Math 3B: Lecture 1. Noah White. September 29, 2017
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1 Math 3B: Lecture 1 Noah White September 29, 2017
2 Class website There are a few places where you will find/receive information about Math 3B: The class website: Piazza CCLE (only for recordings)
3 Instructor and TAs Instructor office hours TA office hours Noah White MS 6304, Thursday 10-11:30am, Friday 9:30-11am Bohyun Kim TBA, TBA Kevin Miller TBA, TBA Ryan Wallace TBA, TBA
4 Discussions and Learning assistants Undergraduate students assisting in discussion sections
5 Discussions and Learning assistants Undergraduate students assisting in discussion sections Your TA will guide discussion in small groups
6 Discussions and Learning assistants Undergraduate students assisting in discussion sections Your TA will guide discussion in small groups These will be your opportunity to actively discuss mathematics, this should be active, not passive, learning.
7 Discussions and Learning assistants Undergraduate students assisting in discussion sections Your TA will guide discussion in small groups These will be your opportunity to actively discuss mathematics, this should be active, not passive, learning. Learning assistants will be available on Piazza
8 Discussions and Learning assistants Undergraduate students assisting in discussion sections Your TA will guide discussion in small groups These will be your opportunity to actively discuss mathematics, this should be active, not passive, learning. Learning assistants will be available on Piazza They will also host study sessions
9 Discussions and Learning assistants Undergraduate students assisting in discussion sections Your TA will guide discussion in small groups These will be your opportunity to actively discuss mathematics, this should be active, not passive, learning. Learning assistants will be available on Piazza They will also host study sessions Connie, Jayesh, Jennifer, Kelsey, and Nick will be a fantastic resource for you this quarter.
10 BruinCast The lectures will be recorded.
11 BruinCast The lectures will be recorded. The recordings will be available on CCLE
12 BruinCast The lectures will be recorded. The recordings will be available on CCLE Study tip: doing problems is much better than watching a video!
13 Communication Mathematical questions should be asked on Piazza Administrative questions should be directed to your TA initially If you need to me include math3b in the subject
14 Textbook S. J. Schreiber, Calculus for the Life Sciences, Wiley
15 Problem sets, homework, and quizzes Problem sets Assigned every week. Long(!!) list of problems. Not graded, but recommended!
16 Problem sets, homework, and quizzes Problem sets Assigned every week. Long(!!) list of problems. Not graded, but recommended! Homework Due in weeks 2, 5, 9. A small number of questions drawn from the problem sets.
17 Problem sets, homework, and quizzes Problem sets Assigned every week. Long(!!) list of problems. Not graded, but recommended! Homework Due in weeks 2, 5, 9. A small number of questions drawn from the problem sets. Quizzes Administered in discussion session in weeks 3, 6, 10. More on the format to come.
18 Homework; collection and collaboration Homework will be collected at the start of the lecture on the dues date.
19 Homework; collection and collaboration Homework will be collected at the start of the lecture on the dues date. Late homework will not be accepted.
20 Homework; collection and collaboration Homework will be collected at the start of the lecture on the dues date. Late homework will not be accepted. You may collaborate in small groups if:
21 Homework; collection and collaboration Homework will be collected at the start of the lecture on the dues date. Late homework will not be accepted. You may collaborate in small groups if: you aknowledge your collaborators,
22 Homework; collection and collaboration Homework will be collected at the start of the lecture on the dues date. Late homework will not be accepted. You may collaborate in small groups if: you aknowledge your collaborators, write up your own solutions, in your own words.
23 Exams There will be two midterms and a final exam Midterm 1 8-8:50am Monday, 23 October, 2017
24 Exams There will be two midterms and a final exam Midterm 1 8-8:50am Monday, 23 October, 2017 Midterm 2 8-8:50am Monday, 20 November, 2017
25 Exams There will be two midterms and a final exam Midterm 1 8-8:50am Monday, 23 October, 2017 Midterm 2 8-8:50am Monday, 20 November, 2017 Final 8-11am Wednesday, 13 December, 2017
26 Exams There will be two midterms and a final exam Midterm 1 8-8:50am Monday, 23 October, 2017 Midterm 2 8-8:50am Monday, 20 November, 2017 Final 8-11am Wednesday, 13 December, 2017 Cheatsheets and calculators You will be allowed a small cheatsheet in each exam. Must be self-written and one side, half a letter size piece of paper. You are also allowed to use non-programmable, non-graphing calculators.
