# MAT1300D - Mathematical Methods I

Instructor: Charles Starling

Office: 585 King Edward, Room 306

Phone: 562-5800 extension 3507.

email: cstar050@uottawa.ca.

Office Hours: Monday 2pm-4pm, Wednesday 4pm-5:15pm or by appointment.

## FINAL EXAM SOLUTIONS

Here there are links to several past midterms and final exams given by my colleague Richard Blute. Work with them for practicing.

Year
Midterm 1
Midterm 2
Final
2007
versions: #1#2
versions: #1, #2
solution version, blank version
2006
versions: #1, blank
versions: #1, #2
solution version, blank version
2005
versions: #1, #2, blank
versions: #1, #2
solution version, blank version
2004
versions: #1, blank
versions: #1, blank
solution version, blank version
2003
versions: #1, #2
versions: #1, #2

Here is a complete breakdown of the topics for each lecture this semester, along with a list of suggested problems related to those topics and typed notes based on those given by me and Dr. Blute. (Note that there may be some variations, depending on the section you are in.) If you have a previous edition of the textbook (5th, 6th or 7th), a list of problems for your edition is given below the table.

Date Appoximate Sections Exercises
Mon 8 Sep
NOTES
Ch.0: A Precalculus Review - Odd numbered problems:
Sec.0.1: 15-27; Sec.0.2: 9-21;
Sec.0.3: 21-37; Sec.0.4: 1-19, 31-45
Wed 10 Sep
NOTES
Ch.1 Sec.1-4: Cartesian Plane, Graphs, Straight Lines, Functions - Odd numbered problems:
Sec.0.5: 1-9, 39-43;
Sec.1.1: 5-9, 17, 21; Sec.1.2: 1-33, 51-55, 59;
Sec.1.3: 5-11, 21-33, 69;
Sec.1.4: 1-7, 17, 19, 25, 27, 31, 47-55, 71, 73
Mon 15 Sep
NOTES
Ch.1 Sec.5,6: Limits, Continuity Odd numbered problems:
Sec.1.5: 1-49; Sec.1.6: 1-27, 53, 55
Sec.4.1: 1-33; Sec.4.2: 31-37
Wed 17 Sep
NOTES
More on limits and continuity
Ch.4 Sec.1,2,4: Exponentials, Logarithms
Odd numbered problems:
Sec.4.1: 1-33; Sec.4.2: 1-11, 31-37
Sec.4.4: 1-17, 23-55, 69, 85-87
Mon 22 Sep
NOTES
More on exponentials, interest rates
Ch.2 Sec.1: Slope of a function, Derivative
Odd numbered problems:
Sec.2.1: 1-9, 15, 17, 19, 27-37, 45, 49, 68-71
Wed 24 Sep
NOTES
Ch.2 Sec.2,4: Rules of differentiation Odd numbered problems:
Sec.2.2: 3-19, 27-53, 57
Sec.2.4: 1-9, 23-35, 45
Mon 29 Sep
NOTES
Sec.2.3:Velocity and Marginals Odd numbered problems:
Sec.2.3: 17-31,39,41
Wed 1 Oct
NOTES
Sec.2.5: The Chain Rule
Sec.2.6: Higher Order Derivatives
Sec.2.7: Implicit Differentiation
Sec.4.3: Derivatives of Exponential Functions
Odd numbered problems:
Sec.2.5: 1-33, 45-57, 65
Sec.2.6: 5, 7, 19, 23, 31, 35, 51-55
Sec.2.7: 3, 5, 7, 13-29
Sec.4.3: 3-25
Mon 6 Oct Midterm #1
Version (a) Solutions
Version (b) Solutions
Sections 0.1-0.5, 1.1-1.6,
2.1-2.4, 4.1, 4.2, 4.4
Wed 8 Oct
NOTES
Sec.4.5: Derivatives of Logarithmic Functions
Sec.4.6: Exponential Growth and Decay.
Sec.3.1: Increasing and Decreasing Functions
Sec.4.5: 1-23, 47, 51, 53
Sec.4.6: 11, 13, 15, 23, 24.
Odd numbered problems:
Sec 3.1:1-17,29
Wed 15 Oct
NOTES
Sec.3.2: Extrema and First-Derivative Test Odd numbered problems:
Sec.3.2: 1-11, 19-27.
Mon 20 Oct
NOTES
Sec.3.3: Concavity and Second Derivative
Sec.3.4: Optimization Problems
Odd numbered problems:
Sec.3.3: 1-15, 27-31, 47
Sec.3.4: 1-7, 13-23, 35
Wed 22 Oct
NOTES
Sec.3.5: Optimization problems / Business and Economics Odd numbered problems:
Sec.3.5: 1-3, 9-11, 15, 19, 20, 21, 27-33
Mon 27 Oct
NOTES
Sec.3.6: Asymptotes Odd numbered problems:
Sec.3.6: 1-27, 39, 41, 47, 51, 53
Wed 29 Oct Midterm #2
Version (a) Solutions
Version (b) Solutions
Sections 2.5, 2.6, 2.7, 4.5, 4.6, 3.1-3.4, Finding a demand function and maximizing
revenue from 3.5 (nothing else from 3.5)
Mon 3 Nov
NOTES
Sec.3.7: Curve Sketching Odd numbered problems:
Sec.3.7: 1-11, 33, 35, 39
Wed 5 Nov
NOTES
Sec.5.1: Antiderivatives and Indefinite Integral Odd numbered problems:
Sec.5.1: 1-19, 33-39, 49, 51, 53
Mon 10 Nov
NOTES
Sec.5.2: The General Power Rule
Sec.5.3: Integral of Exponential and Logarithm
Odd numbered problems:
Sec.5.2: 1-27, 35-39, 43, 45
Sec.5.3: 1-27, 39-47
Wed 12 Nov
NOTES
Sec.5.4: Area and Fundamental Theorem of Calculus Odd numbered problems:
Sec.5.4: 1-35, 43, 57
Mon 17 Nov
NOTES
Sec.5.5: Area Between two Functions
Odd numbered problems:
Sec.5.5: 1-29, 41-44
Wed 19 Nov
NOTES
Sec.6.1: Integration by Parts
Sec.6.5 : Improper Integrals
Odd numbered problems:
Sec.6.1: 1-25, 33, 39, 41
Sec.6.5: 1-22
Mon 24 Nov
NOTES
Sec.7.1: The 3D Coordinate System
Sec.7.2: Surfaces in Space (only first 2 pages)
Sec.7.3: Functions of Several Variables
Odd numbered problems:
Sec.7.1: 1-11
Sec.7.3: 1-9, 15-37
Wed 26 Nov
NOTES
Sec.7.4: Partial Derivatives
Sec.7.5: Extrema of Functions of Two Variables
Odd numbered problems:
Sec.7.4: 1-11, 15-27, 39, 43-51, 55-63
Sec.7.5: 1-23, 37-41
Mon 1 Dec REVIEW QUIZ
SOLUTIONS

