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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

Please mention MATH104 in subject

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

Some additional materials from another book (strictly optional): business problems, compound interest, elasticity of demand, related rates (once you click on the link, click "download" in upper right corner to actually download the pdf files).

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 2****5 **comments: we have solved several problems as a review before the final exam.

**Lecture 1** comments: we have talked about section 1.3

- 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 *videos*: Lecture 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

**Lecture 2** comments: we have talked about

- change of base in logarithms (chapter 1.3)
- business problem: price, quantity, cost, revenue, profit
- demand equation p(q), R=pq, P=R-C
- maximizing a quadratic function
- finding slope of a tangent line numerically (chapter 2.1)
- concept of limit and first examples (chapter 2.1, 2.2)

For a slow review of the topics covered, you can watch:

**Lecture 3** comments: we have talked about material in chapter 2.1,2.2,2.3

- 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).

**Lecture 4** comments: we have talked about section 2.6

- Squeeze theorem (section 2.3)
- Continuity
- Rules for determining continuity
- Continuity on an interval, continuity from right/left
- Intermediate value theorem

**Lecture 5** comments: we have talked about section 3.1

- Average rate of change
- Instantaneous rate of change
- Derivative
- Sketching derivative given graph of function

Graphing derivative given graph of f: video instructions; module/applet/app (incredibly good!)

**Lecture 6** comments: we have talked about sections 3.2, 3.3

- Graph of f ' given graph of f
- Differentiability implies continuity, but not vice-versa
- Derivative of x
^{n}, e^{x} - Derivative of sum, difference, product, quotient

**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

We didn't cover: derivatives of higher order.

**Lecture 8** comments: we have talked about section 3.5.

- 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

**Lecture 9 comments: **we have talked about section 3.6

- Example with marginal quantities
- Chain rule

Video: lecture 9

**Lecture 10 **comments: we have talked about sections 3.7, 3.8

- Logarithmic differentiation
- Implicit differentiation

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

- Logarithmic differentiation
- Implicit differentiation
** **

**Lecture 12** comments: we have talked about

- Relative rate of change
- Exponential vs linear growth
- Elasticity of demand

**Lecture 13** comments: we have talked about

- Elasticity of demand
- Compound interest
- Continuously compounded interest

**Lecture 14** comments: we have talked about

- Present and future values
- Related rates of change

**Lecture 15** comments: we have talked about

- 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

**Lecture 16** comments: we have talked about

- 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

**Lecture 17** comments: we have talked about

- 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

**Lecture 18** comments: we have talked about

- Horizontal asymptotes
- Slant asymptotes
- Finding slant asymptotes for a quotient of two polynomials using long division

Relevant materials: section 2.5,4.3

**Lecture 19** comments: we have talked about

- Graphing example
- An example of optimization problem

Relevant materials: section 4.3,4.4**Lecture 20 **comments: we have talked about

- Optimization problems
- Identifying constraints

Relevant materials: section 4.4

**Lecture 21 **comments: we have talked about

- Optimization problem
- Linear approximation

Relevant materials: section 4.4, 4.5

**Lecture 22 **comments: we have talked about

- Linear approximation in context of trigonometric functions
- Quadratic approximation

Relevant materials: section 4.5, 9.1

**Lecture 2****3 **comments: we have talked about

Relevant material: section 9.1

**Lecture 2****4 **comments: we have talked about

- Error term in linear approximation
- Inverse trigonometric functions and their derivatives

Relevant material: section 9.1, 3.9