27 Grading Your final grade will be calculated using the maximum of the following two grading schemes. 10% (best 4 quizzes/hw) + 40% (midterms) + 50% (final) or 10% (best 4 quizzes/hw) + 30% (best midterm) + 60% (final)
28 Schedule See website
29 Where to get help Piazza Here you can ask questions and answer others questions. Lets take a look...
30 Where to get help Piazza Here you can ask questions and answer others questions. Lets take a look... Office hours Use them wisely! Prepare and seek information first. If you learn something, post it to Piazza!
31 Where to get help Piazza Here you can ask questions and answer others questions. Lets take a look... Office hours Use them wisely! Prepare and seek information first. If you learn something, post it to Piazza! Student Math Center (SMC) Location: MS 3974, times: M-R 9am-3pm. The SMC offers free, individual and group tutoring for all lower division math courses. This service is available on a walk-in basis; no appointment is necessary. Students may ask any of the TAs in attendance for assistance with math problems.
32 What should you know? A nonexhaustive list: Definitions and properties of basic functions.
33 What should you know? A nonexhaustive list: Definitions and properties of basic functions. How to calculate limits.
34 What should you know? A nonexhaustive list: Definitions and properties of basic functions. How to calculate limits. You should have a good feel for what the derivative means. I.e. derivative at a point = tangent slope.
35 What should you know? A nonexhaustive list: Definitions and properties of basic functions. How to calculate limits. You should have a good feel for what the derivative means. I.e. derivative at a point = tangent slope. You need to understand differentiation algebraically as well as geometrically.
36 What should you know? A nonexhaustive list: Definitions and properties of basic functions. How to calculate limits. You should have a good feel for what the derivative means. I.e. derivative at a point = tangent slope. You need to understand differentiation algebraically as well as geometrically. You should also know the definition of the derivative d f (x + h) f (x) f (x) = lim dx h 0 h
37 Differentiation You should be able to differentiate many of the standard functions we will see in this course. This includes: polynomials/power functions d dx (x n ) = nx n 1
38 Differentiation You should be able to differentiate many of the standard functions we will see in this course. This includes: polynomials/power functions d dx (x n ) = nx n 1 exponentials d dx (ex ) = e x
39 Differentiation You should be able to differentiate many of the standard functions we will see in this course. This includes: polynomials/power functions d dx (x n ) = nx n 1 exponentials logarithms d dx (ex ) = e x d dx (ln x) = 1 x
40 Differentiation You should be able to differentiate many of the standard functions we will see in this course. This includes: polynomials/power functions d dx (x n ) = nx n 1 exponentials logarithms trig functions d dx (ex ) = e x d dx (ln x) = 1 x d (sin x) = cos x dx
41 Product rule The product rule lets us differential functions of the form f (x) = g(x)h(x). It says d dx f (x) = g (x)h(x) + g(x)h (x)
42 Product rule The product rule lets us differential functions of the form f (x) = g(x)h(x). It says d dx f (x) = g (x)h(x) + g(x)h (x) Example Let s differentiate the function f (x) = e x sin x. ( ) ( ) d d dx f (x) = dx ex sin x + e ddx x sin x
43 Product rule The product rule lets us differential functions of the form f (x) = g(x)h(x). It says d dx f (x) = g (x)h(x) + g(x)h (x) Example Let s differentiate the function f (x) = e x sin x. ( ) ( ) d d dx f (x) = dx ex sin x + e ddx x sin x = e x sin x + e x cos x
44 Product rule The product rule lets us differential functions of the form f (x) = g(x)h(x). It says d dx f (x) = g (x)h(x) + g(x)h (x) Example Let s differentiate the function f (x) = e x sin x. ( ) ( ) d d dx f (x) = dx ex sin x + e ddx x sin x = e x sin x + e x cos x = e x (sin x + cos x)
45 The chain rule The chain rule is very important! It allows us to differentiate functions of the form f (x) = g(h(x)). It says d dx f (x) = h (x)g (h(x))
46 The chain rule The chain rule is very important! It allows us to differentiate functions of the form f (x) = g(h(x)). It says d dx f (x) = h (x)g (h(x)) Example Let s differentiate f (x) = sin(e x ). In this example h(x) = e x and g(x) = sin x
47 The chain rule The chain rule is very important! It allows us to differentiate functions of the form f (x) = g(h(x)). It says d dx f (x) = h (x)g (h(x)) Example Let s differentiate f (x) = sin(e x ). In this example h(x) = e x and g(x) = sin x
48 The chain rule The chain rule is very important! It allows us to differentiate functions of the form f (x) = g(h(x)). It says d dx f (x) = h (x)g (h(x)) Example Let s differentiate f (x) = sin(e x ). In this example h(x) = e x and g(x) = sin x so h (x) = e x and g (x) = cos x
49 The chain rule The chain rule is very important! It allows us to differentiate functions of the form f (x) = g(h(x)). It says d dx f (x) = h (x)g (h(x)) Example Let s differentiate f (x) = sin(e x ). In this example h(x) = e x and g(x) = sin x so so h (x) = e x and g (x) = cos x f (x) = e x cos(e x )
50 The quotient rule sucks The quotient rule says d dx ( g(x) h(x) ) = g (x)h(x) g(x)h (x) h(x) 2
51 The quotient rule sucks The quotient rule says d dx ( g(x) h(x) ) = g (x)h(x) g(x)h (x) h(x) 2 This is annoying to remember (where does that minus sign go again?). Luckily we can notice g(x) h(x) = g(x)k(x) where k(x) = (h(x)) 1 So we can just use the product rule!
