The classes follow the material provided by the teacher accordingly with the syllabus. The register is tentative and will be brought up to date almost daily.
- April, Thursday 12
- April, Thursday 19
- April, Thursday 26
- May, Thursday 10
- May, Thursday 17
- May, Thursday 24
- May, Thursday 31
- June, Thursday 7
- June, Thursday 14
- June, Thursday 21
- June, Thursday 28
- July, Thursday 5
- July, Thursday 12
- July, Thursday 19
- July, Thursday 26
- August, Thursday 2
1: Definition of a Sequence; 2: Limit of a Sequence; 3: Theorems on Limits of Sequences; 4: Infinity.
Material see: Sequences page 1, Sequences page 2 and Sequences page 3
Optional: 5. Bounded, Monotonic Sequences.
1: Functions; 2: Graph of a Function; Material see: Functions and solved exercises.
3: Bounded Functions; 4: Monotonic Functions;
7: Types of functions; 8: Trascendental Functions.
Material see: Functions.
9: Limits of Functions; 10: Theorems on Limits; 11: Infinity; 12: Special Limits;
13: Continuity; 14: Continuity in an Interval.
Material see: Limits and Continuity and in class exercises.
15. Theorems on Continuity.
Material see: Limits and Continuity and solved exercises.
1: The concept and Definition of a Derivative; 2. The Differentiation of Composite Functions;
3: Rules of Differentiation.
Material see: Derivatives , Extrema, in class exercises I and in class exercises II.
4: Derivatives of Elementary Functions; 5. Higher Order Derivatives; 6. Mean Value Theorems;
7. L'Hospital's Rules; 8: Relative Extrema and Points of Inflection.
Material see: Derivatives , Extrema, in class exercises I and in class exercises II.
1. Expansion of Functions in Power Series; 2: Taylor's Theorem; 3. Some Important Power Series.
Material see: Taylor.
1. Functions of Two or More Variables; 2. Neighborhoods; 3. Regions; 4. Limits.
8. Partial Derivatives; 9. Higher-Order Partial Derivatives;
Material see: Partial Derivatives.
12. Differentiation of Composite Functions: Chain rules; 15. Jacobian; 19. Curvilinear Coordinates.
1. Vector Functions 2. Derivatives of Vector Functions (that is directional derivatives)
3. Gradient, Divergence and Curl.
Material see page 170-171 of Directional Derivatives .
Additional material on Chain rule proof.
Additional material on Vectors .
1. Application to Geometry: Tangent plane and Normal line to a Curve and a Surface;
2. Hesse Matrix: Maxima, Minima and Saddle Points
Material see page 195-200 of Application of Partial Derivatives
Additional material on plane in space and lines and planes in space.
3. Method of Lagrange Multipliers for Maxima and Minima
Material see page 195-200 of Application of Partial Derivatives and Exercise 8.26 .
Correction of the Final Test Sample. Final test Sample Solution.