Course Description
Linear Algebra: matrices, row reduction, determinants, Cramer'srule, vectors, matrix operations, linearcombination, linearfunctions, linearoperators, linear dependence and independence.
Calculus of Variation: the Euler equation and its uses,the Brachistochrone problem. Lagrange's equations.
Tensor Analysis: cartesian tensors, tensors definition and operations, Kronecker delta and Levi-Civita symbol, pseudo vectors and pseudo tensors, curvilinear coordinates, vector operations in orthogonal curvilinear coordinates.
Complex Analysis: complex numbers, Cartesian and polar representation of complex numbers, powers and roots of complex numbers, the exponential and trigonometric functions, hyperbolic functions, logarithms, complex infinite series, complex power series, Euler's formula. Analytic functions, Cauchy-Riemann equations, harmonic functions, complex integration, contour integrals, series representation of analytic functions, Taylor and Laurent series, zeros and singularities, residue theory, applications to real and improper integrals, conformal mappings.
Course Objectives & Outcomes
Objectives
- Equip the student with necessary knowledge of matrices, determinants, vectors, tensors and to the complex number system.
- Enable the student to solve linear equations using determinants.
- Enable the student to calculate algebraic operations onvectors and tensors.
- Develop student's skills in applying curvilinear coordinates and non-curved coordinates for tensors.
- Equip the student with necessary knowledge and skills to enable them handle mathematical operations and problems involving complex numbers, determinants, vectors, and tensors.
Upon successful completion of this course, the student will be able to:
- Solve linear equations.
- State various operations on matrices, vectors and tensors.
- Apply Cramer's method to solve linear equations.
- Conduct various operations on vectors and tensors in different coordinates.
- Solve problems of differentiation, and integration of functions of complex variables.
- Present analytic functions using Taylor and Laurent series.
- Use of the Residue theorem in solving improper integrals.
- Use of the conformal mappings in solving problems.
References
- Boas,M. L., (2006), Mathematical methods in the physical sciences, Third Edition, John Wiley and Sons.,ISBN: 0-471-19826-9.
Course ID: MATH 307
Credit hours | Theory | Practical | Laboratory | Lecture | Studio | Contact hours | Pre-requisite | 3 | 2 | 2 | 4 | Calculus II |
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