# Calculus I Math171

Professor: Thomas Schlumprecht
Office: Blocker 525K Tel: Disconnected due to budget cuts imposed by the Board of Regents and the State of Texas
Hours: Wednesday 3:00 -4:00 PM and Friday 10:30 -11:30 AM and by appointment
E-mail: schlump@math.tamu.edu
Homepage: www.math.tamu.edu/~thomas.schlumprecht

Class time:
Math171-503 MWF  12:40 -1:30 BLOC 164 Tutorial: T   12:45 - 1:35 PM CV223

Help Sessions (for Math151 and 171): Monday, Tuesday, and Wednesday  8:00 - 10:00 PM,  BLOC150

Textbook: Calculus: Early Transcendentals , Stewart

Course Description: Math 171 is the first of a three semester beginning calculus sequence, which is taken, for the most part, by math, chemistry, and physics majors. The department expects that students passing Math 171 be able to follow mathematical proofs and handle routine computations, i.e., limits, derivatives, max-min problems, and calculation of definite integrals using the fundamental theorem of calculus. We expect students to be able to state (write) and apply basic definitions and major theorems. These include, but are not limited to, definitions of limit, continuous function, derivative, definite and indefinite integrals, the intermediate value theorem for continuous functions, the mean value theorem, and the fundamental theorem of calculus. Students are also expected to be able supply simple proofs, e.g., some of the limit theorems, some of the rules of differentiation, and applications of the intermediate and mean value theorems. The list is of course endless, but keep in mind the phrase `simple proofs'. Students should become familiar with the standard notations of logic, set theory, and functions.

Grading.Your grade will be based on weekly quizzes, which are based on the homework and will be given on Fridays, two tests which will be given out side of class and a final exam. The quizzes will count for 25%, each test for 25% and the final for 25%. Your letter grade will be assigned this way: 90-100%, A; 80-89%, B; 70-79%, C; 60-69%, D; 59% or less, F.

Schedule of Tests and Finals:
Exam 1: Tuesday, October 3, 7:30 PM - 9:30 PM Room: BLOC 220
Exam 2: Tuesday, November 7, 7:30 PM - 9:30 PM Room: BLOC 220
Final: Monday, December 11, 10:30 - 12:30 PM (in usual class room BLOC 164

Make-up policy: Make-ups for missed quizzes and exams will only be allowed for a university approved excuse in writing. Wherever possible, students should inform the instructor before an exam or quiz is missed. Consistent with University Student Rules, students are required to notify an instructor by the end of the next working day after missing an exam or quiz. Otherwise, they forfeit their rights to a make-up.

Scholastic dishonesty: Copying work done by others, either in-class or out of class, is an act of scholastic dishonesty and will be prosecuted to the full extent allowed by University policy. Collaboration on assignments, either in-class or out-of-class, is forbidden unless permission to do so is granted by your instructor. For more information on university policies regarding scholastic dishonesty, see University Student Rules.

Copyright policy: All printed materials disseminated in class or on the web are protected by Copyright laws. One xerox copy (or download from the web) is allowed for personal use. Multiple copies or sale of any of these materials is strictly prohibited.

Americans with Disabilities Act (ADA) Policy Statement. The Americans with Disabilities Act (ADA) is a federal anti-discrimination statute that provides comprehensive civil rights protection for persons with disabilities. Among other things, this legislation requires that all students with disabilities be guaranteed a learning environment that provides for reasonable accommodation of their disabilities. If you believe you have a disability requiring an accommodation, please contact Disability Services, in Cain Hall, Room B118, or call 845-1637. For additional information visit http://disability.tamu.edu.

Tentative Schedule: This is a projected roadmap of the course. Modifications necessitated by circumstances are inevitable. Whilst most of the sections below will be covered in lecture, some might be assigned for reading.

