MAT1072 Mathematics 2 (04.03.2025)
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4.03.2025
MAT1072 Mathematics 2 (03.03.2025)
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MAT1072 Mathematics 2 (25.02.2025)
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MAT1072 Mathematics 2 (24.02.2025)
Ders Notu
24.02.2025
MAT1072 Mathematics 2 / Weekly Subjects
Duyuru
19.02.2025
| Week | Subjects | Related Preparation |
|---|---|---|
| 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), | Textbook 1 (Chapter 14) |
| 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, | Textbook 1 (Chapter 14) |
| 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,. | Textbook 1 (Chapter 14) |
| 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. | Textbook 1 (Chapter 14) |
| 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, | Textbook 1 (Chapter 15) |
| 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,. | Textbook 1 (Chapter 15) |
| 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), | Textbook 1 (Chapter 15) |
| 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. | Textbook 1 (Chapter 15,13) |
| 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, | Textbook 1 (Chapter 16,10) |
| 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, | Textbook 1 (Chapter 10) |
| 12 | Quiz; Harmonic Series, Comparison Test, Limit Comparison Test. Ratio and Root Tests. Alternating Series, Alternating Series Test,. | Textbook 1 (Chapter 10) |
| 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, | Textbook 1 (Chapter 10) |
| 14 | Applications of Taylor Series: Approximation, Limit, Non-Elementary Integrals. | Textbook 1 (Chapter 10) |
| 15 | General Applications | Textbook 1 |
| 16 | Final |
MAT1072 Mathematics 2 (17.02.2025)
Ders Notu
17.02.2025