Mathematics 1 & 2  A.Y.2017/2018
Università degli Studi Ca' Foscari of Venice,
A.Y.20172018, Department of Management, curriculum Business
Administration and Management.
***** Very important: first partial *****
You must enroll on the first partial (November 4, 2017, 913,
room 7A) using Esse3, from October 20 to October 31. Please use the
special section for Partial proofs and not the one for full exams.
There will be two shifts for the partial test: the first at 9 and
the second at 11. The subdivision will be according to the first
letter of the surname: approximately AK and LZ, but detailed info
will be given after October 31 here and on Unive Platform (Under "Notices"
in the page of the course). No change between the first and second
shift will be permitted.
You will need to bring your university card with you.
***** Very important: first partial *****
Textbook
Knuth Sydsæter, Peter Hammond, Arne Strøm &
Andrès Carvajal, Essential Mathematics for Economic
Analysis, Pearson, 2016 (V edition).
Teaching material

Approaching the
course.

Saying maths: hints for
reading numbers and mathematical formulas in english and
american english (this material is found on this web site).

Precalculus,
by Luciano Battaia, Giacomo Bormetti and Giulia Livieri: A
prelude to calculus with exercises  Notes for a crashcourse in mathematics (this material is found on
this web site). This
booklet can help in revising basic maths concepts, and
contains mainly the same topics as in the first five chapters
of the textbook.

A brief introduction to
limits. These notes supplement the concept of limit,
treated in paragraphs 6.5 and 7.9 of the textbook.

A dash on derivatives. These
notes are to be considered as a summary of some concepts
included in chapters 6 and 7 of the textbook.

One variable optimization. These
notes are to be considered as a summary of chapter 8 of the
textbook.

A dash of integrals. These notes
are to be considered as a summary of chapter 9 of the
textbook.

Basics of Financial Mathematics.
Outline of the topics covered in class
References to the paragraphs of the textbook are given in
parentheses, when possible.

Lecture 1  September 18, 2017: recalls of selected topics
from chapters 1 to 5 of the textbook. It is important to
remember that all the topics contained in these chapters
are considered known.

Approaching the course.

Informations about the software packages that can help
during the course, in particular Wolfram Alpha and
Geogebra. As far as Geogebra is concerned the software
can be used directly on line in a browser's window
or downloaded and installed to your personal computer.
There is also a version suitable for use on portable
media without leaving setting files on the host
computer: see the web site geogebra.org.

Basic definitions about functions (4.2, 4.3).

Linear functions (4.4).

Lecture 2  September 19, 2017: still recalls of selected
topics from chapters 1 to 5 of the textbook. It is important to
remember that all the topics contained in these chapters
are considered known.

Quadratic functions (4.6).

Power functions (4.8).

Exponentials and logarithms (4.9, 4.10).

Lecture 3  September 20, 2017: still recalls of selected
topics from chapters 1 to 5 of the textbook.
Introduction to limits.

Still exponentials and logarithms.

Properties of logarithms.

Piecewise defined functions. An economic example of such
a function can be found in
Pound Drop, on
this web site.

A graphical approach to limits (6.5, partly). The
limits will be treated in a somewhat different way from
the textbook. Geogebra has been used to illustrate in a
simple way what a limit is. A summary of the
introduction to limits, togheter with exercises, can be
found in
A brief introduction to
limits.

Lecture 4  September 25, 2017: Limits.

Limits for one variable functions.

Continuity.

Lecture 5  September 26, 2017: limits.
Introduction to the concept of derivative.

Still algebra of limits: indeterminate forms.

Rules of limits.

The strength of infinities.

The slope of a curve: for this subject you can use the
pdf A dash on
derivatives, that you can found on this web
site.

Lecture 6  September 27, 2017: differentiation. A concise
summary on differentiation can be found in "A dash on
derivatives".

Slopes of curves (6.1).

Tangents and derivatives (6.2).

Simple rules for differentiation (6.6).

Sums, products and quotients (6.7).

Exponential functions (6.10, partly).

Logarithmic functions (6.11, partly).

Composite functions (chain rule) (6.8).

Lecture 7  October 3, 2017: more on differentiation. One
variable optimization. Mockups of first partial.

More on composite functions (chain rule) (6.8).

Compound or piecewise defined functions.

Kinks.

Increasing and decreasing functions (6.3).

Linear approximations (7.4).

Extreme points (8.1). A summary on one variable
optimization can be found in "One
variable optimization", a pdf you can find on this
web site

Local extreme points (8.6).

Mockups of the first partial. All the proposed mockups,
also for the next lectures, can be found on this web
site in the page
of A.Y. 2016/2017.

