# Syllabus and Problem List for Math 135, spring 1999

Text Calculus of a Single Variable: Early Transcendental Functions, 1995, D. C. Heath, by Roland Larson, Robert Hostetler, and Bruce Edwards

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P.1 The Cartesian Plane 3,10,27,28,33,42,43

P.2 Graphs of Equations 1,5,7,39,43,45,61,65

P.3 Lines in the Plane 1,3,5,7,15,19,23,41,49,55,66
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P.4 Functions 3,5,7,17,21,25,27,29,39,47,67,69,73

P.5 Review of Trig. Functions 5,7,10,13,17,35,37,45,47,61,62,84
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P.6 Inverse Functions 1,5,17,25,31,39,53,59,61,63,79,80

P.7 Exponential & Log. Functions 1,3,5,9,19,25,27,31,33,35,47,48,59,67,69
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1.1 A Preview of Calculus

1.2 An Introduction to Limits 1,7,9,11,13,15,17,19,33,34,35,41
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1.3 Properties of Limits 1,3,9,11,17,21,25,27,29,31,33

1.4 Techniques for Evaluating Limits 3,11,13,15,26,29,33,37,39,40,41,47,55
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1.5 Continuity & One-Sided Limits 1,3,5,7,9,11,15,17,31,34,35,39,41,49,51,71,75

1.6 Infinite Limits 1,3,5,11,15,23,25,29,31,37,41
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2.1 The Derivative & Tangent Lines 1,9,13,15,19,21,23,27--32,37,43,47,51
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2.2 Differentiation; Rates of Change 1a,1d,9,13,15,17,23,39,45,47,51,53,57,60,77,81
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2.3 Products & Quotients; Higher Derivs. 7,15,23,27,31,33,35,43,53,57,59,69,79,82,87,90
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2.4 The Chain Rule 1,4,7,17,21,25,29,41,45,51,55,59,65,71,85,93,101
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First exam at the regular class meeting time & place, covering through 2.4
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2.5 Implicit Differentiation 1,7,11,17,25,29,33,35,37

2.6 Related Rates (Start) 3,5a,9a,11a,13,17,21,24,25,29,33,41,47
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2.6 Related Rates (continued from above)
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3.1 Extrema on an Interval 1,5,7,9,11,17,19,23,29,33,35,37

3.2 Rolle's Theorem; Mean Value Theorem 1,3,9,11,23,27,35,43
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3.3 Monotonicity & First Deriv.Test 3,5,11,15,19,25,29,35,43,45,49
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3.4 Concavity & Second Deriv. Test 3,5,6,11,17,19,21,25,37,41,51,54,57,60
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3.5 Limits at Infinity 1,3,5,7,9,13,19,25,27,31,35,37,39,57

3.6 Summary of Curve Sketching (Start) 9,11,17,19,24,26,29,33,37,43,61,67
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3.6 Summary of Curve Sketching (continued from above)
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3.7 Optimization Problems (Start) 3,7,9,11,15,21,23,26,30,37,43
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3.7 Optimization Problems (continued from above)
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3.9 Differentials 3,9,11,19,21,27,28,34,39
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Second exam at the regular class meeting time & place, covering through 3.9
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4.1 Antiderivatives; Indefinite Integrals 1,7,11,13,17,21,25,27,31,33,41,45,47,49,51,53,55
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4.2 Area 21,27,33,35,37
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4.3 Riemann Sums & Definite Integrals 1,3,7,13,15,19,21,23,33,39,41
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4.4 The Fundamental Theorem of Calculus 5,7,11,19,21,23,27,29,31,33,35,39,43,63,71,81
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4.5 Integration by Substitution 1,3,5,9,17,19,35,39,41,49,51,53,55,61,69,71,76,77,87
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5.1 Substitution with Logarithm 3,5,11,13,23,27,39,41,47
Final Exam, Wednesday, May 5, 4 to 7 PM, location to be announced.

Graphing calculators may be used on exams but calculators and computers with QWERTY keyboards or symbolic differentiation and integration programs are not allowed. Students may bring one sheet of paper containing notes (using both sides!) up to 8.5 by 11 inches in size to any exam. Review problems and other general information regarding this course can be found through the web page (look for Math 135 in spring 1999!) Math 135 web pages which you may wish to bookmark. Certain Math 135 web pages from past semesters which students and instructors may find useful are available at MSLC locations on the $3^{\rm rd}$ floor of the ARC building (Busch campus) and the $3^{\rm rd}$ floor of the Chemistry building (Douglass campus).