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Advanced Engineering Mathematics. Start Course Visit Official Site. Course Description This is a comprehensive mathematics course for engineering students, covering topics including linear algebra, complex variables, laplace and fourier transforms to solve ordinary and partial differential equations, and probability and statistics. The Fourier Transform is one of the many mathematical tools applied to engineering which will be studied in this course.

Advanced Engineering Mathematics with Modeling Applications

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Subject: Mathematics. All rights reserved. Applied Mathematics. Review of Groups, Fields and Matrices Play Video. Basis, Dimension, Rank and Matrix Inverse Linear Transformation, Isomorphism and Matrix Representation System of Linear Equations, Eigenvalues and Eigenvectors Orthogonality, Gram-Schmidt Orthogonalization Process Concept of Domain, Limit, Continuity and Differentiability Analytic Functions, CR Equations Harmonic Functions Line Integral in the Complex Plane Cauchy Integral Theorem Cauchy Integral Theorem Contd.

Cauchy Integral Formula Power and Taylor's Series of Complex Numbers Taylor's, Laurent Series of f z and Singularities Classification of Singularities, Residue and Residue Theorem Laplace Transform and its Existence Properties of Laplace Transform Evaluation of Laplace and Inverse Laplace Transform Fourier Series The Dirichlet Problem for Unbounded Regions. A Dirichlet Problem in 3 Dimensions. The Neumann Problem. Special Functions and Applications. Legendre Polynomials.

Bibliographic Information

Bessel Functions. Some Applications of Bessel Functions. Transform Methods of Solution. Laplace Transform Methods. Fourier Transform Methods. Fourier Sine and Cosine Transforms. Vectors and the Vector Space Rn. Vectors in the Plane and 3 — Space.

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The Dot Product. The Cross Product. Orthogonal Sets and Orthogonalization.

ECE / Advanced Engineering Mathematics - Acalog ACMS™

Orthogonal Complements and Projections. Matrices, Determinants and Linear Systems. Matrices and Matrix Algebra. Row Operations and Reduced Matrices. Solution of Homogeneous Linear Systems.

Advance Engineering Mathematics

Solution of Nonhomogeneous Linear Systems. Matrix Inverses. The Matrix Tree Theorem. Eigenvalues, Diagonalization and Special Matrices. Eigenvalues and Eigenvectors. Special Matrices and Their Eigenvalues and Eigenvectors. Quadratic Forms. Linear Systems. Exponential Matrix Solutions. Nonlinear Systems and Qualitative Analysis. Nonlinear Systems and Phase Portraits. Critical Points and Stability.

Almost Linear Systems, Linearization. Vector Differential Calculus.

HK Dass Advanced Engineering Mathematics

Vector Functions of One Variable. Velocity, Acceleration, and Curvature. The Gradient Field. Divergence and Curl. Streamlines of a Vector Field. Vector Integral Calculus. Line Integrals. Independence of Path and Potential Theory.

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Surface Integrals. Applications of Surface Integrals. Fourier Series. Fourier Series On [-L, L]. Fourier Sine and Cosine Series. Integration and Differentiation of Fourier Series. Properties of Fourier Coefficients. Phase Angle Form. Complex Fourier Series, Filtering of Signals.

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Fourier Transforms. The Fourier Transform. Complex Numbers and Functions. Geometry and Arithmetic of Complex Numbers. Complex Functions, Limits. The Exponential and Trigonometric Functions. The Complex Logarithm. The Integral of a Complex Function. Series Representations of Functions. Power Series. The Laurent Expansion. Singularities and the Residue Theorem. Classification of Singularities. The Residue Theorem. Evaluation of Real Integrals. Conformal Mappings. The Idea of a Conformal Mapping.

Construction of Conformal Mappings. Skip to main content. Search form Search.