Lecture 8  October 4, 2017: more on differentiation. One
variable optimization. Mockups of first partial.

Higher order derivatives (6.9).

Convex and concave functions (6.9).

Inflection points (8.7).

Increasing and decreasing functions (6.3).

L'Hôpital's rule (7.12).

Higher order approximations (7.5).

Sample exercises.

Mockups of the first partial. All the proposed mockups can be found on this web
site in the page
of A.Y. 2016/2017.

Lecture 9  October 9, 2017: antiderivatives. Mockups of first partial.
See, on this web site, the pdf
A dash of integrals
for a summary of integration theory.

Indefinite integrlas (9.1).

Some important integrals.

Some general rules.

Sample exercises.

Mockups of the first partial. All the proposed mockups can be found on this web
site in the page
of A.Y. 2016/2017.

Lecture 10  October 10, 2017: more on antiderivaties,
definite integral. Mockups of first partial.

Integration of composite functions.

Integration by parts (9.5).

Area and definite integrals (9.2).

A geometrical interpretation of definite integrals.

Sample exercises.

Mockups of the first partial. All the proposed mockups can be found on this web
site in the page
of A.Y. 2016/2017.

Lecture 11  October 11, 2017: conclusions on definite
integrals, improper integrals. Mockups of first partial.

Properties of definite integrals (9.3).

More on areas and definite integrals.

Areas involving piecewise defined functions.

Improper integrals (9.7).

Infinite intervals of integration.

Integration of unbounded functions.

Sample exercises.

Mockups of the first partial. All the proposed mockups can be found on this web
site in the page
of A.Y. 2016/2017.

Lecture 12  October 16, 2017: basics of Financial Mathematics:
use the pdf Basics of Financial
Mathematics, that you can find on this web site. Mockups of first partial.

Further formulas concerning the exponential and
logarithmic functions with a general base.

Final observations about maxima and minima, in
particular concerning the Extreme Value Theorem.

Areas between the graphs of two continuous functions.

The Fundamental Problem of Financial Mathematics.

Interest rate, Present Value, Future Value, accumulation
factor, actualization factor.

Financial regimes and the compound interest.

Subdivision of the period in subperiods and the
effective rate of interest.

Continuous compounding.

Mockups of the first partial.

Lecture 13  October 17, 2017: basics of Financial Mathematics:
use the pdf Basics of Financial
Mathematics, that you can find on this web site. Mockups of first partial.

Streams of Cash Flow.

Geometric Progressions.

Annuities. Ordinary annuities. Due annuities.

Mockups of the first partial.

Lecture 14  October 18, 2017: Mockups of first partial.

Mockups of the first partial.

Lecture 15  October 23, 2017: Mockups of first partial.

Mockups of the first partial.
Selected exercises from the texbook.

Chapter 6: 6.6.3; 6.7.3, 6.7.4; 6.8.3; 6.10.1, 6.10.4;
6.11.3,6.11.6,6.11.7; Review exercises n. 3, 5, 14, 15.

Chapter 7: 7.12.1, 7.12.2, 7.12.3, 7.12.4, 7.12.5.

Chapter 8: 8.2.1, 8.2.5, 8.2.6, 8.2.7; 8.4.2; 8.6.2, 8.6.3;
8.7.2, 8.7.3; Review exercises n. 1, 6, 7.

Chapter 9: 9.1.1, 9.1.2, 9.1.4, 9.1.5, 9.1.6, 9.19,
9.1.10,9.1.11, 9.1.12; 9.2.3, 9.2.4, 9.2.5; 9.3.1, 9.3.2,
9.3.3; 9.5.1, 9.5.2; 9.7.1, 9.7.9; Review exercises n. 1, 2,
3, 4.

Chapter 11: 11.1.6, 11.1.7; 11.2.4, 11.2.5; Review exercises
n. 6, 7, 9, 10, 12.

Chapter 13: 13.3.1, 13.3.2, 13.3.3; 13.5.1, 13.5.2; Review
exercises: 4.

Chapter 14: 14.1.1, 14.1.3.c, 14.1.4.
Exercises.
See the page
of A.Y. 2016/2017 for a collection of exercises,
mockups and old exams.
Practice lessons.
You can find the exercises solved or proposed during practice
lessons by prof. Somenzi Damiano Marino on his I.S.A. section of
Unive Platform (http://static.unive.it/isa/index/docente/persona/10594999).
You must use your username and password.
copyright 2017 et seq. luciano battaia
first published on 2017/09/18  last updated on 2017/10/19