• Week 1: Supplement: 1.1 (Vectors), 1.2 (The Dot Product), 1.3 (Vector Functions),
• Week 2: 2.2 (Limit of a Function), 2.4 (Precise Definition of a Limit),
• Week 3: 2.3 (Calculating Limits Using Limit Laws), 2.5 (Continuity), 2.6 (Limits at Infinity, Horizontal Asymptotes) 2.7 (Tangents, Velocities, and Other Rates of Change)
• Week 4: 3.1 (Derivatives), 3.1b+1.4 (Exponential Functions and their Derivatives), 3.2 (Differentiation Formulas),
• Week 5: 3.3 (Derivatives of Trigonometric Functions), 3.4 (The Chain Rule), 3.5 (Implicit Differentiation),
• Week 6: 3.5b Review, Exam 1 1.5, 3.6b (Inverse Functions, and their derivatives), 3.6 (Logarithmic Functions),
• Week 7: 3.6b (Derivatives of Logarithmic Functions), 3.6c (Inverse Trigonometric Functions and their derivatives), 3.9 (Related Rates),
• Week 8: 3.10 (Linear Approximation), supplement: (Higher Derivatives), (Derivatives of Vector Functions), (Slopes and Tangents of Paremterized Forms)
• Week 9: 4.1 (Maximum and Minimum Values), 4.2 (The Mean Value Theorem),
• Week 10: 4.3 (The Shapes of Curves), 4.4 (Indetermined Forms), 4.7 (Applied Maximum and Minimum Problems),
• Week 11: Review, Exam II supplement: (Sigma Notation),
• Week 12: 5.1 (Area), 5.2 (The Definite Integral),
• Week 13: 5.2 (The Definite Integral, continuation), 5.3 (The Fundamental Theorem of Calculus),
• Week 14: 5.3 (The Fundamental Theorem of Calculus,continuation), 5.4 (Indefinite Integrals) 5.5 (Substitution Rule)
• Week 15: 5.4 6.1 (Area between curves) Review.

## Homework for Math171

On this page weekly class notes (first without solutions to problems, one week later with solutions) will be uploaded and the weekly homeworks will be announced.

NOTE: homework is NOT to be turned in. But there will be a quizz on Fridays, starting September 8, consisting of one or two of the assigned problems, from class notes as well as text book, and/or it will be asked for the statement of a defintion and theorem (from boxed in part of class notes).

Class Notes for Week 1 and Homework 1 (due Friday, September 8)

• Section 1.1  Section 1.2  Section 1.3
• with solutions: Section 1.1  Section 1.2  Section 1.3

• Assignments:
• Read Section 1.3, I will not be able to cover it in class, but some of the problems will be discussed in the lab
• Do Problems in Section 1.1, 1.2, 1.3
Textbook problems: Chapter 1 (supplement)
• Section 1.1: Pg. 53 # 3, 5, 9, 13, 17, 19, 21, 25, 27, 29
• Section 1.2: Pg. 60 # 1, 5, 7, 13, 15, 17, 21, 25, 31, 35, 37, 41, 43, 47, 51, 53
There will be quiz on Friday, September 8, consisting of 2-3 problems from the four items above.

Class Notes for Week 2 and Homework 2 (due Friday, September 15)

• Sections 2.1,2,4
• with solutions: Sections 2.1,2,4

• Assignments (this assignment will be more on the "theoretical side", thus more reading as usual and less problems):
• Read carefully the class notes,
• Know the exact definition ("$$\varepsilon-\delta$$ defintion") of the statements:
$$\lim_{x\to a} f(x)= L,\quad \lim_{x\to a^+} f(x)= L, \text{ and } \lim_{x\to a^-} f(x)= L$$.
Know Theorems 1 and 2 from the course notes.
• Know how to do the problems in course notes (but I might only ask a problem like Problem 1, the other are problay too time consuming for a quiz)
Textbook problems: Chapter 2
• Section 2.2: 5, 6, 19, 20, 21, 22 (the problems 19 - 22 you do not need to use the $$\varepsilon-\delta$$ defintion, )
• Section 2.4: 1, 2, 3, 19, 20 (in problems 19, 20 you need to use the $$\varepsilon-\delta$$ defintion, )
There will be quiz on Friday, September 15, consisting of from the four items (2,3,4,5) above.

