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Engineering Mathematics - Skill Up
Course Description
Engineering Mathematics builds a strong foundation in essential topics like Calculus, Differential Equations, Linear Algebra, Matrices, and Complex Analysis. Combining theory with practical applications, the course develops analytical and problem-solving skills through structured lessons, exercises, and real-world engineering examples, enabling learners to model, analyze, and solve complex engineering problems efficiently.
Course Overview
This course is designed to provide engineering students with a strong mathematical foundation, covering essential topics such as Calculus, Differential Equations, Linear Algebra, Matrices, Complex Analysis, and more. It equips learners with the analytical tools and problem-solving techniques needed to tackle mathematical challenges in engineering effectively.
Each week focuses on a specific mathematical domain, with daily topics accompanied by practice problems and application-oriented examples.
Course Highlights
- Develop a solid understanding of limits, continuity, and differentiation for solving real-world engineering problems.
- Master integration, multivariable calculus, and differential equations for modeling dynamic systems and circuits.
- Learn vectors, matrices, eigenvalues, and eigenvectors for applications in mechanics, control systems, and signal processing.
- Explore complex numbers, Laplace transforms, and Fourier series for analyzing engineering systems and vibrations.
- Access curated examples and problem sets for hands-on practice and conceptual clarity.
- Build confidence for exams, competitive tests, and engineering projects with a strong focus on applied mathematics.
Course Content
- Introduction to matrices and their applications in engineering.
- Determinants and their properties, including applications of determinants.
- Basic Matrices: Row, Column, Square, Identity, Diagonal.
- Structural Matrices: Scalar, Triangular, Symmetric, and Skew-Symmetric, Orthogonal.
- Advanced Matrices: Hermitian and Skew-Hermitian, Involutory, Idempotent, Nilpotent, and Complex Matrices.
- Inverse and rank of a matrix; rank of a matrix using elementary transformations.
- Rank-Nullity theorem and its implications.
- System of linear equations: Solving using Cramer's Rule, and solving using the inverse of matrices.
- Gauss-Jordan method and LU Decomposition for solving systems of equations.
- Characteristic equation of a matrix.
- Cayley-Hamilton theorem and its applications.
- Eigenvalues and eigenvectors.
- Diagonalization of a matrix.
- Practice with Previous Year Questions (PYQs).
- Introduction to limits.
- Rolle's Theorem.
- Lagrange's Mean Value Theorem.
- Cauchy's Mean Value Theorem.
- Successive differentiation (nth order derivatives).
- Leibniz's theorem and its application.
- Envelope of the family of one and two parameters.
- Curve tracing.
- Cartesian and Polar coordinates.
- Partial derivatives
- Total derivative
- Euler's Theorem
- Taylor Theorem
- Maclaurin' THeorem
- Maxima and Minima of functions of several variables
- Lagrange Method of Multipliers
- Jacobians
- Approximation of errors
Pricing
