**Instructor:** Hemanshu
Kaul

**Office:** 234B, Engineering 1

**Phone:** (312) 567-3128

**E-mail:** kaul [at]
math.iit.edu

**Time:** 11:25am, Monday-Wednesday-Friday.

**Place:** 103, Engineering 1.

**Lab/Recitation:** 1:50pm, Friday at 029/025 Engineering 1.

**Office Hours:** 2pm-3pm, Monday, and 11am-12pm, Thursday. Also by appointment.

**Teaching Assistant:** Frederico Luca Vidozzi, __vidofre@iit.edu__

**TA Office Hours:** 3:20pm-4:20pm, Monday, at 035 E1 (primarily for Maple labs and recitation)

**Tutoring Service:** Maple tutoring and
Mathematics tutoring at the Academic Resource Center.

A detailed description of the lecture topics and the course objectives is in the official course syllabus.

The Course Information Handout has the complete description of the student evaluation policy as well as other relevant information. Read it carefully! Updated!

*Thursday, 12/7*: All the select solutions are online.*Friday, 12/1*: Homework assigned from today onwards need not be submitted. But, be sure to solve all the exercises and ask me for help if needed.*Thursday, 11/30*: I have decided to replace the Maple lab tomorrow with a Recitation. This will allow the remaining students to present problems in class. See details below.*Monday, 11/13*: Check the examination date and syllabus for Exam #2 below. Also, more select solutions will be uploaded below over the week. Be sure to ask me questions before Friday, 11/17, as I will be out of town that weekend.*Wednesday, 10/11*: I will not be available for office hours tomorrow at 11am-noon. Instead, stop by between 3pm-4pm.*Friday, 10/6*: Exam 1` will be held in class on Monday, 10/9. To make up for the missed lecture, an extra class will be held on Monday, 10/16 at 4:45pm.*Friday, 10/6*: Recitation homework is due on Wednesday, 10/11.*Monday, 10/2*: Recitation problems for Friday have been uploaded below.*Friday, 9/29*: Examination on Monday, 10/2.*Friday, 9/15 :*Use the TA office hours on Monday (see above) to get help on Maple. Make sure you have submitted all Trigonometry homeworks by Monday. Also, more select solutions have been uploaded below.*Wednesday, 9/13 :*The material related to the Maple Lab #1 has been uplinked below. To use the files, download and then open with Maple 10.*Wednesday, 9/13 :*Please note the updated office location and office hours, and TA office hours.*Tuesday, 9/12 :*Please note the correct section number and updated due dates for the homework assigned on Friday 9/8, and Monday 9/11.*General:*Check this webpage for homework assignments on Monday, Wednesday and Friday evenings. Remember that you are required to submit even-numbered problems only.*General:*The special Trigonometry Review Session will be held at 1:50pm in 027, Engineering 1, instead of the lab/recitation on the first three Fridays - 8/25, 9/1, and 9/8 .*Friday, 8/25*: Due to construction, the lecture classroom has been temporarily moved to 244, E1. We are back in 103, E1 for the rest of the semester.

*Exam # 1*: October 2, Monday. Topics: All sections covered in class till 9/25 Monday. Review Session: During the recitation on September 29, Friday.*Exam # 2*: November 20, Monday. Topics: Sections 3.8 to 3.10, Sections 4.1 to 4.10 (except 4.6 & 4.8), and Section 7.5. Review Session: During the class and the recitation on November 17, Friday.*Final Exam*: December 11, Monday, 2pm to 4pm. Topics: Everything done during the semester. Review Session: During the recitation on December 8, Friday.

