Differential Calculus with Applications to Life Sciences
MATH 102105

Winter 2014
Math 105 Week 2 Learning Goals
1 Overview
This week, we will be learning about partial derivatives of functions oi' two
variabies. Those are analogs of the derivative of a function of a single variable,
and many aspects of these will be familiar. However,
Differential Calculus with Applications to Life Sciences
MATH 102105

Winter 2014
Math 105 Week 6 Learning Goals
1 Overview
This week will be about the Fundamental Theorem of Calculus that connects
differential calculus with integration. We use this result to evaluate definite
integrals of functions f that cannot be evaiuate with Riema
Differential Calculus with Applications to Life Sciences
MATH 102105

Winter 2014
Math 105 Week 7' Learning Goals
1 Overview
Last week we discussed two methods of integration, namely substitution and
integration by parts. As we saw, these methods are extremely useful in sim~
plii'yii‘ig and evaiuating certain ii‘itegrals. Unfortunately
Differential Calculus with Applications to Life Sciences
MATH 102105

Winter 2014
Math 105 Week 8 Learning Goals
1 Overview
Over the past few weeks, we have covered numerous techniques for evaluating
deﬁnite and indeﬁnite integrals in various forms, but these techniques cannot
be used on every integral. In these cases we can use numeri
Differential Calculus with Applications to Life Sciences
MATH 102105

Winter 2014
Math 105 Week 12 Learning Goals
1
Overview
Last week we started on innite series. In particular we learned about two
tests of convergence and/or divergence: namely the divergence test and the
integral test. This week we will learn a few more such tests de
Differential Calculus with Applications to Life Sciences
MATH 102105

Winter 2014
Math 105 Week 9 Learning Goals
1
Overview
This week we give a very brief introduction to random variables and probability
theory. Most observable phenomena have at least some element of randomness
associated to what we observe and how we observe it. Exper
Differential Calculus with Applications to Life Sciences
MATH 102105

Winter 2014
Math 105 Week 11 Learning Goals
1
Overview
In rstsemester calculus, you learned what it meant to talk about the limit
of a function. We begin this week by discussing what it means to talk about
the limit of an innite list of numbers (which we call an inn
Differential Calculus with Applications to Life Sciences
MATH 102105

Winter 2014
292 At’PIJCA’t‘iONS or: his Datuvm‘wa
Citminim 4 
89. Legs with different bases Show thatf =2 log,.r and
g(x) =1 iogbx, where a / l and b > I, grow at a comparable
rate as x —~> oo.
Factorial growth rate The factorial function is usually deﬁned for
pos
Differential Calculus with Applications to Life Sciences
MATH 102105

Winter 2014
Math 105 Week 1 Learning Goals
1 Overview
In this introductory week, we will (ieﬁne scalar functions of several variables,
and discuss their geometric interprcitatious. This is a subset of the material
contained in sections 12.1 and 12.2 of the textbook.
Differential Calculus with Applications to Life Sciences
MATH 102105

Winter 2014
Chapter 7: Vectors and the
Geometry of Space
Section 7.6
Surfaces in Space
Written by Richard Gill
Associate Professor of Mathematics
Tidewater Community College, Norfolk Campus, Norfolk,
VA
With Assistance from a VCCS LearningWare Grant
In this lesson we
Differential Calculus with Applications to Life Sciences
MATH 102105

Fall 2013
MATH 102  MIDTERM TEST 1
University of British Columbia
Last name (print):
First name (print):
ID number:
Section number:
Date: September 30, 2014.
Time: 6:00 p.m. to 7:00 p.m.
Number of pages: 9 (including cover page)
Exam type: Closed book
Aids: No cal
Differential Calculus with Applications to Life Sciences
MATH 102105

Fall 2013
Multiple choice (continued)
3. Consider a differential equation dy/dt = f (y). Shown in AD is the phase line (state space) diagram (f (y) versus y).
Which of the following is the correct pairing of these sketches with the sketch of a solution y(t) to the
Differential Calculus with Applications to Life Sciences
MATH 102105

Fall 2013
Multiple choice
Each multiple choice question is worth 2 pts. No partial points will be given for work shown.
Enter your answers using the bubbles on the front page.
1. According to the graphs in the figure below, which of the following is true?
(a) f (x)
Differential Calculus with Applications to Life Sciences
MATH 102105

Fall 2013
A. Multiple choice questions
Enter your choice for each multiple choice question in the box at the bottom of the page. There
are two pages at the end of the exam that can be used for rough work. No partial marks will be given
for this section.
A.1 Let f (
Differential Calculus with Applications to Life Sciences
MATH 102105

Fall 2013
O 5 H 2. JoaoANN STEVENSON
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Differential Calculus with Applications to Life Sciences
MATH 102105

Winter 2014
MATH 105 101
Midterm 1 Sample 1
MATH 105 101 Midterm 1 Sample 1
1. (20 marks)
(a) (5 marks) Let
f (x, y) = arctan(xy)
Compute fxx (1, 1) and fxy (1, 1). Simplify your answer.
(b) (5 marks) Find all vectors in R3 of length 10 which are parallel to the vect
Differential Calculus with Applications to Life Sciences
MATH 102105

Winter 2014
Math 105 Week 13 Learning Goals
1
Overview
We continue our study of power series, focusing on the relation between known
functions and their power series representations.
2
Learning Objectives
These should be considered a minimum, rather than a comprehens