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MTH
31
Syllabus
- Calculus and Analytic Geometry I (4 credits / 6 hours per week)
Prerequisite:
Math 30 or equivalent
TEXT : Calculus (Fourth Edition) by James Stewart, Brooks/Cole, Pub.
(Students who do not need Math 33 may use single Variable
Calculus (Fourth Edition) by James Stewart, Brooks/Cole, Pub.)
SECTION TOPIC SUGGESTED EXERCISES
Chapter Two: Limits and Rates of Change
2.1 The Tangent and Velocity Problems 71/ 1,3,5,7
2.2 The Limit of a Function 81/ 1-5, 12, 13, 14, 21-26
2.3 Calculating Limits Using Limit Laws 91/ 1, 3-23 odd
2.5 Continuity 112/ 3, 7, 9, 11, 15, 17, 19, 21,
25, 34, 35, 37, 39, 42, 43, 45
2.6 Tangents, Velocities, and 121/ 1, 7, 9, 11, 17
Other Rates of Change
Review 124/ 1-11 odd, 17, 23, 27-31 odd
Chapter Three: Derivatives
3.1 Derivatives 134/ 1, 5 ,7, 13, 15, 17, 19, 25
3.2 The Derivative as a Function 144/ 1, 3, 4, 7, 17, 19, 21
3.3 Differentiation Formulas 156/ 1-35 odd, 49, 51
3.4 Rates of Change in the 167/ 1-7 odd, 8, 13, 16
Natural and Social Sciences
3.5 Derivatives of Trigonometric Functions 175/ 1-17 odd, 21, 29, 35-43 odd
3.6 The Chain Rule 183/ 1-41 odd, 51,55
3.7 Implicit Differentiation 190/ 1-19 odd, 25, 27, 41, 43, 45
3.8 Higher Derivatives 196/ 1, 5-19 odd, 23-29 odd
3.9 Related Rates 203/ 1-23 odd
3.10 Linear Approximations and Differentials 211/ 5, 7, 9, 11-25 odd, 27-35 odd
Review 214/ 7, 11, 13-35, 43, 49, 57, 67, 71, 73, 78
Chapter Four: Applications of Differentiation
4.1 Maximum and Minimum Values 230/ 3, 5, 15-23 odd, 31-57 odd
4.2 The Mean Value Theorem 238/ 1, 3, 7, 8, 11-17 odd
4.3 How Derivatives Affect the Shape 247/ 1, 5, 7, 11-19 odd, 27-35 odd
of a Graph
4.4 Limits at Infinity; Horizontal 260/ 3, 7-19 odd, 31, 35
Asymptotes
4.5 Summary of Curve Sketching 270/ 1-21 odd
4.7 Optimization Problems 282/ 3,5,7,11,17,25,29
4.9 Newton’s Method 297/ 5-15 odd
4.10 Anti-derivatives 304/ 3-31 odd
Review 307/ 1-27 odd, 35, 41, 46, 49-55 odd
Chapter Five: Integrals 5.1 Areas and Distance 323/ 1, 3, 5, 13, 15, 19 5.2 The Definite Integral 334/ 3, 5, 9, 11, 15, 19, 31, 33, 39 5.3 The Fundamental Theorem of Calculus 344/ 3-31 odd, 39, 41, 43 5.4 Indefinite Integrals and the 352/ 1-11 odd, 17-27 odd, 53, 55 Total Change Theorem 5.5 The Substitution Rule 361/ 1-31 odd, 37-53 odd Review 364/ 2, 5, 9-23 odd, 35, 37, 39
5/99 A.W.