*Friday, 8/25*: Section 1.1: Exercises 5, 6, 7, 8, 23, 24, 26, 27, 44, 47, 48, 53. Due Wednesday, 8/30 in class. Select Solutions 1.*Monday, 8/28*: Section 1.2: Exercises 3, 4, 6, 9. Section 1.3: Exercises 3, 4, 10, 11, 20. Due Friday, 9/1 in class. Select Solutions 2.*Wednesday, 8/30*: Section 1.3: Exercises 6, 13, 14, 19, 24, 32, 36, 37, 40, 44. Due Wednesday, 9/6 in class. Select Solutions 3.*Friday, 9/1*: Section 2.2: Exercises 4, 6, 8, 31b, 32a. Due Friday, 9/8 in class. Select Solutions 4.*Wednesday, 9/6*: Section 2.3: Exercises 4, 6, 7, 12, 13, 15, 21, 25, 26, 30, 36, 38, 42, 45, 48a, 55. Due Monday, 9/11 in class. Select Solutions 5.*Friday, 9/8*: Section 2.4: Exercises 2, 20, 21, 22, 25. Due Friday, 9/15 in class. Select Solutions 6.*Monday, 9/11*: Section 2.5: Exercises 10, 11, 13, 14, 18(sketch of graph not required), 21, 22, 24, 26, 31, 32, 34. Due Monday, 9/18 in class. Select Solutions 7.*Wednesday, 9/6*: Section 2.5: Exercises 40, 45, 46. Section 2.6 : Exercises 6a, 6b, 8, 9. Due Monday, 9/18 in class. Select Solutions 8.*Friday, 9/15 :*Section 3.1: Exercises 3, 7, 8, 14, 16, 17, 18. Section 3.2: Exercises 4, 22, 24, 25, 28. Due Wednesday, 9/20 in class. Select Solutions 9.*Monday, 9/18*: Section 3.2 : Exercise 40abc. Section 3.3 : Exercises 2, 5, 7, 10, 14, 17, 19, 20, 22, 25, 32, 34, 39, 40, 52, 55a, 58, 67, 81a(to be submitted). Due Friday, 9/22 in class. Select Solutions 10.*Wednesday, 9/20*: Section 3.5: Exercise 2, 5, 8, 12, 15, 16, 18, 20, 24, 36, 40, 42. Due Monday, 9/25 in class. Select Solutions 11.*Friday, 9/22*: Section 3.6: Exercise 3, 4, 10, 12, 16, 19, 23, 26, 28, 34, 39, 40, 45, 55, 61, 62, 72. Due Wednesday, 9/27 in class. Select Solutions 12*Monday, 9/25*: Section 3.7 : Exercise 7, 9, 12, 13, 16, 20, 22, 24, 25, 28, 32ab, 36. Due Friday, 9/29 in class. Select Solutions 13*Wednesday, 9/27*: Section 3.7 : Exercise 42, 46, 48, 51. Due Wednesday, 10/4 in class. Read Section 3.4. Select Solutions 13 part2*Friday, 9/29*: Section 3.8 : Exercise 10, 12, 13, 14, 17, 18, 24, 26, 30, 34, 36, 38, 40, 53, 56, 59. Due Friday, 10/6 in class. Select Solutions 14*Monday, 10/2*: Examination. No Homework.*Wednesday, 10/4*: No Homework.*Friday, 10/6*: Section 3.9 : Exercise 8, 10, 14, 19, 20, 25, 31, 34. Submit both odd and even number problems. Due Friday, 10/13 in class. Also, read Examples 3 and 5 from the book. Select Solutions 15*Monday, 10/9*: Examination 1`. No Homework.*Wednesday, 10/11*: No Homework.