TITLE OF THE COURSE
At the end of the course the students will be able to:
Matrices, Differential calculus, Integral calculus, Theory of equations
- Relate an augmented matrix to a system of linear equations.
- Apply the Cayley-Hamilton Theorem to compute powers of a given square matrix.
- Compute limits, derivatives, and definite & indefinite integrals of algebraic, logarithmic and exponential functions.
- Compute definite and indefinite integrals of algebraic and trigonometric functions using formulas and substitution.
- Applied to solve higher degree polynomials.
Groups, Differential Calculus, Integral Calculus, Differential equations-I
- Construct and describe groups. They will learn basic properties of groups and get familiar with important classes of groups. They will understand the crucial concept of simple groups.
- Use technological tools such as computer algebra systems or graphing calculators for visualization and calculation of multivariable calculus concepts.
- Develop the ability to apply differential equations to significant applied and/or theoretical problems
Groups, Sequences and Series of Real Numbers, Differential Calculus
- Understand the proof, statement and simple uses of Lagrange’s Theorem.
- Recognize the embedded infinite geometric series in geometric applications.
- Understand the consequences of the intermediate value theorem for continuous functions.
Groups, Fourier series, Mathematical Methods-I, Differential Equations-II
- Demonstrate familiarity with permutation groups and be able to decompose permutations into 2-cycles. Familiar with Fourier series and their applications and be notionally aware of their convergence.
- Laplace transforms is used to simplify calculations in system modeling.
- Demonstrate an understanding of solution techniques for second and higher order differential equations; be familiar with qualitative tools for linear equations applications.
Rings, Integral domains, Fields, Vector Differential calculus,
- Demonstrate familiarity with some of the applications of algebra to other fields, e.g. cryptography.
- Apply derivative concepts to find tangent lines to level curves and to solve optimization problems.
- Analyze the error incumbent in any such numerical approximation.
Calculus of variation, Line and multiple integral, Integral theorems
- Compute the curl and the divergence of vector field.
- Apply triple integrals to find volumes and center of mass.
- Compute the area of parametric surfaces in 3-dimensional space.
Linear algebra, PDE
- Compute inner products and determine orthogonality on vector spaces, including Gram-Schmidt orthogonalization.
- Be familiar with the modeling assumptions and derivations that lead to PDEs.
Complex analysis, Numerical methods-II
- Applications in many scientific areas, including signal processing, control theory, electro magnetism etc.
- Implement a variety of numerical algorithms using appropriate technology.