Class notes

Math 100 Small Class notes - UBC 2022

11 views 0 purchase

Course
MATH 100

Institution
University Of British Columbia (UBC )

There is a big class and a small class in MATH 100 UBC. The file includes content from all lectures with practice problems downloadable from an online pdf book.

[Show more]

Preview 2 out of 11 pages

View example

Uploaded on December 19, 2022
Number of pages 11
Written in 2022/2023
Type Class notes
Professor(s) Mark mac lean, natalia accomazzo scotti
Contains All classes

class
math
ubc
2022
derivative
notebook
multiple variable function

tranghane Member since 1 year 76 documents sold

CA$6.47

Added

Add to cart Add to wishlist

100% satisfaction guarantee
Immediately available after payment
Both online and in PDF
No strings attached

Week 1 Large Class Learning Objectives
September 13, 14, 15 (2022)

Topics: Comparing power, log, and exponential functions; trigonometric functions; parse trees

Learning Objectives:
• Sketch basic power functions.
• Determine which term in a polynomial function will dominate for small x and for large x.
• Sketch two-term polynomial functions by determining which term dominates for small x and for large
x. For example, sketch f (x) = x2 − x4 .
√
• Sketch familiar functions such as ex , log x, sin x, cos x, tan x, 1/x, x, and |x|.
• Demonstrate that ex eventually dominates any given power function and use this fact for sketching.
For example, sketch f (x) = ex − x4 .
• Given a complicated function, describe it using a parse tree.
• Given a complicated function, describe in words the order in which to apply operations.

Textbook sections:
• First steps in graph sketching: Section 1.4 of Differential calculus for the life sciences
• Parse trees: CLP-1 Section 0.5
Additional problems:
1. Exercises 1.4, 1.5, 1.6, 1.13, 1.26 from Differential calculus for the life sciences
2. Additional problems on asymptotic reasoning and sketching.
3. The Lennard-Jones potential
12 6 !
R R
V (r) = ε −2 , ε, R > 0
r r

describes the potential energy of a diatomic molecule where the atoms are a distance r > 0 apart.
(a) Write V (r) as a rational function. A rational function is the quotient of two polynomials.
(b) What function is a good approximation for V (r) for small r? For large r?
(c) Draw a rough sketch of V (r).
4. The Morse potential
2
M (r) = ε 1 − e−a(r−R) , ε, a, R > 0
is an alternative to the Lennard-Jones potential.
(a) What function is a good approximation for M (r) for small r? For large r?
(b) Draw a rough sketch of M (r).

1

, Week 2 Large Class Learning Objectives
September 20, 21, 22 (2022)

Topics: Limits; horizontal and vertical asymptotes

Learning Objectives:
• Explain using both words and pictures what lim f (x) = L, lim− f (x) = L, and lim+ f (x) = L mean
x→a x→a x→a
(including the case where L is equal to ∞ or −∞).

• Explain using using both words and pictures what lim f (x) = L and lim f (x) = L mean (including
x→∞ x→−∞
the case where L is equal to ∞ of −∞).
• Find the limit of a function at a point given the graph of the function.

• Evaluate limits of polynomial, rational, trigonometric, exponential, and logarithmic functions.
• Explain using both informal language and the language of limits what it means for a function to have
a horizontal or vertical asymptote.
• Given a simple function, find its vertical and horizontal asymptotes by asymptotic reasoning or by
taking limits.
• Use limits to find information about the shape of a function and in some cases produce a sketch.
• Explain why it is not true that a function cannot cross its horizontal asymptote.

Textbook sections:
• The Limit of a Function: CLP-1 Section 1.3
• Limits at Infinity: CLP-1 Section 1.5

• Domain, Intercepts and Asymptotes: CLP-1 Section 3.6.1
Additional Problems:
1. CLP-1 Problem Book Section 1.3: Q1-Q17.
2. CLP-1 Problem Book Section 1.5: Q1-Q7, Q27.

3. CLP-1 Problem Book Section 1.5: Q8, Q13-Q15, Q17-Q19 — but solve these problems using asymptotic
reasoning (investigating the behaviour of functions by determining which terms are “dominant”).
4. CLP-1 Problem Book Section 3.6.1: Q1, Q4, Q5.

1

The benefits of buying summaries with Stuvia:

Guaranteed quality through customer reviews

Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.

Quick and easy check-out

You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.

Focus on what matters

Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!

Frequently asked questions

What do I get when I buy this document?

You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.

Satisfaction guarantee: how does it work?

Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.

Who am I buying these notes from?

Stuvia is a marketplace, so you are not buying this document from us, but from seller tranghane. Stuvia facilitates payment to the seller.

Will I be stuck with a subscription?

No, you only buy these notes for CA$6.47. You're not tied to anything after your purchase.

Can Stuvia be trusted?

4.6 stars on Google & Trustpilot (+1000 reviews)

70055 documents were sold in the last 30 days

Founded in 2010, the go-to place to buy study notes for 14 years now

Start selling

Class notes

Math 100 Small Class notes - UBC 2022

Document information

Subjects

Written for

Seller

Reviews received

Content preview