Dr. Öğr. Üyesi Büşra MENİZ

Week

Subjects

1

Functions: Domain and Range of a Function, Functions and Graphics, Some Elementary Functions (Polynomials, Rational Functions, Algebraic Functions), Some Concepts Related to Functions (Even-Odd Functions, Bounded Function, Increasing-Decreasing Functions, Implicit Function), 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, Hyperbolic-Inverse Hyperbolic Functions. Limits: Limit of a Function, One-sided Limits, Theorems on Limits (Limit Rules), Squeezing (Pinching) Theorem,

3

Infinite Symbols and Limit. 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 Transcendent 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 Graphics, Some Elementary Functions (Polynomials, Rational Functions, Algebraic Functions), Some Concepts Related to Functions (Even-Odd Functions, Bounded Function, Increasing-Decreasing Functions, Implicit Function), 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, Hyperbolic-Inverse Hyperbolic Functions. Limits: Limit of a Function, One-sided Limits, Theorems on Limits (Limit Rules), Squeezing (Pinching) Theorem,

3

Infinite Symbols and Limit. 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 Transcendent 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

9

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

Week

Subjects

1

Functions: Domain and Range of a Function, Functions and Graphics, Some Elementary Functions (Polynomials, Rational Functions, Algebraic Functions), Some Concepts Related to Functions (Even-Odd Functions, Bounded Function, Increasing-Decreasing Functions, Implicit Function), 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, Hyperbolic-Inverse Hyperbolic Functions. Limits: Limit of a Function, One-sided Limits, Theorems on Limits (Limit Rules), Squeezing (Pinching) Theorem,

3

Infinite Symbols and Limit. 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 Transcendent 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. Vectors: Vectors, Dot Product, Angle Between Two Vectors, Perpendicular Vectors, Vector Product, Parallel Vectors,

14

Lines in Space (Vectorial and parametric equations, Angle between lines), Planes (Vectorial and general equation in space), Angle Between Line and Plane.

15

General Question Solutions

16

Final