*Friday, 10/13*: Section 3.10 : Exercise 6, 7, 22, 24, 25, 28, 30, 31, 32, 35, 40. Due Wednesday, 10/18 in class. Select Solutions 16*Monday, 10/16*: Section 4.1 : Exercise 31, 34, 36, 40, 41, 42, 43, 48, 51, 53, 54, 55, 56, 69. Due Monday, 10/23. Select Solutions 17*Wednesday, 10/18*: Section 4.3 : Exercise 12, 13, 15, 16. Due Wednesday, 10/25. Select Solutions 18*Monday, 10/23*: Section 4.3 : Exercise 12c, 13c, 15c, 16c, 18, 24, 26, 32, 34, 35, 38, 40, 49, 50. Due Friday, 10/27. Select Solutions 18*Wednesday, 10/25*: Section 4.2 : Exercise 3, 4, 6, 13, 15, 16, 17, 18, 20, 23, 24, 26, 29, 31. Due Monday, 10/30. Select Solutions 19*Friday, 10/27 :*Section 4.4 : Exercise 8, 11, 15, 18, 20, 23, 27, 28, 30, 32, 36 (no graphing needed), 39(no graphing needed), 44, 53, 55a. Due Wednesday, 11/1. Select Solutions 20*Monday, 10/30 :*Section 4.7 : Exercise 2, 3, 14, 17, 19, 20, 24, 25, 34, 41, 42, 46, 47.Due Monday, 11/6. Also read Section 4.5, especially Examples 1, 2, 3. Select Solutions 21*Wednesday, 11/1*: Section 4.9 : Exercise 6, 7, 12, 14, 16, 20, 21, 27a, 29, 30ab, 32, 34, 35. Due Wednesday, 11/8. Select Solutions 22*Friday, 11/3*: Section 7.5 : Exercise 3, 6, 9, 11, 12, 17, 22, 23, 24, 25, 30, 31, 35, 38, 43, 44. Due Friday, 11/10. Select Solutions 23*Monday, 11/6*: Section 4.10 : Exercise 5, 8, 13, 16, 21, 22, 23, 26, 27, 30, 31, 35, 36, 37. Due Monday, 11/13. Select Solutions 24*Wednesday, 11/8*: Section 5.1 : Exercise 3, 4a, 17, 18, 19, 20, 22. Due Wednesday, 11/15. Select Solutions 25*Friday, 11/10*: Section 5.1 : Exercise 11, 13.*Monday, 11/13*: Section 5.2 : Exercise 17, 18, 21, 22, 24, 28, 33, 36, 39, 40. Due Monday, 11/27. Select Solutions 26*Wednesday, 11/15*: Section 5.2 : Exercise 41, 43, 47, 50, 52, 54, 57, 58, 60, 65, 66, 67, 68. Due Monday, 11/27. Select Solutions 26*Friday, 11/17*: No Homework.*Monday, 11/20*: No HW (Examination).*Wednesday, 11/22*: No HW.*Monday, 11/27*: Section 5.3: Exercise 8, 9, 12, 13, 14, 16, 18, 19, 24, 26, 29, 32, 33, 36, 44, 45. Section 5.4: Exercise 8, 9, 13, 14, 23, 25, 26, 32, 33, 34, 37. Due Monday, 12/4. Select Solutions 27 Select Solutions 28*Wednesday, 11/29*: Section 5.5 : Exercise 3, 6, 9, 12, 18, 19, 22, 26, 27, 28, 31, 32, 42, 44, 50, 51. Due Wednesday, 12/6. Select Solutions 29*Friday, 12/1*: Section 5.5 : Exercise 43, 53, 54. Section 6.1 : Exercise 1,6,7,9 (you do not need to draw the approximating rectangle). Not to be submitted. Select Solutions 29 Select Solutions 30*Monday, 12/4*: Section 6.1 : Exercise 12, 15, 18, 19, 22, 24, 30. (you do not need to draw the approximating rectangle). Not to be submitted. Select Solutions 30*Wednesday, 12/6*: Section 6.2 : Exercise 2, 3, 4, 6, 8, 9, 12, 13, 17, 31, 32, 34. Solve/ study examples in section 6.2.Not to be submitted. Select Solutions 31*Friday, 12/8*: No HW.

