Calculus and Analytic Geometry I

University credit, 26 assignments, 5 exams, $995 tuition, $60 administration fee, Prerequisites: Knowledge of algebra and trigonometry at a level consistent with a grade of B or better in a college-preparatory pre-calculus sequence. This is course U600-221.

 

This course consists of the first 5 modules of a 13-module sequence covering the fundamental ideas of calculus. Each module contains five or six lessons and a module exam. Math 221 covers the principle of differentiation, including a brief treatment of the rigorous notion of limit, applications of differentiation to a variety of situations, basic integration and the Fundamental Theorem of Calculus, applications of integration to a variety of problems, and the calculus of exponential, logarithmic, and trigonometric functions. The modular sequence continues with courses U600-222 and U600-234.

Prerequisite: Knowledge of algebra and trigonometry at a level consistent with a grade of B or better in a college-preparatory pre-calculus sequence. 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.
• Course Guide for Mathematics U600-221, Wilson, UW-Extension Independent Learning, available through MBS at direct.mbsbooks.com/uwlearning.htm (choose "Buy Course 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 26 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 261: Differentiation

• Lesson 1: Preliminaries
• Lesson 2: Limits
• Lesson 3: Continuity and Tangents
• Lesson 4: The Derivative of a Function
• Lesson 5: Differentiation Rules
• Lesson 6: More Functions to Differentiate

Module 262: Applications of Differentiation

• Lesson 7: Related Rates
• Lesson 8: The Mean Value Theorem
• Lesson 9: Derivatives and Graphing
• Lesson 10: Optimization
• Lesson 11: Numerical Techniques

Module 263: Basic Integration

• Lesson 12: Indefinite Integrals and Applications
• Lesson 13: Indefinite Integrals by Substitution
• Lesson 14: Riemann Sums and the Definite Integral
• Lesson 15: Properties of the Definite Integral
• Lesson 16: The Fundamental Theorem of Calculus

Module 264: Applications of Integration

• Lesson 17: Area
• Lesson 18: Volumes by Slicing
• Lesson 19: Volumes by Shells, Arc Length
• Lesson 20: Moments and Centers of Mass
• Lesson 21: Work, Pressure, and Force

Module 265: Transcendental Functions

• Lesson 22: The Natural Logarithm
• Lesson 23: The Exponential Function
• Lesson 24: Other Exponential and Log Functions
• Lesson 25: Limiting Rates of Growth
• Lesson 26: Inverse Trigonometric Functions