

11. Use technology for evaluating integrals, series, and polar and parametric equations.

2. Evaluate improper integrals.

3. Use integrals to find area, volume and arc length; application to physics and engineering.

4. Evaluating differential equations by Euler’s method and the separation of variables.

5. Evaluating infinite sequences and series.

6. Using convergence tests and estimating series.

7. Using power series and representing functions by power series.

8. Using Taylor and Maclaurin series.

9. Understand two-dimensional vector functions and their applications.

10. Understand polar equations and their application to differentiation and integration.

11. Use technology for evaluating integrals, series, and polar and parametric equations.

**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. Techniques of Integration

a. Integration by parts

b. Integration by substitution

i. Partial fractions

ii. Trigonometric substitutions

c. Integration using tables

2. Improper Integrals

a. L'Hopital's rule

b. Infinite limits of integration

c. Integration over discontinuities

3. Applications of the Definite Integral

a. Volumes using the cross-sectional area

b. Volumes of solids of revolution

c. Arc length

d. Work, hydrostatic pressure and force, moments, and center of mass

4. Modeling and Differential Equations

a. Exponential growth and decay

b. Separable differential equations

c. Logistic models

5. Infinite sequences and series

a. Sequences and series

b. Geometric series

c. Tests for positive terms (integral, comparison, ratio, n'th root)

d. Alternating series

e. Absolute and conditional convergence

f. Power series

g. Taylor and Maclaurin series

h. Applications including binomial series and solution to differential equations

6. Polar coordinates

a. Graphing with polar coordinates

b. Integration and differentiation using polar coordinates

c. Applications including area and arclength and surface area

7. Vectors and vector functions

a. Two-dimensional vectors and dot products

b. Vector-valued functions

c. Projectile motion

8. Recommended Technology

a. Use of technology to evaluate integrals

b. Use of technology to investigate improper integrals

c. Use Euler's method and technology to evaluate differential equations

d. Use technology for graphing, integrating, and differentiating parametric and

polar equations

a. Integration by parts

b. Integration by substitution

i. Partial fractions

ii. Trigonometric substitutions

c. Integration using tables

2. Improper Integrals

a. L'Hopital's rule

b. Infinite limits of integration

c. Integration over discontinuities

3. Applications of the Definite Integral

a. Volumes using the cross-sectional area

b. Volumes of solids of revolution

c. Arc length

d. Work, hydrostatic pressure and force, moments, and center of mass

4. Modeling and Differential Equations

a. Exponential growth and decay

b. Separable differential equations

c. Logistic models

5. Infinite sequences and series

a. Sequences and series

b. Geometric series

c. Tests for positive terms (integral, comparison, ratio, n'th root)

d. Alternating series

e. Absolute and conditional convergence

f. Power series

g. Taylor and Maclaurin series

h. Applications including binomial series and solution to differential equations

6. Polar coordinates

a. Graphing with polar coordinates

b. Integration and differentiation using polar coordinates

c. Applications including area and arclength and surface area

7. Vectors and vector functions

a. Two-dimensional vectors and dot products

b. Vector-valued functions

c. Projectile motion

8. Recommended Technology

a. Use of technology to evaluate integrals

b. Use of technology to investigate improper integrals

c. Use Euler's method and technology to evaluate differential equations

d. Use technology for graphing, integrating, and differentiating parametric and

polar equations

**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 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.

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 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)

**IX. Instructional Materials **

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

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 grading homework, chapter or major tests, quizzes, individual or group projects, calculator/computer projects and a final examination.

Evaluation methods can include grading 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.