### Differential Calculus with Applications to Commerce and Social Sciences, UBC, Winter 2012,sections 101 and 104 taught by Yuri Burda

Main website for the course contains syllabus, course policies and other general information about the course.

This webpage is specific to sections 101 and 104 taught by Yuri Burda.

Section 101 meeting TR2-3:20 in CHEMD200
Section 104 meeting TR8-9:20 in MATX1100

Office hours: T11-13, R4-6 in LSK126D

E-mail: yburda at math dot ubc dot ca

Marking scheme: 50% final exam, 2 midterms 15% each on Oct 4, Nov 8, 15% webwork,
5% in class quizzes during last 10 minutes of Thursday lecture on Sep20, Sep 27, Oct 18, Nov 1
(worth 2%,2%,1%,0% --- no need to bring doctor's note for missing one quiz, just do well on the others!)

The book that we use is W. Briggs, L. Cochran, Calculus Early Transcedentals, third edition, volume 1

Past exams and some solutions

Your grades so far are posted: morning section (104), afternoon section (101) (now with midterm 2 grades).

Additional midterm 2 practice test. Some of the solutions to this test are also available.

Lecture 2comments: we have solved several problems as a review before the final exam.

Videos: lecture 25

• exponential growth models, exponential functions, rules for working with exponentials, the "special" base e,
• inverse functions, existence of inverse funcitons, horizontal line test for determining invertibility, graphing inverse functions,
• logarithm as the inverse of exponential, domain of logarithm, rules for working with logarithms, natural logarithm, applying logarithms to solve simple equations with exponentials

We didn't cover: definition of one-to-one function (only section 101), change of base for the logarithm, more complicated equations with exponentials.
Correction for section 101: in last example 2000+100(ln 2-ln 3)/ln 2 is approximately 1941.5, not 1959.45 as I've written down

Relevant videosLecture 1
For slower review of the topics covered, you can watch:
Slow introduction to exponents

Exponential growth

Inverses of functions: 1 2 3 4
Logarithms

• change of base in logarithms (chapter 1.3)
• business problem: price, quantity, cost, revenue, profit
• demand equation p(q), R=pq, P=R-C
• finding slope of a tangent line numerically (chapter 2.1)
• concept of limit and first examples (chapter 2.1, 2.2)
Relevant videos: Lecture 2
For a slow review of the topics covered, you can watch:
Limits 1 2 3 4

• limits of the form polynomial/polynomial
• limits with a square root in the expression
• computing limits of complicated expressions by computing limits of their parts
• change of variable in limits
• functions defined by cases
• one-sided limits
We didn't talk about squeeze theorem on which problem 9 in homework is based. Please just draw the graph of x^2+2x+2 around the point x=-1 to see what happens (how the function is "squeezed" between y=1 and the parabola y=x^2+2x+2).
Relevant videos: Lecture 3

• Squeeze theorem (section 2.3)
• Continuity
• Rules for determining continuity
• Continuity on an interval, continuity from right/left
• Intermediate value theorem
Video: lecture 4

• Average rate of change
• Instantaneous rate of change
• Derivative
• Sketching derivative given graph of function
Relevant videos: lecture 5
derivatives 1 2 3
Graphing derivative given graph of f: video instructions module/applet/app (incredibly good!)

• Graph of f ' given graph of f
• Differentiability implies continuity, but not vice-versa
• Derivative of xn, ex
• Derivative of sum, difference, product, quotient
Relevant videos: lecture 6

Lecture 7 comments: we have talked about sections 3.2, 3.3, 3.4, this time with more advanced/subtle examples.

• More on product and quotient rules
• More on continuity vs differentiability
• Derivative of ln, sin, cos
• Quiz
Relevant videos: lecture 7
We didn't cover: derivatives of higher order.

• An example with sin(x)
• Velocity as derivative of position with respect to time
• Acceleration as derivative of velocity with respect to time
• Instantaneous rate of growth
• Average cost
• Marginal cost
• Minimal average cost happens when average cost is equal to marginal cost
• Marginal profit and optimal production levels
Relevant videos: lecture 8

• Example with marginal quantities
• Chain rule

Video: lecture 9

• Logarithmic differentiation
• Implicit differentiation
Video: lecture 10

Lecture 11 comments: we have talked more on sections 3.7, 3.8

• Logarithmic differentiation
• Implicit differentiation
Video: lecture 11

• Relative rate of change
• Exponential vs linear growth
• Elasticity of demand
Relevant materials: beginning of 6.8, notes on elasticity of demandproblems on elasticity of demand
Video: lecture 12

• Elasticity of demand
• Compound interest
• Continuously compounded interest
Video: lecture 13

• Present and future values
• Related rates of change
Relevant materials: section 3.10, related rates in business
Video: lecture 14

• Some formulas from geometry (useful in problems on related rates)
• Absolute maxima and minima
• Local maxima and minima
• Critical points
Relevant materials: section 4.1
Video: lecture 15

• Intervals of increase/decrease of a function
• Local extrema are where the derivative changes sign
• Concavity
• Inflection points
• Second derivative test
Relevant materials: section 4.2,4.3
Video: lecture 16

• Examples where f '(x) and f ''(x) tell much more about f near 0 than f '(0) and f ''(0)
• Infinity as limit
• Vertical asymptotes
• Limits at infinity
Relevant materials: section 4.2,2.4,2.5,4.3
Video: lecture 17

• Horizontal asymptotes
• Slant asymptotes
• Finding slant asymptotes for a quotient of two polynomials using long division
Relevant materials: section 2.5,4.3
Videos: lecture 18, long division 1 2

• Graphing example
• An example of optimization problem
Relevant materials: section 4.3,4.4
Videos: lecture 19

• Optimization problems
• Identifying constraints
Relevant materials: section 4.4
Videos: lecture 20

• Optimization problem
• Linear approximation
Relevant materials: section 4.4, 4.5
Videos: lecture 21

• Linear approximation in context of trigonometric functions
Relevant materials: section 4.5, 9.1
Videos: lecture 22

• Taylor polynomials
Relevant material: section 9.1
Videos: lecture 23

• Error term in linear approximation
• Inverse trigonometric functions and their derivatives
Relevant material: section 9.1, 3.9
Videos: lecture 24

If you haven't done so, please take a couple minutes to send me some anonymous informal feedback on the lectures so far --- now obsolete.
Ċ
Yura Burda,
Nov 7, 2012, 11:28 AM
Ċ
Yura Burda,
Nov 1, 2012, 7:04 PM