Below is a list of practice problems from the 5th, 6th and 7th editions of the book that correspond to the material we will be covering.

### Topic 1-Limits, Continuity, Exponentials

#### Problems-5th Edition

• p. 45, # 1-15,27-45,63-67
• p. 58, # 1-41,53
• p. 69, # 1-27,33-39
• p. 266, # 1-39,45-51

#### Problems-6th Edition

• p. 45, # 1-7,15-21,31,45-55,71,73
• p. 59, # 1-45
• p. 69, # 1-25,35-39
• p. 262, # 1-33
• p. 270, # 31-37

#### Problems-7th Edition

• p. 45, # 1-7,17,19,25,27,31,47-55,71,73
• p. 59, # 1-49
• p. 69, # 1-27,53,55
• p. 262, # 1-33
• p. 270, # 31-37

### Topic 2-Exps, Logs, Derivatives

#### Problems-5th Edition

• p. 266, # 53
• p. 283, # 1-15,23-29,41,43,49,51,55,59,65
• p. 90, # 1-5,11,15,17,19,21,25,31,39,49-53

#### Problems-6th Edition

• p. 270, # 1-11
• p. 287, # 1-17,23-55,69,85-87
• p. 90, # 1-9,15,17,19,27-37,45,49,51,66-69

#### Problems-7th Edition

• p. 270, # 1-11
• p. 287, # 1-17,23-55,69,85-87
• p. 90, # 1-9,15,17,,19,27-37,45,49,68-71

### Topic 3-Basic Differentiation, Product Rule, Quotient Rule, Chain Rule

#### Problems-5th Edition

• p. 102, # 3-19,27-31,37-51
• p. 128, # 1-9,19-31,41
• p. 138, # 1-7,13-29,41-53,67

#### Problems-6th Edition

• p. 102, # 3-19,27-53
• p. 128, # 1-9,23-35,45
• p. 138, # 1-7,13-29,41-53,67

#### Problems-7th Edition

• p. 102, # 3-19,27-53,57
• p. 128, # 1-9,23-35,45
• p. 138, # 1-33,45-57,65

### Topic 4-Marginal functions,higher-order derivatives, implicit differentiation, exponential and logarithmic derivatives

