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MAT805 - Genel Matematik I

Instructor: Dr. Öğretim Üyesiİsmail Özgür Özer
Teaching Assistants:
Course Book: Robert A. Adams and Christopher Essex, Seventh Edition
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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