“CALCULUS” in Life
2014-2015 Fall
1 Preliminaries
1.1 Numbers
1.2 Can you cut an apple exactly in half? (real line,
intervals)
1.3 What do we remember from high school?
1.4
(Radicals, Factors, roots, rational expressions, inequalities)
Descartes and Cartesian coordinates (equation of
line, circle, parabola, distance)
2 Functions
2.1 Functions are everywhere
2.2 Features of functions (Domain and range, surjective,
2.3
injective, one-to-one functions, even, odd functions,
combination and composition of functions)
Reading a graph (and graphing by shifting, scaling,
reflecting)
Can what is done be undone? (Inverse functions)
2.4
2.5 Special functions
2.5.1 Trigonometric functions and inverses
2.5.2 Exponential functions and inverses (logarithm)
3 Limits and Continuity
3.1 Limit (Calculating limit, Sandwich theorem, limit at infinity)
3.2 Can you draw the function without lifting pen?
(definition of continuity, intermediate value theorem,
Intermediate value theorem of Bolzano, wobbly table
theorem)
4 Differentiation
4.1 Geometric meaning of derivative (Tangent, rate of
4.2
4.3
change-derivative, graph of derivative, tangent line, normal
line)
Derivative of special functions (power rule,
derivative of inverse function, derivative of trigonometricexponential and logarithmic functions)
Differentiation rules (The product and quotient rule,
chain rule, implicit differentiation)
4.4 Application of derivatives
4.4.1 Extreme values (Local extremas, global extremas,
4.4.2
4.4.3
4.4.4
4.4.5
first derivative test, second derivative test
Curve sketching
Optimization
Mean value theorem, Rolle’s theorem
L’Hopital rule
Grading:
% 20 Midterm I
% 20 Midterm II
% 35 Final
% 10 Quiz
% 15 Participation (attendance, project, homework)
Textbook:
Thomas’ Calculus
Supplementary book :
“Calculus: An Integrated Approach to Functions and Their
Rates of Change” by Robin J. Gottlieb
Weeks
1st (8-10 October)
Topıcs
Welcome to world of Math! Level scanning exam
2nd (13-17 October)
Numbers, Can you cut an apple exactly in half ?
Evaluation of exam, Descartes and Cartesian
coordinates,
3rd (20-24 October)
Functions are everywhere, Features of functions,
Reading a graph,
Can what is done be undone?
4th (27-31 October)
Special functions, trigonometric functions and inverses,
½Tuesday+Wednesday:
Exponential functions and inverses,
no class
5th (3-7 November)
Limit
6th (10-14 November)
Continuity
7th (17-21 November)
Geometric meaning of derivative
8th (24-28 November)
Review,
MIDTERM I
9th (1-5 December)
Derivative of special functions,
Differentiation rules
10th (8-12 December)
Extreme values
11th (15-19 December)
Curve sketching
12th (22-26 December)
Optimization
13th (29 December- 2January)
Thursday: no class
Review,
MIDTERM II
14th (5-9 January)
Mean value theorem, Rolle’s theorem
15th (12-16 January)
L’Hopital rule
16th (19-24 January)
FINAL!
Course learning objectives:
At the end of this course students will be able to
 list the hierarchy of number systems and identify any
number’s belonging,
 construct function with the sufficient data they
obtained and examine the function’s features and
examine whether it is continuous or discrete or none
of them,
 paraphrase a formulated function into words and argue
the behavior of the function as we change the value or
the form of the function,
 evaluate a given limit if it exists,
 state the advantages of continuous functions rather
than discontinuous ones and apply related theorems in
case of need,
 criticize discontinuous functions from the perspective
of existence of limit for discontinuous points and
predict the behavior of the function at that point,
 interpret the geometric meaning of derivative at any
point and use it in construction of formulas for some
geometrical shapes,
 calculate the derivative of any function,
 find the maximum and minimum values of any
function, and sketch the graph of the function
 apply derivative rules to optimize a given source.
Course aim:
This course aims to create an awareness of functions
occurring around us, to provide the learners to see the
hidden mathematics in life and to guide them in the analyses
and use of these functions.