Class Notes for Week 3 and Homework 3 (due Friday, September 22)

• Section 2.3     Section 2.5
• with solutions: Section 2.3    Section 2.5

• Assignments (this assignment will be more on the "theoretical side", thus more reading as usual and less problems):
• Read the class notes, and now how to state:
The algebraic rules of limits (Theorem 1, section 2.3) The Squeeze Theorem (Theorem 8, section 2.3), Defintion of continuity (section 2.5), and the Intermediate Value Theorem (Theorem 3, secton 2.3)
• Problems in course notes
Textbook problems: Chapter 2
• Section 2.3: 1, 2,, 3, 5, 1,3 16, 21, 26, 29, 31, 37, 39, 45, 46
• Section 2.5 1,3, 11, 15, 39, 40, 45, 46

Class Notes for Week 4 and Homework 4 (due Friday, September 29)

• Section 2.6     Section 2.7     Sections, 2.8, 3.1     Section 3.2
• with solutions: Section 2.6     Section 2.7     Sections, 2.8, 3.1     Section 3.2

• Assignment
• Read the class notes, and now how to state: Definiton of limits at $$\pm\infty$$ (Section 2.1 first Definition), defintion of differentiable, and derivative, know the rules of differentiation.
• Know how to do the problems in course notes.
Textbook problems: Chapter 2/3
• Section 2.6: 3, 4, 13, 14, 15 16, 24, 28, 29
• Section 2.7: 37, 39 41, 42
• Section 2.8: 21, 23, 26, 31
• Section 3.2: 1,2, 7,11
(after introducing exponential functions and their derivatives, we will do more of the problems from section 3.2)

Class Notes for Week 5 and Homework 5
(there will not be a quiz on Friday, October 6, but material is relevant for Exam 1, on Tuesday October 3)
Exam 1, Tuesday, October 3, 7:30 - 9:30 PM Bloc 220

Class Notes for Week 6 and Homework 6 (Due October 13)

Class Notes for Week 7 and Homework 7 (Due October 20)

Class Notes for Week 8 and Homework 8 (Due October 27)

• Supplement     Supplement     Supplement
• with solutions: Supplement     Supplement     Supplement

• Assignments
• Know how to do the problems in course notes
Textbook problems Chapter 3:
• Section 3.7 from supplement (page 203): 1, 3, 6, 7, 9., 10
• Section 3.8 from supplement (page 210): 55, 59
• Section 3.9 from supplement (page 214): 1, 4, 7, 10
Class Notes for Week 9 and Homework 9 (Due November 3)
• Section 4.1     Sections 4.2,3
• with solutions: Section 4.1     Sections 4.2,3

• Assignments
• Read carefully classnotes and know the defintion of absolute maximum, minumum on interval, Extreme Value Theorem, Fermat's Theorem, local maximum, minumum, Mean Value Theorem, Rolle's Theorem, first derivative test, second derivative test,
• Know how to do the problems in course notes
Textbook problems Chapter 3 and Chapter 1.
• Section 4.1: 7, 15 17, 19, 29, 34, 35, 37, 47, 49, 54, 55 60
• Section 4.2: 5, 7, 11, 17
• Section 4.3: 7, 9, 10, 12, 15, 17, 19, 21, 22

Class Notes for Week 10 and Homework 10 (Due November 10)
(there will not be a quiz on that homework, but it is relevant for Exam II)

• Section 4.4     Section 4.7
• with solutions: Section 4.4     Section 4.7

• Assignments
• Read carefully classnotes, remember the 7 types of indetermnined forms.
• Know how to do the problems in course notes.
Textbook problems Chapter 4.
• Section 4.4: 1-4, 8, 13, 19, 27, 31, 33,39, 53,56
• Section 4.7: 2, 12, 18, 21, 32

Exam 2, Tuesday, November 7, 7:30 - 9:30 PM Bloc 220 (this time I will make sure that I will have the key to the room...;})

Class Notes for Week 12 and Homework 11 (Due November 20)
( Note: Quiz will be on Monday, Nov. 20, not on a Friday )

Final: Monday, December 11, 10:30 - 12:30 PM (in usual class room BLOC 164)

Class Notes for Week 14 and Homework 12 (Due December 4)
( Note: Quiz will be on Monday, Dec. 4, not on a Friday )

Class Notes for Week 15 and Homework