MATH 125 Section 006: Calculus I
Fall 2013
4 Credit Hours
Primary Instructor: Dr. Paul Allen
Core Designation: Mathematics
Syllabus subject to change.
PREREQUISITE: A grade of C- or higher in MATH 112 and MATH 113 (or MATH 115) or a mathematics placement score in the 440-600 range.
DESCRIPTION: First course in the three part basic calculus sequence for students majoring in mathematics, science, or engineering. Topics include limits, continuity, differentiation, applications of differentiation, and integration. Applications of the derivative are covered in detail, including approximations of errors using differentials, maxima and minima problems, curve sketching, optimization problems, and
LEARNING OUTCOMES FOR 100- AND 200-LEVEL COURSES:
1) Students will be able to identify key concepts in the arts, sciences, humanities, or mathematics to provide a broad perspective.
2) Students will be able to demonstrate effective written communication skills.
LEARNING OUTCOMES FOR THIS COURSE:
1) Students will develop a basic understanding of the concepts of calculus and be able to apply them to real situations.
2) Students will be able to find limits of functions.
3) Students will be able to calculate (and simplify) derivatives involving rational, exponential, trigonometric, inverse trigonometric, and hyperbolic functions.
4) Students will be able to apply derivatives to various applications including optimization problems, linear approximation, and curve sketching.
5) Students will be able to calculate (and simplify) integrals using some basic techniques of integration.
6) Students will be able to use integration to find the area of certain types of planar regions.
CHAPTERS COVERED:
1 Functions and Limits*
2 Derivatives (Section 2.7 is optional and will not be covered.)
3 Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions
(Section 3.4 is optional and will not be covered, section 3.7 omit)
4 Applications of Differentiation
5 Integrals
7 Applications of Integration (Cover section 7.1 only: Areas Between Curves)
TEST MATERIAL: Test problems will be similar to the assigned exercises. The assigned exercises cover
all material that will appear on the tests. Students should keep their solutions to homework problems in a
notebook that can be reviewed when studying for examinations.
SECTIONS TO BE COVERED PAGE ASSIGNED EXERCISES
1.3 The Limit of a Function .. 33 3, 4, 5, 11, 15
1.4 Calculating Limits .. 43 2, 11, 12, 13, 15, 17, 24, 33, 34 35, 37,
41, 45, 47, 49, 50
1.5 Continuity .. 54 3, 4, 15, 16, 17, 18, 19, 21, 29, 31, 33, 39, 41
1.6 Limits Involving Infinity .. 67 1, 2, 13, 14, 15, 19, 24, 25, 31, 32, 34
2.1 Derivatives and Rates of Change .. 80 3, 5, 21, 23, 25, 29
2.2 The Derivative as a Function .. 92 3, 21, 23, 27, 33, 34, 35, 36
Test 1 Thursday, September 12 Covers all material from sections 1.3 through 2.2
SECTIONS TO BE COVERED PAGE ASSIGNED EXERCISES
2.3 Basic Differentiation Formulas .. 105 5, 7, 9, 11, 13, 15, 27, 31, 37, 38, 39
2.4 The Product and Quotient Rules .. 112 1, 3, 4, 11, 13, 18, 27, 41, 42
2.5 The Chain Rule .. 120 1, 5, 6, 7, 9, 12, 17, 23, 27, 31, 35
2.6 Implicit Differentiation .. 127 3, 5, 13, 19, 20, 29, 30
2.7 Related Rates (OMIT)
2.8 Linear Approximations and Differentials .. 138 1, 2, 3, 4, 5, 6
3.1 Exponential Functions (Pre-calculus Review Material)
3.2 Inverse Functions and Logarithms (Pre-calculus Review Material)
3.3 Derivatives of Log and Exponent Function.. 169 1, 3, 5, 7, 19, 20, 21, 23, 24, 25, 27, 29, 33, 42, 43,
45, 49, 51, 55, 57, 69, 70
3.4 Exponential Growth and Decay (OMIT)
Test 2 Tuesday, October 8 Covers all of the above material from sections 2.3 through 3.4
SECTIONS TO BE COVERED PAGE ASSIGNED EXERCISES
3.5 Inverse Trigonometric Functions .. 183 7, 8, 9, 16, 17, 19
3.6 Hyperbolic Functions .. 189 17, 26, 27, 28, 29, 31, 33, 36, 37
3.7 L’Hospitals Rule (OMIT) This section will be covered in Calculus II
4.1 Maximum and Minimum Values .. 209 3, 5, 23, 25, 35, 39, 41
4.2 The Mean Value Theorem ... 215 1, 2, 3, 7, 9, 10, 11
4.3 Derivatives and The Shapes of Graphs .. 222 1, 3, 7, 9, 23, 25, 27, 31
4.4 Curve Sketching . . 230 1, 3, 5, 25, 37, 39
4.5 Optimization Problems .. 238 9, 11, 19, 22
4.6 Newton’s Method .. 245 6, 7, 8
Test 3 Wednesday, October 30 Covers the above material from sections 3.5 through 4.6
SECTIONS TO BE COVERED PAGE ASSIGNED EXERCISES
4.7 Antiderivatives .. 252 1, 3, 5, 7, 9, 19, 23, 25
5.1 Areas and Distances .. 266 1, 5
5.2 The Definite Integral . . 279 1, 7, 13, 29, 31, 33, 35
5.3 Evaluating Definite Integrals .. 289 1, 3, 5, 7, 13, 21, 27, 33, 35
5.4 The Fundamental Theorem of Calculus .. 298 1, 2, 3, 5, 7, 9, 11
5.5 The Substitution Rule .. 306 1, 3, 5, 7, 9, 11, 13, 19, 39 43
Test 4 Thursday, November 21 Covers all of the above material from sections 4.7 through 5.5
SECTIONS TO BE COVERED PAGE ASSIGNED EXERCISES
7.1 The Area Between Curves .. 369 1, 2, 3, 5, 9, 11, 13, 15
Comprehensive Final Exam Section 006 Tuesday, December 10 8:00 AM - 10:30 AM
Comprehensive Final Exam Section 008 Monday, December 9 11:30 AM - 2:00 PM
COURSE GRADES: Grades will be determined from four tests, and a comprehensive final examination. The lowest score from the four tests will be dropped; that is, the best three of your test scores together with the final exam score will be used (counting each 25%) to calculate your course average. If your final exam grade is higher than your course average, then the final exam score alone will be used to determine course grade. Students who miss fewer than 5 classes (excused or unexcused) will receive a 3% bonus towards their final course grade.
If you miss a test (for any reason) that test will be counted as your dropped test score. If you miss a further test and have a good reason for so doing (such as a serious, varifiable illness, etc.) then your final exam score will be counted as that missed test grade. There are no make-up exams. Do not miss the final exam!
No make-up exams will be given. See the section on Course Grades.
CLASS ATTENDANCE: Students are expected to attend all classes. Roll will be taken during every class when students sign by their name on the class roll that is circulated each period. Students who are tardy and miss the attendance sign in sheet must be sure to sign it before leaving the room after class is dismissed; otherwise, they will be considered as officially abscent. Students are solely responsible for any work missed during an absence.
TEXT: Essential Calculus - Early Transcendentals (2nd edition)
AUTHOR: Stewart
PUBLISHERS: Brooks/Cole
Class Key: ua 8171 3138 Students who purchase an electronic copy of the textbook through WebAssign will need the class key to view their book.
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