*Friday, 8/25*: Trigonometry Review Session 1 Homework. Due Friday, 9/1 in the review session.*Friday, 9/1*: Trigonometry Review Session 2 Homework. Due Friday, 9/8 in the review session.*Friday, 9/1*: Trigonometry Review Session 3 Homework. Due Friday, 9/15 in the Lab.*Friday, 9/15*: Maple Lab #1 : First we go through Fasshauer's Introduction To Maple, then through Maple Worksheet 1. Neatly written solutions to the exercises at the end of the worksheet are due by Wednesday, 9/20, in class.

You might find the Introduction To Maple by David Maslanka, and the Crash Course in Maple by Alexander Walz, useful to practice with.*Friday, 9/22*: Maple Lab #2 : Maple Worksheet 2. Printouts of the nicely written solutions to the exercises at the end of the worksheet are due by Wednesday, 9/27, in class.*Friday, 9/29*: Recitation : Prepare exercises from homeworks and the review problems in the book for a review for Exam #1.*Friday, 10/6*: Recitation : Prepare exercises: 84(section 3.3), 86(section 3.3), 44(section 3.5), 53(section 3.7), 61b(section 3.8), 54a (page 215); for presentation in class during the recitation. Read the description for recitation problems in the Course Information Handout. Recitation homework (announced in class) due on Wednesday, 10/11 in class.*Friday, 10/13*: Maple Lab #3 : Maple Worksheet 3. Printouts of the nicely written solutions to the exercises at the end of the worksheet are due by Wednesday, 10/18, in class.*Friday, 10/20*: Fall Break.*Friday, 10/27*: Recitation : Ask questions and be prepared to answer questions from Chapters 3 and 4.*Friday, 11/3*: Recitation : Ask questions and be prepared to answer questions from Chapter 4.*Friday, 11/10*: Maple Lab #4 : Maple Worksheet 4. Printouts of the nicely written solutions to the exercises at the end of the worksheet are due by Wednesday, 11/15, in class. Be sure to write detailed and well explained answers.*Friday, 11/17*: Recitation : Prepare exercises from homework and the review problems in the book for a review for Exam #2.*Friday, 11/24*: Thanksgiving Break.*Friday, 12/1*: Recitation : Prepare exercises: 47 (page 310), 54 (page 349), 58 (page 366), 53 (page 371), 66 (page 367); for presentation in class during the recitation. Read the description for recitation problems in the Course Information Handout. Recitation homework (detailed and well-written explanation of the solution of one of the recitation problems) due on Wednesday, 12/6 in class.*Friday, 12/8*: Recitation : Prepare exercises from homework and the review problems in the book for a review for the Final Exam.