#### Problems-5th Edition

• p. 117, # 17-31
• p. 145, # 5,19,23,27,35,47-53
• p. 152, # 3,9,13,15,19
• p. 275, # 3-25
• p. 292, # 1-25,47-55

#### Problems-6th Edition

• p. 117, # 19-31
• p. 145, # 5,19,23,29,35,51-55
• p. 152, # 3,9,13,15,19,21
• p. 279, # 3-25
• p. 296, # 1-25,47-55

#### Problems-7th Edition

• p. 117, # 17-31
• p. 145, # 5,7,19,23,31,35,51-55
• p. 152, # 3,5,7,13-29
• p. 279, # 3-25
• p. 296, # 1-23,47,51,53

### Topic 5-Exponential growth and decay, related rates, concavity, extrema and optimization

#### Problems-5th Edition

• p. 302, # 11,13,15,21,22
• p. 160, # 1-13,17,19,21
• p. 179, # 1-17,29
• p. 189, # 1-11,19-27
• p. 198, # 1-13,23-29
• p. 207, # 1-7,13-21,18
• p. 217, # 1-4,15,19,20

#### Problems-6th Edition

• p. 306, # 11,13,15,23,24
• p. 160, # 1-13,17,19,21
• p. 179, # 1-17,29
• p. 189, # 1-11,19-27
• p. 198, # 1-13,27-31
• p. 207, # 1-7,13-21,18
• p. 217, # 1-4,15,19,20

#### Problems-7th Edition

• p. 306, # 11,13,15,23,24
• p. 160, # 1-13,17,19,21,23,25
• p. 179, # 1-17,29
• p. 189, # 1-11,19-27
• p. 198, # 1-15,27-31,47
• p. 207, # 1-7,13-23,35
• p. 217, # 1-3,15,19,20,21

### Topic 6-More optimization, elasticity, asymptotes, curve sketching

#### Problems-5th Edition

• p. 217, # 9-11,15,19,21,27-33
• p. 228, # 1-31,37,39,45,49,51
• p. 238, # 1-9,31-37

#### Problems-6th Edition

• p. 217, # 9-11,15,19,21,27-33
• p. 228, # 1-31,39,41,47,51,53
• p. 238, # 1-11,31-37

#### Problems-7th Edition

• p. 217, # 9-11,15,19,21,27-33
• p. 228, # 1-27,39,41,47,51,53
• p. 238, # 1-11,33,35,39

### Topic 7-Antidifferentiation, exponential and logarithmic integrals

#### Problems-5th Edition

• p. 322, # 1-17,25-35,43-47,57-63
• p. 331, # 1-23,33-39
• p. 338, # 1-23,33-41

#### Problems-6th Edition

• p. 326, # 1-17,25-35,45-49,59-69
• p. 335, # 1-27,35-47
• p. 342, # 1-23,35-41

#### Problems-7th Edition

• p. 326, # 1-19,33-39,49,51,53
• p. 335, # 1-27,35-39,43,45
• p. 342, # 1-27,39-47

### Topic 8-Integration and Area

#### Problems-5th Edition

• p. 348, # 1-29,39,41,45,47,49
• p. 357, # 1-27,37-39
• p. 390, # 1-31

#### Problems-6th Edition

• p. 353, # 1-33,47,49,53,55
• p. 362, # 1-25,41,43
• p. 394, # 1-25,41

#### Problems-7th Edition

• p. 353, # 1-35,43,57
• p. 362, # 1-29,41-44
• p. 394, # 1-25,33,39,41

### Topic 9-Integration by Parts

#### Problems-5th Edition

• p. 399, # 1-15,31,33,57-61

#### Problems-6th Edition

• p. 403, # 1-17,29,31,59-63

#### Problems-7th Edition

• p. 403, # 1-17,29,31,63,65

### Topic 10-Improper integrals, functions of several variables

#### Problems-5th Edition

• p. 440 # 1,3,5,9,37
• p. 458 # 1-11
• p. 476 # 1-11,15-29,33-37

#### Problems-6th Edition

• p. 444 # 1-11,39
• p. 462 # 1-13
• p. 480 # 1-9,15-29,33-37

#### Problems-7th Edition

• p. 444 # 1-11,39
• p. 462 # 1-11
• p. 480 # 1-9,15--37

### Topic 11-Partial derivatives and local extrema

#### Problems-5th Edition

• p. 487 # 1-11,15-27,35,39-47,51,53
• p. 497 # 1-23,41-45

#### Problems-6th Edition

• p. 491 # 1-11,15-27,39,43-51
• p. 501 # 1-23,37-41

#### Problems-7th Edition

• p. 491 # 1-11,15-27,39,43-51,55-63
• p. 501 # 1-23,37-41