Cramer’s rule. Using the inverse of a coefficient matrix to solve a linear systems and some applications about this.
| Vectors: Definition of Vectors,The sum of vectors and Subtraction of vectors and Multiplication of vectors, Dot product of two vectors and their properties, Vector product of two vectors(Cross product of vectors ) and their properties, Mixed product of three vectors(Triple product) and their properties, Double vector product(double cross) and their properties and some applications about this. |
Line Integrals: Line Integral of Vector Fields, Line Integral with Respect to Coordinates.
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). Change of Variables in Double Integrals. Vector Valued Functions in Space: Definition, Limit and Continuity of Vector Valued Functions, Derivatives (Velocity and Acceleration Vectors)
Dear friends, Please try to solve the related questions I have sent you in the attachment. Do not hesitate to send me an e-mail if you are stuck or do not understand.
System of linear equations: solving systems of linear equations with aid of equaivalent matrices, linear homogeneous equations and some applications about this.
from the previous week- Lagrange Multipliers
Multiple Integrals: Double Integrals over Rectangles, Double Integrals by Volume, Evaluation of Double Integrals: Fubini's Theorem (First Form), Double Integrals over General Regions, 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.
Definition of a determinant. Laplace expansion of a matrix. Properties of a determinant. The adjoint of a matrix, Using the adjoint matrix to find an inverse matrix and some applications about this.
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.
Elementary row and column operations in the Matrices. Row-Echelon form and reduced row-echelon form. Rank of a matrix. Inverses of matrices and some applications about this.
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.
Some Special Matrices and matrix applications.(Symmetric Matrix,Anti symmetric matrix, periodic matrix, idempotent matrix, Nilpotent matrix, orthogonal matrix, A conjugate of a matrix and its properties, hermitian matrix,Anti hermitian matrix, regular matrix, singuler matrix, and their applications.
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, with "Chain Rule for Functions of Two and Three Variables [For Functions with One and Two Independent Variables], Implicit Derivative"
Definition of matrix, types of matrix, Equality of Matrices, Addition and subtraction of matrices, matrix multiplication by a scalar, Some properties about them. Multiplying matrices and Some properties about it. Transposes of matrices and properties of the transpose.
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),