*Friday, 8/25*: Function, Domain, Range, Representations of functions, Piecewise functions, Absolute value of a number, Even and Odd functions. (From Section 1.1)*Monday, 8/28*: Increasing and decreasing functions, Types of functions and their graphs - linear, polynomial, power, rational, algebraic, trigonometric, exponential, logarithmic; Vertical and horizontal shifts of functions. (From Sections 1.2 and 1.3)*Wednesday, 8/30*: Vertical and horizontal stretching and reflecting of functions, Algebra of functions, Compositions of functions. (From Section 1.3)*Friday, 9/1*: Limit of a function, One-side limits, Infinite limits, Vertical asymptote. (From Section 2.2)*Wednesday, 9/6*: 11 Limit laws, Direct substitution property, Simplification property, One-sided limits method, Squeeze theorem. (From Section 2.3)*Friday, 9/8*: Precise definition of a limit and of one-sided limits, epsilon-delta proofs. (From Section 2.4)*Monday, 9/11*: Continuous functions, definition at a point and on an interval, Algebra of continuous functions, Continuity of polynomial, rational, root, and trigonometric functions, Continuity of composition of functions. (From Section 2.5)*Wednesday, 9/6*: Continuity of composition of functions, Intermediate Value Theorem, Tangent line to a curve. (From Sections 2.5 and 2.6)*Friday, 9/15 :*Derivative at a number, Derivative as the slope of the tangent line, Derivative as a function, "Differentiable on an open interval", Differentiability of |x|. (From Sections 3.1 and 3.2)*Monday, 9/18*: Differentiable functions are continuous, Vertical tangent line, Derivative of a constant function, Power rule, Constant multiple rule, Sum/ Difference rule, Product rule, Quotient rule, Finding tangent line using derivative. (From Sections 3.2 and 3.3)*Wednesday, 9/20*: Limit of (sin x)/x as x tends to zero, Limit of (cos x -1)/x as x tends to zero, Derivatives of sin x and cos x, and using them to find other trigonometric derivatives. (From Section 3.5)*Friday, 9/22*: Chain rule, Power rule with Chain rule, Applying Chain rule in combination with other rules. (From Section 3.6)*Monday, 9/25*: Implicit differentiation. (From Section 3.7)*Wednesday, 9/27*: Orthogonal curves, Examples of rates of change in natural and social sciences. (From Sections 3.7 and 3.4)*Friday, 9/29*: Higher order derivatives, Formulas for nth order derivatives, Using "patterns" to simplify calculating higher order derivatives. (From Section 3.8)*Monday, 10/2*: Examination 1.*Wednesday, 10/4*: Discussion of Exam scores and solutions.*Friday, 10/6*: How to compute the rate of change of one quantity in terms of the rate of change of another related quantity - many examples. (From Section 3.9)*Monday, 10/9*: Examination 1`.*Wednesday, 10/11*: Discussion of Exam scores and solutions.*Friday, 10/13*: Linear Approximation/ Linearization, Differentials and approximation error. (From Section 3.10)*Monday, 10/16*: Global maximum/ minimum, local maximum/ minimum, Extreme Value theorem, Fermats theorem, Critical number, Closed Interval method for finding global max/ min, Increasing/ Decreasing test, First derivative test for local max/ min. (From Sections 4.1 and 4.3)*Wednesday, 10/18*: 3-step procedure for finding critical numbers with illustrating examples, Discussion with examples for Increasing/ Decreasing test, and First derivative test for local max/ min. (From Sections 4.1 and 4.3)*Friday, 10/20*: Fall Break*Monday, 10/23*: Concave Upward/ Downward, Concavity test, Inflection point, Second Derivative test, 5-step procedure for analyzing the behavior of a function and graphing it using 1st and 2nd derivatives. (From Section 4.3)*Wednesday, 10/25*: Rolles theorem, Mean value theorem, and their applications. (From Section 4.2)*Friday, 10/27 :*Limits as x tends to infinity or minus infinity and their limit rules , Horizontal asymptotes, Infinite limits at infinity. (From Section 4.4)*Monday, 10/30 :*Summary of curve sketching (H.W.), Optimization problems, Firstr Derivative test for global extreme values. (From Section 4.7)*Wednesday, 11/1*: Newtons Method. (From Section 4.9)*Friday, 11/3*: One-to-one functions and their inverses, derivative of inverse functions, Inverse Sine function and its derivative. (From Sections 7.1 and 7.5)*Monday, 11/6*: Inverse Cosine and Tan functions and their derivatives, finding limits using horizontal asymptotes of arctan, Antiderivatives, General antiderivatives, Rules for finding antidrivatives, Using side conditiopns to eliminate arbitrary constants from antiderivatives. (From Sections 7.5 and 4.10)*Wednesday, 11/8*: Area of the region under a curve and bounded by two vertical lines - Example and definition based on approximation by rectangular strips, Sigma notation and formulas for sum of first n positive integers or their squares or their cubes. (From Section 5.1)*Friday, 11/10*: Area of the region under a curve and bounded by two vertical lines - Example and three definitions including one using sample points, Distance traveled as the area of the region defined by the velocity vs. time curve, Definition of definite integral. (From Sections 5.1 and 5.2)*Monday, 11/13*: Definite integral - terminology and Riemann Sum, Summation formulas and limits. (From Section 5.2)*Wednesday, 11/15*: Properties and comparison properties of definite integrals, Fundamental Theorem of Calculus I and II. (From Sections 5.2 and 5.3)*Friday, 11/17*: Review for Exam #2*Monday, 11/20*: Examination.*Wednesday, 11/22*: Discussion of Exam #2.*Monday, 11/27*: Fundamental Theorem of Calculus I and II, and its applications. Indefinite integrals, Notation and Formulas. (From Sections 5.3 and 5.4)*Wednesday, 11/29*: Substitution Rule for indefinite and definite integrals. (From Section 5.5)*Friday, 12/1*: Substitution Rule for definite integrals, Integrals of symmetric functions, Area of the region bounded by two curves- special case. (From Sections 5.5 and 6.1)*Monday, 12/4*: Area of the region bounded by two curves- general case, Finding area by integrating w.r.t. y instead of x. (From Section 6.1)*Wednesday, 12/6*: Examples for finding area by integrating w.r.t. y instead of x, Finding volume by area of cross-sectional slices. (From Sections 6.1 and 6.2)*Friday, 12/8*: Examples for volumes of solids formed by rotation around x- or y-axis with either circular or annular cross-sections, Motivation for volumes by cylindrical shells. (From Sections 6.2 and 6.3)

- Student companion site for the textbook.
- Calculus I notes by Paul Dawkins.
- Common Math Errors by Paul Dawkins.
- Algebra and Trigonometry Review by Paul Dawkins.
- A Crash Course in Maple by Alexander Walz.
- A Brief Guide to MAPLE.
- Ask Dr. Math