Calculus and Analytic Geometry 2

University credit, 25 assignments, 5 exams, $995 tuition, $60 administration fee, Prerequisites: see below. This is course U600-222.

This course continues the studies begun in Math 221, and covers the 6th through 10th modules of a 13-module sequence on the fundamental ideas of calculus. Each module contains five lessons and a module exam. Math 222 covers differential equations and initial-value problems, techniques of integration, infinite series, power series and convergence criteria, conic sections, parametric curves, and polar coordinates. This course is followed by U600-234, Multivariable Calculus.

Prerequisite: Successful completion of a first-term calculus course including integration and the calculus of exponential, logarithmic, and trigonometric functions. See the prerequisite page for more details.

Course Materials

• Calculus and Analytic Geometry, 9th ed., Thomas and Finney, Addison-Wesley 1996, ISBN: 0-201-53174-7. This book has also been reissued as Thomas's Calculus, Alternate Edition 9/e, with new ISBN: 0-321-11771-9. The content of the two versions is identical; students may use either one. The reissued text is available through the MBS bookstore, or you can search for available copies of the 1996 printing here.
• Course Guide for Mathematics U600-222, Wilson, UW-Extension Independent Learning, available through MBS at direct.mbsbooks.com/uwlearning.htm (choose "Buy Materials", then "Independent Learning") or 800-325-3252.
• Student Handbook, available at learn.wisconsin.edu/il/studenthandbook/studenthandbook.pdf, or on paper by request to Learner Services, toll-free 1-877-UW-LEARN (877-895-3276).

Format of Course

The course consists of 25 lessons and 5 module exams. Each lesson consists of:

• A reading assignment from the text.
• Exercises to test your understanding of the material. (Solutions to these self-test problems are provided in the course guide.)
• A written assignment, from the text, to submit for grading and feedback.

At the end of each module is a sample exam, with solutions provided. The actual exam is mailed to a proctor selected by the student in accordance with Independent Learning's guidelines.

Grading

Score	Letter Grade
NOTE: The grading scale was revised on Nov 13, 2003. This grading scale applies to all students who complete the course after that date.
93-100	A
90-92	AB
83-89	B
80-82	BC
73-79	C
65-72	D
0-64	F

Each lesson and each exam is graded on a 100-point scale. The final score is computed as a weighted average, with the average of the lessons counting for 40%, and the average of the exams counting 60%. The exam average must be at least 65 for a passing grade. Assuming this is the case, the average of all your work is converted to a letter grade as shown in the table.

Course Outline

Module 266: Differential Equations

• Lesson 1: Hyperbolic Trigonometric Functions
• Lesson 2: First-Order Differential Equations
• Lesson 3: Euler's Method
• Lesson 4: Integration by Parts
• Lesson 5: Integration by Partial Fractions

Module 267: Integration Techniques and Infinite Series

• Lesson 6: Trigonometric Integrals
• Lesson 7: Improper Integrals
• Lesson 8: Numerical Integration
• Lesson 9: Infinite Sequences
• Lesson 10: Infinite Series

Module 268: Series and Power Series

• Lesson 11: Comparison Tests for Convergence
• Lesson 12: The Ratio and Root Tests
• Lesson 13: Absolute and Conditional Convergence
• Lesson 14: Power Series
• Lesson 15: Taylor and Maclaurin Series and Polynomials

Module 269: Conic Sections and Parametric Equations

• Lesson 16: Conic Sections
• Lesson 17: Eccentricity
• Lesson 18: Parametrized Curves
• Lesson 19: Polar Coordinates
• Lesson 20: Integration in Polar Coordinates

Module 270: Vectors in the Plane and in Space

• Lesson 21: Vectors in the Plane
• Lesson 22: Vectors in Space
• Lesson 23: The Dot Product
• Lesson 24: The Cross Product
• Lesson 25: Lines and Planes in Space