MTH U241 - Calculus I (Engineering/Science)

Course Information

Problem solving sessions:
Tuesday 3-4:30 in 150 DG (Blake)
Tuesday 4:30-6 in 404 RB (Alex)
Wednesday 3-4:30 in 104G WV (Kara)
Wednesday 6-7:30 in 409 RB (Nick)

Course Description

The course covers the standard topics of calculus I: limits and derivatives, the calculation of derivatives, applications of differentiation to solving the kinds of problems encountered in science and engineering, and an introduction to integration. The emphasis is on applications of developed techniques, but some proofs and mathematical reasoning will be introduced when they are required for better understanding.

TOPICS AND ASSIGNMENTS (subject to change by instructor) 
 
Chapter 1: Functions and Models
      1.1 Representing Functions, p. 22: 1,2,10,23,25,27,43-45,47,57,58,64
      1.4 Graphing Calculators, p. 54: 2, 6-10, 15,18,29
      1.7 Parametric Curves, p. 79: 1,5-7,9-12,16,20,21,25,29,30

Chapter 2: Limits and Derivatives
      2.1 Tangents and Velocities, p. 97: 2,3(iv,viii),7
      2.2 Limit of a Function, p. 106: 1,3,4,16,17
      2.6 Velocities and Rates of Change, p. 145: 2,3,8,13,16
      2.7 Derivatives, p. 153: 3-7,15,19-22,29
      2.8 Derivative as a Function, p. 165: 2-7,9,12,32,37,39
      2.9 What f’ Says About f, p. 172: 1-3,8,10,15,18,21,23,25,26 

Chapter 3: Differentiation Rules 
      3.1 Polynomials & Exp. Functions, p. 190: 3-25(odds),32,37,38,41,50,57
      3.2  Product & Quotient Rules, p. 198: 3,6,7,10,11,23,29,31,32,38,46(a)
      3.3 Rates of Change, p. 210: 1,3,8,11,14,15,24,33
      3.4 Trig. Functions, p. 218: 1,3,4,7,8,19,23,26,29,35,37
      3.5 The Chain Rule, p. 228: 1-29(odds),41-43,47,60,65
      3.6 Implicit Differentiation, p. 238: 7,11,13,14,17,29,31,36,41,43,44,55
      3.7 Log Functions, p. 245: 3-13(odds),14,24,29-32
      3.8 Linear Approx., p. 252: 1,2,5,9,28-30,34 

Chapter 4: Applications of Differentiation
      4.1 Related Rates, p. 267: 8,9,11,14,18,27,30,33
      4.2 Maxima & Minima, p. 274: 4,9,23,24,29,32,37-43(odds)
      4.3 Derivatives & Curves, p. 286: 6,7,11,17,21,24,25,29,30,37,48
      4.4 Graphing with Calculus & Calculator, p. 295: 1,3,8,11,20,21
      4.6 Optimization Applications, p. 311: 3,4,10,12,16,22,38
      4.8 Newton’s Method, p. 325: 4,8,11,15
      4.9 Antiderivatives, p. 332: 1,7,12,21,29,33,34,40,46,48,55  

Chapter 5: Integrals
      5.1 Areas & Distances, p. 352: 3,4,18,
      5.2 The Definite Integral, p. 364: 2,11,17,18,21,27,31,35,40,43,44,49,50
      5.3 Evaluating Def. Integrals, p. 374: 3,6,11,14,17,20,27,29,38,45,48,53,55,57,59
      5.4 The Fundamental Theorem of Calculus, p. 383: 2,5,8,9,17,22
      5.5 Substitution Rule, p. 392: 1-13(odds),18,21,24,30,31,33,45,47,53

More information and resources can be found on the web page by Professor Maxim Braverman (course coordinator).

Grading: weekly quizzes (50%), final exam (50%).

Homework: will be regularly assigned and discussed in class. You are expected to work on all of the homework problems assigned for each topic. Although the homework is not counted in grading, the quizzes and the final exam will consist of similar problems so doing it is very essential.

Attendance: You are expected to attend class, and are responsible to be aware of any changes in the syllabus announced in class. Students are responsible for all information given when they are absent. No make-up tests or exams are expected in this course.

Calculators: You are expected to have a graphing calculator and be reasonably proficient in its use.

Final Exam: There will be a common final for all sections of this course. Department regulations require that the final count for 50% of your course grade. All students are required to take the final on the day it is given. Exam conflicts must be resolved in advance with the Registrar’s Office and your instructor. Do not make advance travel arrangements for any dates during finals week.

If you have a concern about the course or the instructor that cannot be resolved by speaking with the instructor, the next step is to speak with the course coordinator Professor Maxim Braverman, 457 LA, x8769, maximbraverman@neu.edu. If the course coordinator does not settle the matter, please contact Professor Alex Martsinkovsky (Undergraduate Director), 471 LA, x5510, alexmart@neu.edu.

It is University policy that no grade, including an incomplete, can be changed after one year. Exceptions must be authorized by the Academic Standing Committee.

