Mathematics II D

1. Demonstrate basic knowledge of calculus and linear algebra
2. Outline basic definitions and describe basic methods of calculus and linear algebra
3. Explain, connect and interpret basic concepts of calculus and linear algebra
4. Make conclusions by using logical reasoning (analogy, contradiction, implication)
5. Demonstrate mathematical reasoning and problem solvers skills
6. Demostrate an ability to communicate mathematics by team work, discussion and written material

Lectures which contain a large number of examples and problems

More examples for students which need more practice.

From workbook

1. Lectures: Sequences. Arithmetic and geometric series. Limit. Geometric series. Exercises: Sequences. Arithmetic and geometric series. Limit. Geometric series.
2. Lectures: Matrices and determinants. Laplace's Sarrus's rules. Cramer's rule for the inverse of a matrix. Exercises: Matrices and determinants. Laplace's Sarrus's rules. Cramer's rule for the inverse of a matrix.
3. Lectures: Basic skills for solving systems of linear equations. Exercises: Basic skills for solving systems of linear equations.
4. Lectures: Vectors: addition of vectors, scalar multiplication of vector Exercises: Vectors: addition of vectors, scalar multiplication of vector
5. Lectures: Vectors: scalar, vector and mixed vector product. Exercises: Vectors: scalar, vector and mixed vector product.
6. Lectures: Basic notion of function: domain, bijection, (odd)even functions, periodicity. Exercises: Basic notion of function: domain, bijection, (odd)even functions, periodicity.
7. Lectures: Functions: inverse functions, limit functions, continuity of functions. Exercises: Functions: inverse functions, limit functions, continuity of functions.
8. Lectures: Derivatives: definition, properties, table of elementary derivations. Exercises: Derivatives: definition, properties, table of elementary derivations.
9. Lectures: Derivatives: chain rule and derivative of an inverse. Exercises: Derivatives: chain rule and derivative of an inverse.
10. Lectures: Tangent and normal line of the graph of the function. Exercises: Tangent and normal line of the graph of the function.
11. Lectures: Increasing and decreasing functions, extrema, sketching the graph of a function. Exercises: Increasing and decreasing functions, extrema, sketching the graph of a function.
12. Lectures: Integrals. Area under curve and the definite integral. Antiderivative. Indefinite integral. Exercises: Integrals. Area under curve and the definite integral. Antiderivative. Indefinite integral.
13. Lectures: Definit integral. Basic elements of numerical integration. Exercises: Definit integral. Basic elements of numerical integration.
14. Lectures: Basic skills for solving the first-order differential equations. Exercises: Basic skills for solving the first-order differential equations.
15. Lectures: Basic skills for solving the second-order differential equations. Exercises: Basic skills for solving the second-order differential equations.