The course aims to provide the basic information about functions, limit, derivative, integral as well as their appicaitons in various disciplines including physical and engineering sciences.

Learning Outcomes

CTPO

TOA

Upon successful completion of the course, the students will be able to :

LO - 1 :

learn how to model with functions

1,2

1

LO - 2 :

learn about limit, derivative and applications

1,2

1

LO - 3 :

learn about integral and their applications

1,2

1

CTPO : Contribution to programme outcomes, TOA :Type of assessment (1: written exam, 2: Oral exam, 3: Homework assignment, 4: Laboratory exercise/exam, 5: Seminar / presentation, 6: Term paper), LO : Learning Outcome

Contents of the Course

Functions (polynomials, rational, trigonometric, hyperbolic, exponential, logarithmic and inverse trigonometric functions) graphs of basic functions, shifting and scaling graphs, limit, continuity, differentiation and applications (Intermediate Value Theorem, L'hopital's rule, Mean Value Theorem, Optimization problems, sketching the graph of a function), integration techniques

Course Syllabus

Week

Subject

Related Notes / Files

Week 1

Functions and their graphs, composite functions, polynomial and rational functions, transcendental functions

Week 2

Inverse functions, exponential and logarithmic functions, functions derived from verbal expressions, applications

limits at infinity, limits-a mathematical approach, tangent line problem, application

Week 5

Derivative, power and sum rules, product and division rules, trigonometric functions

Week 6

Chain rule, implicit differentiation, derivative of inverse functions, exponential functions

Week 7

Logarithmic functions, hyperbolic functions, rectilinear motion, related rates

Week 8

Extrema of functions, mean value theorem, limits with L'Hopital rule, drawing graphs, first and second derivative test

Week 9

Midterm exam

Week 10

Optimization, linearization and differentials, applications

Week 11

Indefinite integral, integration by a change of variable, area, definite integral

Week 12

Main theorem of calculus, rectilinear motion, area, volumes of solids: slicing method

Week 13

Volumes of solids: cylindirical shells, arch length, area of a surface of revolution, mean value of a function(work, fluid pressure and force, mass and center of weight)

Week 14

Integral, integration by a change of variable, integration by parts, powers of trigonometric functions

Week 15

Trigonometric change of variables, simple fractions, improper integrals

Week 16

Final exam

Textbook / Material

1

Zill, D.G, Wright, W.S., 2012; Matematik Cilt I (Calculus Early Transcendentals), Çeviri Editörü Prof. Dr. İsmail Naci Cangül, Nobel Yayıncılık, Ankara.