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# MAT805 - Genel Matematik I

Instructor: Dr. Öğretim Üyesiİsmail Özgür Özer
Teaching Assistants:
 Araş.Gör. Salih Çağrı Özer Araş.Gör. İlhan Kahraman
Course Book: Robert A. Adams and Christopher Essex, Seventh Edition
Grading:
Other Resources:
Course Outline:
 1. Week P1: Real numbers and the real line: inequalities, intervals, quadratic inequalities, the absolute value. P2: Cartesian coordinates in the plane: increments and distances, straight lines, equations of straight lines (point-slope, two-point, two-intercept and general). P3: Graphs of quadratic equations: circles and disks, equations of parabolas, shifting a graph, ellipses and hyperbolas. P4: Functions and their graphs: domain, graphs, even and odd functions. 2. Week P5: Combining functions to make new functions: sums, differences…, composite functions, piecewise defined functions. P6: Polynomials and Rational Functions. P7: The Trigonometric Functions. 3. Week Chapter 1 1.1 Examples of Velocity, Growth Rate, and Area: examples 1,2,3; the area of a circle. 1.2 Limits of Functions 1.3 Limits at Infinity and Infinite Limits 1.5: The Formal Definition of Limit 4. Week Chapter 1 1.4: Continuity: continuity at a point, continuity on an interval, there are lots of continuous functions, continuous extensions and removable discontinuities, continuous functions on closed finite intervals. Chapter 2 2.1: Tangent Lines and Their Slopes 2.2: The Derivative 2.3: Differentiation Rules 5. Week Chapter 2 2.4: The Chain Rule 2.5: Derivative of Trigonometric Functions 6. Week Midterm 1 7. Week Chapter 2 2.6: Higher Order Derivatives 2.8: The Mean Value Theorem: Increasing and decreasing functions 2.9: Implicit Differentiation 2.10: Antiderivatives and Initial Value Problems: Antiderivatives, The definite integral 2.11: Velocity and Acceleration (briefly) 8. Week Chapter 3 3.1: Inverse Functions 3.2: Exponential and Logarithmic Functions 3.3: The Natural Logarithm and Exponential 3.5: The Inverse Trigonometric Functions (Genel ters fonksiyonların tanımına dayanılarak anlatılacak, örneğin Definition 13 ve Definition 14 tanım olarak değil, özellik olarak anlatılacak). 3.6: Hyperbolic Functions 9. Week Chapter 4 4.3: Indeterminate Forms 4.4: Extreme Values 4.5: Concavity and Inflections (convex and concave functions) 4.6: Sketching the Graph of a Function 10. Week 4.8: Extreme Value Problems 11. Week Midterm 2 12. Week Chapter 5 5.1 Sums and Sigma Notation 5.2 Areas as Limits of Sums 5.3 The Definite Integral 5.4 Properties of the Definite Integral 13. Week Chapter 5 5.5 The Fundamental Theorem of Calculus 5.6 The Method of Substitution
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