Math 104 Section 103
Differential Calculus with applications to Commerce and the Social Sciences.
Online Course Material

NEWS

EXAM Saturday December 16 3:30-6:00 in MATH 100

• Math Tutorial Centre hours during December check for MATH 104/184 time slots.

• Office hours for the period Dec 12 until Dec 15: Tuesday Dec 12 9-10:30, Wednesday Dec 13 9-11 with 15 minutes lost to another engagement (9:45-10), Friday Dec 15 9-10 and 2-5. There were some inquiries about test 4; please ask any questions by Friday morning; I will not entertain questions about any tests after 10 am on Friday.

The Math Club sells exam packages the last week of classes in MATH ANNEX 1119.

2005 Final Exam, You would be well advised to attempt this final after some studying and certainly without looking at the solutions. Reading solutions is a lower quality learning exercise from doing the Mathematics. Solutions to Final
• Test 1 Sept 22, Solutions to Test 1
• Test 2 Oct 6, Solutions to Test 2
• Test 3 Oct 27, Solutions to Test 3
• Test 4 Nov 17, Solutions to Test 4

• The Math 104/184 average on Test 1 was 47. While this may not be much comfort, the typical class average would be 64 by final grade time.
The Math 104/184 average on Test 2 was 65. Great work.
The Math 104/184 average on Test 3 was 64. Great work.
The Math 104/184 average on Test 4 was 62. Great work. Maybe not quite as great.

The Math 104 average on the precalculus assessment was 6.3/10. If you have a lower score than you would like to have you might vist Rajiv Gupta's webpage which has some suggestions (if you scroll down) at Rajiv Gupta

A Course Syllabus is posted on the website which has practice problems listed.

Chapter 0
You should have reviewed all of Chapter 0 and you should try the problems
Section 0.4 25,27,29,33
Section 0.5 19,21,22,23
These relate to our initial discussions of a firm with some added ideas. Terms like price, demand, supply, fixed cost, break even are used.

Chapter 1

Section 1.1 (many limit computations) 1,5,9,15,21,25,29,31,35,37,41,43,49,51,57

Section 1.2 (includes various infinite limits) 13,15,17,19,25,29,35,41,45,67

Section 1.3 13, 15, 17, 19, 21, 25, 23, 29, 33

Chapter 2.

section 2.1 17,21,23,27,35

section 2.2 3,7,13,15,19

section 2.3 3,9,13,19,39

Section 2.4 1, 5, 9, 11, 13, 15, 23, 25, 27, 29, 31, 33, 35, 37, 39, 67, 69, 71, 73, 74, 79

Chapter 3

Section 3.1 (slopes, tangent lines) 13,15,19,21,23,25,29,33

Section 3.2 (limit definition of derivative, estimates of derivatives, tangent lines, power rule) 1,3,4,5,9,11,17,23,24,25,33,37,47,49,51,53,55

Section 3.3 (derivatives as rates of change e.g. marginal revenue, marginal cost, marginal profit, velocity, acceleration) 1,3,5,11,12,13,37,38,39,41,43,45

Section 3.4 (linear approximations) 1, 3, 7, 15, 17, 21, 23, 25, 27, 39, 45

Section 3.5 (derivatives of exponential and logarithms) 1,5,9,11,13,17,19,29,34,39,41,43,45,47,55,57,61,65 We also expect you to know that the derivative of the sin(x) is the cos(x), and the derivative of cos(x) is -sin(x).

Section 3.6 (product rule, quotient rule) 5,7,9,11,13,17,19,21,29,30,31,32

Section 3.7 (chain rule) 1, 5, 7, 9, 11, 13, 17, 19, 21, 25, 27, 29, 31.

Section 3.8 (Implicit Differentiation and Related Rates) 1, 5, 7, 9, 11, 13, 17, 19, 21, 25, 27, 29, 31

End of chapter review problems 39, 41, 43, 49, 65, 67, 69, 75.

Newton-Raphson method for root finding. Solve 1, 3, 4, 12 from notes.
Notion of finding a maximum or a minimum of a function by determining when the derivative is zero.

Chapter 4

Section 4.1 (includes First Derivative test) 3,5, 9, 11, 13, 17, 19, 23, 25, 33, 35, 37, 39, 53, 55, 59, 61

Section 4.2 (includes Second Derivative test) 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 35, 37, 39, 45, 47, 58, 59

Section 4.3 (curve sketching) 1, 3, 5, 7, 11, 15, 19, 23, 25, 29, 31

Section 4.4 (application) 1, 5, 7, 15, 19, 21, 31, 32

Section 4.5 (further applications, elasticity of demand) 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 23, 25, 27, 28, 30

Chapter 8

Section 8.1 (angles) 1, 7, 11, 17, 19, 23, 25, 27

Section 8.2 (basics of trigonometric functions e.g. circle definition as compared with SOHCAHTOA) 1, 3, 11, 13, 22, 23, 24, 25

Section 8.3 (derivatives of trigonometric functions) 3, 5, 9, 11, 13, 15,

Handout on inverse trigonometric functions and their derivatives. Problems 4, 5, 7, 8, 9, 10, 11

Chapter 10

Section 10 has refrerence to integrals which you have not covered so you ought to ignore those reference. Focus on the linear, quadratic approximations to begin with and then in 10.2 you discover that extending your approximations further results in equality, a result we discussed early on when discussing Zeno's paradox.

Section 10.1 (Taylor's Formula) 5, 9, 11, 12, 13, 15, 17, 21, 23, 27, 45, 47

Section 10.2 (Taylor Series) 1, 3, 5, 7, 15, 17, 21, 23, 25, 27, 35
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This section 103 of MATH 104 will meet for lectures in conjunction with a section of MATH 184. The students in MATH 104 will have taken Calculus in Secondary School whereas the students in MATH 184 will not have taken such a Calculus course. Both groups of students have (at least C+ in) Principles of Mathematics 12. Both groups of students will be writing the same exam in December and the same term tests during the Fall. Math 184 students will have an extra tutorial (and one extra academic credit) to help them with the transition to Calculus.
The notes look authoritative when typed so be wary. They may look perfect but may still contain errors! I don't have an editor.
Course Coordinator Keqin Liu's webpage for MATH 104

Course page for MATH 184 that contains certain extra exercises that may be useful for MATH 104 students.
I arrive most days by 9:00. I typically do not read my email from home (i.e. evenings and weekends).

• Course Outline: grading scheme etc.
• Course Syllabus including suggested problems from the various chapters
• The Precalculus Assessment test is posted with solutions on Rajiv Gupta's website: Rajiv Gupta. including suggested problems from the various chaptersI'd recommend you check it ou as well as the algebra drill that I've posted for 184.
• Course Syllabus including suggested problems from the various chapters
• AMS Exam Database with old exams useful for study purposes. MATH 140 was a precursor to MATH 104 but was typically a little easier.
• Newton Raphson Method notes and problems , Solutions to problems in notes.
• Some hard Problems from Andrew Adler which will become accessible as the term progresses. You will be able to do question 1 after the limit definition of the derivative.
• Chain Rule and Product Rule motivation, not a proof.