MAT123 | Mathematics I

Fall ARŞİV
Ders Listesi
Ders Tanımı ve İçeriği
In this course we present mainly the theory of function in one variable. The syllabus is as follows:

Preliminaries (with early trancendantals)
Limits and Continuity
Differentiation
Applications of differentiation
Integration
Techniques of integration
Sequences, series, and power series.
Evaluation: 1 Midterm Exam, 1 Final Exam (50 points minimum)

Grade = midterm mark (times 0.5) + final mark (times 0.5 )

Attendance is required: Students whose unattendence exceed 30% of theoretical hours or 20% of practical hours (recitations) will fail the course with F1 mark.

Presentations (based on the following textbooks) delivered at classes are uploaded weekly.

Recommended Textbooks:
ˆ Calculus: A Complete Course, 9th Edition by R. A. Adams and C. H. Essex, Pearson Education.
ˆ Thomas’ Calculus, 14th Edition by G. B. Thomas, M. D. Weir and J. H. Hass, Pearson Education.
Ders Materyalleri
Ders Notları 26
The Max-Min Theorem, The Intermediate Value Theorem, Formal definition of limit
Dosya (PDF)
The concept of limit
Dosya (PDF)
Limits involving infinity, Continuity
Dosya (PDF)
Preliminaries
Dosya (PDF)
Fuctions, Graphs, Polynomials and Rational Functions, Roots and Factorization
Dosya (PDF)
Trigonometric functions, inverse functions, exponential and logarithmic functions
Dosya (PDF)
Inverse trigonometric functions and hyperbolic functions
Dosya (PDF)
Derivatives, Derivative as a function, one-sided derivatives, Differentiation rules
Dosya (PDF)
The Chain Rule, Derivatives of trigonometric functions, using differentials
Dosya (PDF)
The Mean Value Theorem, Rolle's Theorem, Implicit Differentiation
Dosya (PDF)
Derivatives of inverse functions, Logarithmic Differentiation, Related Rates Problems
Dosya (PDF)
Finding Roots of Equations: Newton's Method, Indeterminate Forms in Limits - L'Hospital's Rule
Dosya (PDF)
Critical points, Finding absolute extreme values, Concavity
Dosya (PDF)
Sketching the graph of a function
Dosya (PDF)
Extreme value problems
Dosya (PDF)
Area Problem and Definite Integral
Dosya (PDF)
The Fundamental Theorem of Calculus
Dosya (PDF)
The substitution method, trigonometric integrals, areas of plane regions
Dosya (PDF)
Integration by Parts, Integrals of Rational Functions
Dosya (PDF)
Inverse Substitutions, Improper Integrals
Dosya (PDF)
Applications of Integration
Dosya (PDF)
Sequences
Dosya (PDF)
Sequences (cont.), Infinite series
Dosya (PDF)
Infinite Series (cont.), Convergence Tests
Dosya (PDF)
Power Series
Dosya (PDF)
Taylor and Maclaurin series
Dosya (PDF)
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