🏷️ LIMITED TIME OFFER: GET 20% OFF GRADE+ YEARLY SUBSCRIPTION →

Verified Documents at University of British Columbia

Integral Calculus with Applications to Commerce and Social Sciences
University of British Columbia
Verified Notes

Browse the full collection of course materials, past exams, study guides and class notes for MATH 105 - Integral Calculus with Applications to Commerce and Social Sciences at …

PROFESSORS

All Professors

Keqin Liu

Wang, Jun

Yeager, Elyse

LIU, KEQIN

ISSA, AHMAD ISSA KHALID

Verified Documents for LIU, KEQIN

Class Notes

Taken by our most diligent verified note takers in class covering the entire semester.

MATH 105 Lecture Notes - Lecture 8: Antiderivative, 32X

Given a function, f(x), an anti-derivative of f(x) is any function f(x) such that. If f(x) is any anti-derivative of f(x) then the most general anti-de

MATH 105 Lecture Notes - Lecture 9: Antiderivative

MATH 105 Lecture Notes - Lecture 10: Scalar Multiplication, Parallelogram, Negative Number

Which gives them a direction" and magnitude. Operations are allowed between points and vectors: Adding a point to a vector gives a point. To add or sub

MATH 105 Lecture 11: Math 105 Lecture 11

MATH 105 Lecture 12: MATH 105 Lecture 12

MATH 105 Lecture 13: MATH 105 Lecture 13

We first make a chart for function evaluations: Sketch the graph of the following piecewise function. when we graph piecewise functions we are really g

MATH 105 Lecture 14: MATH 105 Lecture 14

MATH 105 Lecture 15: Math 105 Lecture 15 (1)

MATH 105 Lecture Notes - Lecture 16: Asymptote, Inflection

The domain of a function f ( x ) is the set of all input values ( x -values) for the function. The range of a function f ( x ) is the set of all output

MATH 105 Lecture 17: MATH 105 Lecture 17

Use newton"s method to find the root of x 4 5x 3 +9x+3=0 accurate to six decimal places in the interval [4,6]. First, recall that newton"s method solve

MATH 105 Lecture 18: MATH 105 Lecture 18

Find two positive numbers whose sum is 300 and whose product is a maximum. The first step is to write down equations describing this situation. Let"s c

MATH 105 Lecture Notes - Lecture 22: Regression Analysis, Dependent And Independent Variables

Definition: an approach in regression analysis to approximate the solution for a best-fit curve to a given set of points by minimizing the sum of the s

MATH 105 Lecture 23: Math 105 Lecture 23

MATH 105 Lecture Notes - Lecture 24: Product Rule, Pythagorean Theorem

If y is written in terms of x, i. e. , y = f(x), then this is easy to do using the chain rule: . y = dy/dt = dy/dx dx/dt = dy/dx x. That is, find the d

MATH 105 Lecture 25: MATH 105 Lecture 25

MATH 105 Lecture Notes - Lecture 26: Exponential Function, Logarithm

MATH 105 Lecture Notes - Lecture 27: Growth Factor

MATH 105 Lecture Notes - Lecture 28: Product Rule, Integrating Factor

MATH 105 Lecture Notes - Lecture 29: Separation Of Variables

A separable differential equation appears in the following form: In order to separate a differential equation, all the y"s need to be multiplied by the

MATH 105 Lecture 30: MATH 105 Lecture 30

It states that the rate of change of the temperature of an object is proportional to the difference between its own temperature and the ambient tempera

MATH 105 Lecture 31: MATH 102 Lecture 31 (1)

It states that the rate of change of the temperature of an object is proportional to the difference between its own temperature and the ambient tempera

MATH 105 Lecture 32: MATH 102 Lecture 32 (1)

We have used the fact that t a is constant to eliminate its derivative, and we plugged in y for (t - t a ) in the last step) By defining this variable,

MATH 105 Lecture 33: MATH 105 Lecture 33

The general first order ivp (initial value problem) is dy/dt = f(t,y) y(t 0 ) = y 0 (1) Where f(t,y) is a known function and the values in the initial

MATH 105 Lecture 34: MATH 105 Lecture 34

We then approximate y 1 and construct a line through the point (t 1 , y 1 ) that has a slope f(t 1 , y 1 ). This gives: y = y 1 + f(t 1 ,y 1 ) (t - t 1

MATH 105 Lecture Notes - Lecture 35: Trigonometric Functions, A Reminder, Unit Circle

MATH 105 Lecture 36: MATH 105 Lecture 36

Some handy rules to memorize: lim sin / = 1 lim (cos -1)/ = 1. This limit is simple because there is only a 6 in the denominator that we can just facto

MATH 105 Lecture Notes - Lecture 37: Trigonometric Functions

While this limit may look intimidating, we can rewrite it as by splitting up the fraction. Now, we want a t in the denominator of the first and in the

MATH 105 Lecture Notes - Lecture 38: Inverse Trigonometric Functions

MATH 105 Lecture Notes - Lecture 39: Separation Of Variables

A separable differential equation appears in the following form: In order to separate a differential equation, all the y"s need to be multiplied by the

MATH 105 Lecture 40: MATH 105 Lecture 40

MATH 105 Lecture Notes - Lecture 41: University Of Manchester