52 Example Question Differentiate f (x) = sin 1 x
53 Example Question Differentiate f (x) = sin 1 x Solution We should use the chain rule. Notice f (x) = g(h(x)) where h(x) = x 1 and g(x) = sin x
54 Example Question Differentiate f (x) = sin 1 x Solution We should use the chain rule. Notice f (x) = g(h(x)) where h(x) = x 1 and g(x) = sin x
55 Example Question Differentiate f (x) = sin 1 x Solution We should use the chain rule. Notice f (x) = g(h(x)) where h(x) = x 1 and g(x) = sin x so h (x) = x 2 and g (x) = cos x
56 Example Question Differentiate f (x) = sin 1 x Solution We should use the chain rule. Notice f (x) = g(h(x)) where h(x) = x 1 and g(x) = sin x so so h (x) = x 2 and g (x) = cos x f (x) = h (x)g (h(x)) = 1 x 2 cos(x 1 )
57 Example Question Differentiate f (x) = x 1 x + 1
58 Example Question Differentiate f (x) = x 1 = (x 1)(x + 1) 1 x + 1 Solution We should use the product/quotient rule. Notice f (x) = g(x)h(x) where h(x) = (x + 1) 1 and g(x) = x 1 h (x) = (x + 1) 2 and g (x) = 1
59 Example Question Differentiate f (x) = x 1 = (x 1)(x + 1) 1 x + 1 Solution We should use the product/quotient rule. Notice f (x) = g(x)h(x) where h(x) = (x + 1) 1 and g(x) = x 1 h (x) = (x + 1) 2 and g (x) = 1
60 Example Question Differentiate f (x) = x 1 = (x 1)(x + 1) 1 x + 1 Solution We should use the product/quotient rule. Notice f (x) = g(x)h(x) where h(x) = (x + 1) 1 and g(x) = x 1 so h (x) = (x + 1) 2 and g (x) = 1 f (x) = g (x)h(x) + g(x)h (x)
61 Example Question Differentiate f (x) = x 1 = (x 1)(x + 1) 1 x + 1 Solution We should use the product/quotient rule. Notice f (x) = g(x)h(x) where h(x) = (x + 1) 1 and g(x) = x 1 so h (x) = (x + 1) 2 and g (x) = 1 f (x) = g (x)h(x) + g(x)h (x) = 1 x + 1 x 1 (x + 1) 2 = 2 (x + 1) 2
62 Example Question Differentiate F (x) = sin x 2 1 sin x 2 + 1
63 Example Question Differentiate F (x) = sin x 2 1 sin x Solution We should notice that F(x) = f(g(x)) so we can use the chain rule! f (x) = x 1 x + 1 and g(x) = sin x 2 f (x) = 2 (x + 1) 2 and g (x) = 2x cos x 2
64 Example Question Differentiate F (x) = sin x 2 1 sin x Solution We should notice that F(x) = f(g(x)) so we can use the chain rule! f (x) = x 1 x + 1 and g(x) = sin x 2 f (x) = 2 (x + 1) 2 and g (x) = 2x cos x 2
65 Example Question Differentiate F (x) = sin x 2 1 sin x Solution We should notice that F(x) = f(g(x)) so we can use the chain rule! f (x) = x 1 x + 1 and g(x) = sin x 2 so f (x) = 2 (x + 1) 2 and g (x) = 2x cos x 2 F (x) = g (x)f (g(x))
66 Example Question Differentiate F (x) = sin x 2 1 sin x Solution We should notice that F(x) = f(g(x)) so we can use the chain rule! f (x) = x 1 x + 1 and g(x) = sin x 2 so f (x) = 2 (x + 1) 2 and g (x) = 2x cos x 2 F (x) = g (x)f (g(x)) = 2x cos x 2 2 (sin x 2 + 1) 2
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