Homework:
Sep. 5: read Section 1.1; pp. 22-24, #1, 23, 25, 27, 43, 45, 57, 64.
Sep. 6: read Section 1.7; pp. 79-82, #5-7, 9, 16, 21, 29.
Sep. 10: read Sections 2.1, 2.2, 2.6; pp. 97-98, #3(iv,viii), 7; pp. 145-146, #2, 3, 8, 13, 17.
Sep. 12: read Section 2.2; do the problems from this list; p. 147, #27.
Sep. 13: read Section 2.7; pp. 153-154, #3-5, 7, 15, 19-22.
Sep. 17: read Section 2.8; pp. 165-166, #1, 3, 5, 7, 9, 19, 23, 25.
Sep. 19: read Section 2.9; pp. 172-174, #1, 3, 8, 13, 15, 23.
Sep. 20: read Section 3.1; pp. 190-191, #3-23 (odds), 27, 37, 41.
Sep. 24: read Section 3.2; pp. 198-199, #3, 5, 6, 7, 10, 11, 23, 29.
Sep. 26: read Section 3.3; pp. 210-211, #1, 3, 8, 11, 14, 15.
Sep. 27: read Section 3.4; pp. 218-219, #1, 3, 4, 7, 8, 23, 29, 35.
Oct. 1: read Section 3.5 up to Example 7; p. 228, #1-15 (odds).
Oct. 3: p. 228, #17-29 (odds); read Section 3.6 up to Example 3; p. 238, #7, 11, 13.
Oct. 4: read Section 3.6, pp. 237-238; pp. 238-239, # 15, 17, 29, 31.
Oct. 10: review Sections 3.5, 3.6; p. 238, # 3, 5, 9, 19, 21.
Oct. 11: p. 239, #33, 35, 36; read Section 3.7; pp. 245-246, #3-13(odds), 25.
Oct. 15: p. 246, #17, 19, 23, 27-35 (odds).
Oct. 17: review Sections 3.6, 3.7; read Section 3.8 up to Differentials (p. 250); p. 252, #1, 2, 5, 9.
Oct. 18: read the rest of Section 3.8; p. 253, #23, 25, 27, 28.
Oct. 22: read Section 4.1; p. 267, #8, 9, 11, 16, 17.
Oct. 24: review Sections 3.8, 4.1; p. 267, #13, 15, 20.
Oct. 25: read Section 4.2; pp. 275-276, #23, 25, 29, 37-43 (odds).
Oct. 29: read Section 4.3; p. 287, #7, 9, 11, 13.
Oct. 31: p. 287, #21, 25, 29; read section 4.4; p. 295, #1, 3, 8.
Nov. 1: read Section 4.6; pp. 311-312, #3, 4, 9, 11, 16, 22.
Nov. 5: pp. 311-313, #13, 21, 33, 38.
Nov. 7: review Section 4.6; read Section 4.8; p. 326, #5, 9, 10, 15.
Nov. 8: read Section 4.9; pp. 332-333, #1, 7, 9, 12, 21, 39.
Nov. 14: pp. 332-334, #3, 5, 11, 19, 49.
Nov. 15: read Sections 5.1, 5.2; p. 352, #3, 5; p. 364, #1, 9, 11, 31.
Nov. 19: read Section 5.3; p. 374, #3, 5, 7, 11, 17, 19, 27, 29, 37, 38.
Happy Thanksgiving!
Nov. 26: p. 375, #55, 57, 59; read Section 5.4; pp. 383-384, #5, 7, 9, 18.
Nov. 28: p. 384, #19; read Section 5.5; p. 392, #1-13 (odds), 19, 21.
Nov.29: review 2006 final exam (see below).

Quizzes:
Quiz 1: Thursday, Sep. 13 (sections 1.1, 1.7, 2.1, 2.2, 2.6). Solutions.
Quiz 2: Thursday, Sep. 20 (sections 2.7, 2.8, 2.9). Solutions.
Quiz 3: Thursday, Sep. 27 (sections 3.1, 3.2). Solutions.
Quiz 4: Thursday, Oct. 4 (sections 3.4, 3.5). Solutions.
Quiz 5: Thursday, Oct. 11 (sections 3.5, 3.6). Solutions.
Quiz 6: Thursday, Oct. 18 (sections 3.6, 3.7). Solutions.
Quiz 7: Thursday, Oct. 25 (sections 3.8, 4.1). Solutions.
Quiz 8: Thursday, Nov. 1 (sections 4.2, 4.3). Solutions.
Quiz 9: Thursday, Nov. 8 (section 4.6). Solutions.
Quiz 10: Monday, Nov. 19 (sections 4.8, 4.9). Solutions.
Quiz 11: Thursday, Nov. 29 (sections 5.1-5.4). Solutions.

I will be available for last minute questions on Thursday December 6 at 10:00 AM - 12:00 PM, or by appointment on Friday or Tuesday.

Final Preparation: 2006 Final Exam, 2006 Final Exam Solutions, 2005 Final Exam, More final preparation problems  

Final Exam: Wednesday December 12 at 10:30 AM in 170F West Village
(allowed: calculators, one sheet of notes).