MAT123 | Mathematics I

Fall ARCHIVE
Course List
Course Description and Content
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.
Course Materials
Lecture Notes 26
The Max-Min Theorem, The Intermediate Value Theorem, Formal definition of limit
File (PDF)
The concept of limit
File (PDF)
Limits involving infinity, Continuity
File (PDF)
Preliminaries
File (PDF)
Fuctions, Graphs, Polynomials and Rational Functions, Roots and Factorization
File (PDF)
Trigonometric functions, inverse functions, exponential and logarithmic functions
File (PDF)
Inverse trigonometric functions and hyperbolic functions
File (PDF)
Derivatives, Derivative as a function, one-sided derivatives, Differentiation rules
File (PDF)
The Chain Rule, Derivatives of trigonometric functions, using differentials
File (PDF)
The Mean Value Theorem, Rolle's Theorem, Implicit Differentiation
File (PDF)
Derivatives of inverse functions, Logarithmic Differentiation, Related Rates Problems
File (PDF)
Finding Roots of Equations: Newton's Method, Indeterminate Forms in Limits - L'Hospital's Rule
File (PDF)
Critical points, Finding absolute extreme values, Concavity
File (PDF)
Sketching the graph of a function
File (PDF)
Extreme value problems
File (PDF)
Area Problem and Definite Integral
File (PDF)
The Fundamental Theorem of Calculus
File (PDF)
The substitution method, trigonometric integrals, areas of plane regions
File (PDF)
Integration by Parts, Integrals of Rational Functions
File (PDF)
Inverse Substitutions, Improper Integrals
File (PDF)
Applications of Integration
File (PDF)
Sequences
File (PDF)
Sequences (cont.), Infinite series
File (PDF)
Infinite Series (cont.), Convergence Tests
File (PDF)
Power Series
File (PDF)
Taylor and Maclaurin series
File (PDF)
Discussion Topics
No topics yet. Be the first to start a discussion!
Değerlendirme Kağıdı