LECTURE NOTES IN LINEAR ALGEBRA AND DIFFERENTIAL CALCULUS
CONTENTS
LECTURE 1. MATRICES AND DETERMINANTS
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LECTURE 2. INVERSE MATRICES. SYSTEMS OF LINEAR ALGEBRAIC EQUATIONS. METHODS FOR SOLVING OF LINEAR SYSTEMS
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LECTURE 3. VECTORS. VECTOR (CROSS) PRODUCT OF TWO VECTORS. MIXED PRODUCT OF THREE VECTORS
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LECTURE 4. GENERAL EQUATION OF A PLANE. POINT-DIRECTION(CANONICAL) AND PARAMETRIC EQUATIONS OF A STRAIGHT LINE IN SPACE. GENERAL EQUATION OF A STRAIGHT LINE
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LECTURE 5. SECOND ORDER CURVES. ELLIPSE, HYPERBOLA. PARABOLA. POLAR COORDINATE SYSTEM
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LECTURE 6. NUMBER SETS. SEQUENCES OF NUMBERS. THE LIMIT OF A NUMBER SEQUENCE. MONOTONE SEQUENCES
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LECTURE 7. THE CONCEPT OF A FUNCTION. INVERSE FUNCTIONS. COMPOSITE FUNCTIONS. HYPERBOLIC FUNCTIONS. PARAMETRICALLY GIVEN FUNCTIONS
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LECTURE 8. THE LIMIT OF A FUNCTION AT A POINT. LIMIT THEOREMS. ONE-SIDED LIMITS. THE LIMIT AT INFINITY. INFINITELY SMALL AND INFINITELY LARGE FUNCTIONS
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LECTURE 9. COMPARISON OF INFINITESIMALS. EQUIVALENT INFINITESIMALS. ASYMPTOTIC RELATIONS
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LECTURE 10. CONTINUITY OF A FUNCTION AT A POINT. CONTINUITY ON A CLOSED INTERVAL. DISCONTINUOUS FUNCTIONS
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LECTURE 11. DIFFERENTIABILITY OF A FUNCTION. THE DIFFERENTIAL. DIFFERENTIATION OF INVERSE AND PARAMETRICALLY GIVEN FUNCTIONS
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LECTURE 12. DERIVATIVES AND DIFFERENTIALS OF HIGHER ORDERS. MEAN VALUE THEOREMS. L’ HOPITALS RULE
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LECTURE 13. TAYLOR’S FORMULA. MACLAURIN’S FORMULAS FOR SOME ELEMENTARY FUNCTIONS
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LECTURE 14. INVESTIGATING FUNCTIONS BY MEANS OF DERIVATIVE
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LECTURE 15. THE CONCEPT OF A FUNCTION OF SEVERAL VARIABLES. SURFACES OF THE SECOND ORDER
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LECTURE 16. LIMITS AND CONTINUITY OF A FUNCTION OF SEVERAL VARIABLES. PARTIAL DERIVATIVES AND DIFFERENTIALS
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LECTURE 17. DERIVATIVES OF COMPOSITE FUNCTIONS. IMPLICIT FUNCTIONS AND THEIR DERIVATIVES. HIGHER ORDER PARTIAL DERIVATIVES AND DIFFERENTIALS
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LECTURE 18. VECTOR FUNCTION OF A SCALAR ARGUMENT. TANGENT LINE AND NORMAL PLANE TO A SPATIAL CURVE
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LECTURE 19. TANGENT PLANES AND NORMAL LINES TO A SURFACE. SCALAR FIELDS. DIRECTIONAL DERIVATIVE. THE GRADIENT
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LECTURE 20. EXTREMUM OF A FUNCTION OF SEVERAL VARIABLES
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LECTURE 21. CONDITIONAL EXTREMUM. THE METHOD OF LAGRANGE’S MULTIPLIERS. THE LEAST SQUARES METHOD
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