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Complex Numbers III. Linear Algebra 1. Vectors, Vector Space 2. Dependence, Dimension, Basis 3. Subspace 4. The Scalar Product 5. Linear Transformation, Matrix 6. Multiplication of Linear Transformations 7. Multiplication of Matrices 8. Row Matrices, Column Matrices 9. Rank of a Matrix Determinants Solution of a Non-homogeneous System of Equations Solution of a Homogeneous System of Equations Latent Roots Analytical Geometry 1.

Research Area: Algebra, Combinatorics, Number Theory – Department of Mathematics | CSU

Coordinates 2. The Geometry of the Plane and of the Straight Line 3. Homogeneous Coordinates 4. Circle and Sphere 5. Conic Sections 6.

Handbook of Number Theory I

Curves of the Second Degree 7. Polar Theory for Conic Sections 8. Surfaces of the Second Degree 9. Investigation of Surfaces of the Second Degree Polar Theory of Quadratic Surfaces V. Analysis Differential and Integral Calculus 1. The Concept of Function - Interval - Neighborhood 2. The Concept of Limit 3. Algebra of Limits 4. The Concept of Continuity 5. Derivative 7. Algebra of Derivatives 9. The Derivatives of the Trigonometric Functions Limit Properties of Composite Functions Generalized Mean Value Theorem Extreme Values Points of Inflection Primitive Functions Change of Variables - Differentials - Integration by Parts The Concept of Area Fundamental Theorem of Integral Calculus Properties of Definite Integrals Method of Integration by Parts and Method of Substitution Mean Value Theorem Logarithmic Function Inverse Function The Exponential Function Some Logarithmic and Exponential Limits The General Logarithm The Cyclometric Functions Leibniz's Formula The Hyperbolic Functions The Primitives of Cosn x and Sinn x n is an Integer The Primitives of Irrational Algebraic Functions The Concept of Function The Concept of Limit Continuity Partial Differentiation Partial Derivatives of the Second Order Composite Functions-Total Differential Change of the Independent Variables Functions of More Than Two Variables Extreme Values of Functions of Two Variables The Concept of Content—Double Integral Properties of Integrals