Dr. Öğr. Üyesi Büşra MENİZ

Week

Subjects

1

Functions: Domain and Range of a Function, Functions and Graphs, Some Elementary Functions (Polynomials, Rational Functions, Algebraic Functions), Some Concepts Related to Functions (Even-Odd Functions, Bounded Functions, Increasing-Decreasing Functions, Implicit Functions), Combinations of Functions (Sum, Difference, Product and Quotient), Composition of Functions, Piecewise Functions. Transcendental Functions: Trigonometric Functions

2

Inverse of a Function, Inverse Trigonometric Functions, Exponential and Logarithmic Functions. Limits: Limit of a Function, One-sided Limits, Theorems on Limits (Limit Rules), Squeezing (Pinching) Theorem

3

Infinite Symbols and Limits. Continuity: Continuity at a Point, Continuity over a Set, Types of Discontinuity, Intermediate Value and Extreme Value Theorems. Derivative: Derivative at a Point, Derivative as a Function, One-sided Derivatives, Derivative over an Interval,

4

Differentiability and Continuity, Differentiation Rules, Higher Order Derivatives, Chain Rule, Implicit Differentiation, Derivatives of Transcendental Functions, Tangent and Normal Lines, Linearization and Differentials.

5

Applications of the Derivative: Rolle and Mean Value Theorems, Increasing-Decreasing Functions, Extremum Values of Functions: First and Second Derivative Tests, Indeterminate Forms, Concavity and Points of Inflection, Asymptotes, Simple Curve Drawings.

Week

Subjects

1

Functions: Domain and Range of a Function, Functions and Graphs, Some Elementary Functions (Polynomials, Rational Functions, Algebraic Functions), Some Concepts Related to Functions (Even-Odd Functions, Bounded Functions, Increasing-Decreasing Functions, Implicit Functions), Combinations of Functions (Sum, Difference, Product and Quotient), Composition of Functions, Piecewise Functions. Transcendental Functions: Trigonometric Functions

2

Inverse of a Function, Inverse Trigonometric Functions, Exponential and Logarithmic Functions. Limits: Limit of a Function, One-sided Limits, Theorems on Limits (Limit Rules), Squeezing (Pinching) Theorem

3

Infinite Symbols and Limits. Continuity: Continuity at a Point, Continuity over a Set, Types of Discontinuity, Intermediate Value and Extreme Value Theorems. Derivative: Derivative at a Point, Derivative as a Function, One-sided Derivatives, Derivative over an Interval,

4

Differentiability and Continuity, Differentiation Rules, Higher Order Derivatives, Chain Rule, Implicit Differentiation, Derivatives of Transcendental Functions, Tangent and Normal Lines, Linearization and Differentials.

5

Applications of the Derivative: Rolle and Mean Value Theorems, Increasing-Decreasing Functions, Extremum Values of Functions: First and Second Derivative Tests, Indeterminate Forms, Concavity and Points of Inflection, Asymptotes, Simple Curve Drawings.

6

Definite Integral: Antiderivatives, Sigma Notation and Limits of Finite Sums, Riemann Sums, Definite Integral, Properties of the Definite Integral, Area of a Region Bounded by a Curve, Mean Value Theorem for Definite Integrals

7

Fundamental Theorem of Calculus (Part 1, Part 2), Indefinite Integral: Integration Tables, Change of Variables in Indefinite-Finite Integrals [Calculus of some trigonometric integrals]. Integration Techniques: Integration by Parts

8

Midterm 1

9

Trigonometric Substitution, Integrals of Rational Functions (Partial Fractions). Applications of the definite integral: Areas of Plane Regions (Two or more curves).

10

Volumes of Solids of Revolution: Disk and Washer Techniques, Cylindrical Shell Technique, Arc Length, Areas of Revolution Surfaces.

11

Improper Integrals: Integrals of Type I and Type II.

12

Quiz, Parametric and Polar Curves: Polar Coordinates, Relationship between Polar and Cartesian Coordinates, Introduction of Polar Curves (Line, circle, and cardioid curves in polar coordinates), Area in Polar Coordinates, Length of a Polar Curve,

13

Planar Curves and Parametrization, Parametric Derivative, Length of a Parametric Curve.

14

Final