Arş. Gör. Dr. Dilara ERDEMİR

1

Functions of Several Variables: Functions of Two and Three Variables: Domain and Range, Graphs, Level Curves and Level Surfaces, Limits and Continuity in Functions of Two Variables (Two-Way Test for the Absence of Limit, Continuity of Composite Functions),

2

A Brief Look at Quadratic Surfaces (plane, sphere, ellipsoid, elliptic paraboloid, cylinder, cone), Functions of More Than Two Variables. Partial Derivatives: Partial Derivatives of Functions of Two and Three Variables, Partial Derivatives and Continuity, Equality of Second Order Partial Derivatives and Mixed Derivatives, Higher Order Partial Derivatives, Differentiability,

3

Chain Rule for Functions of Two and Three Variables [For Functions with One and Two Independent Variables], Implicit Derivative , Directional Derivatives and Gradient Vector: Definition and Calculation of Directional Derivative in the Plane, Gradient Vector, Tangents to Level Curves and Gradients, Directional Derivative in Space,.

4

Tangent Planes and Differentials: Tangent Plane and Normal Line to a Surface. Linearization a Function of Two Variables, Differentials, Extreme Values: Local Extreme Values, Necessary Conditions for Local Extreme Values, Critical and Saddle Points, Second Derivative Test for Local Extreme Values.

5

Multiple Integrals: Double Integrals over Rectangles, Double Integrals by Volume, Evaluation of Double Integrals: Fubini's Theorem (First Form), Double Integrals over General Regions,

6

Double Integrals over Non-rectangular Bounded Regions, Volumes (volume between two surfaces), Fubini's Theorem (More Comprehensive Figure) Finding the Limits of Integration, Using Orthogonal Sections, Using Horizontal Sections, Properties of Double Integrals, Calculating Area in Double Integrals,.

7

Mean Value Theorem. Double Integrals in Polar Form: Finding the limits of integration, Converting Cartesian Integrals to Polar Integrals, Area and volume calculations using polar coordinates (volume between two surfaces),

8

Midterm 1

9

Change of Variables in Double Integrals. Vector Valued Functions in Space: Definition, Limit and Continuity of Vector Valued Functions, Derivatives (Velocity and Acceleration Vectors), Arc Length Along a Space Curve, Vector Fields.

10

Line Integrals: Line Integral of Vector Fields, Line Integral with Respect to Coordinates. Infinite Sequences: Convergence and Divergence of Sequences (definitions), Calculation of Limits of Sequences, Squeeze Theorem for Sequences, Continuous Function Theorem on Sequences,

11

Frequently Encountered Limits, Successively Defined Sequences, Bounded Monotone Sequences, Monotone Sequence Theorem. Infinite Series: Geometric Series, n. Term Test for Divergent Series, Combining Series, Adding or Deleting Term, Convergence Tests for Series with Positive Terms: Integral Test, p Series,

12

Quiz; Harmonic Series, Comparison Test, Limit Comparison Test. Ratio and Root Tests. Alternating Series, Alternating Series Test,.

13

Absolute and Conditional Convergence. Power Series: Radius of Convergence of a Power Series, Derivative and Integral of Power Series, Taylor and Maclaurin Series: Maclaurin and Taylor Polynomials, Maclaurin and Taylor Series,

14

Applications of Taylor Series: Approximation, Limit, Non-Elementary Integrals.

15

General Applications

16

Final