Course Number: MS152
Course Title: Calculus I

STUDENT LEARNING OUTCOMES

General 

1. The four main topics: limits, continuity, derivatives, and an introduction to integrals, will be covered.
2. The Mean Value Theorem and the Fundamental Theorem of Calculus will be developed, emphasizing a geometric/conceptual understanding
3. The basic applications of the derivative will be covered and used to develop problem solving skills

Specific 

 1. The student will understand the intuitive concept of a limit
 2. The student will be able to formally prove simple limits using the 8,s method
 3. The student will be proficient in using the basic rules to calculate a wide variety of limits; including polynomials, rational functions, radical
     functions, and trig functions
 4. The student will have a geometric understanding of the Pinching Theorem and its use in evaluating the two important limits: (sin x)/ x and
     (1 - cos x)/x
 5. The student will understand the intuitive concept of continuity
 6. The student will be able to formally determine whether various simple functions, and piece-wise defined functions are continuous
 7. The student will be able to classify discontinuities as either removable or essential
 8. The student will have a geometric understanding of the Intermediate Value Theorem
 9. The student will have a geometric understanding of the derivative as the slope of a tangent line
10. The student will be able to calculate various simple derivatives using the definition
11. The student will be able to use the basic rules to calculate the derivatives of a wide variety of functions
12. The student will understand the concepts involved in the proofs of the basic rules, including an introduction to mathematical induction
13. The student will be proficient in the use of the Chain Rule to calculate complicated derivatives
14. The student will understand the concepts involved in implicit differentiation
15. The student will be able to take the derivative of implicit functions, including conic sections
16. The student will be able the solve basic rate of change problems
17. The student will be able to solve a wide range of max/min application problems
18. The student will have a geometric understanding of the Mean Value Theorem
19. The student will be able to apply the Mean Value Theorem to basic problems
20. The student will understand the application of the derivative to curve sketching
21. The student will understand use of the derivative in simple numerical analysis, including Newton's Method of finding roots
22. The student will have a geometric understanding of the concept of an integral, including the notion of the area under a curve
23. The student will understand the concepts involved in the Fundamental Theorem of Calculus
24. The student will be able to use the Fundamental Theorem of Calculus to evaluate simple integrals