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Learn MoreENGINEERING MATHEMATICS
Rating: 4.3 out of 54.3(29 ratings)
279 students
What you'll learn
- ENGINEERING MATHEMATICS
Explore related topics
Course content
4 sections • 52 lectures • 3h 13m total length
- Introduction to Sets, vectors & Matrices3:53
Explore the basics of sets, vectors, and matrices in mathematics. See how data forms like marks and tables become vectors and matrices, and distinguish vectors from scalars.
- Vectors3:29
- Algebraic operations on Vectors5:57
- Triple Product2:51
- Dependent Vectors6:27
- Orthogonal & Orthonormal Vectors6:02
Explore orthogonal vectors and orthonormal vectors, where the dot product is zero and unit vectors have length one, and a real matrix is orthogonal when its inverse equals its transpose.
- Normalizing Vector & Projection of Vectors6:50
- Matrices7:13
- Types of Matrices - 14:55
Explore real matrices and their types—symmetric, skew symmetric, and orthogonal—through transposes, the identity, and determinant conditions, with examples identifying each type.
- Types of Matrices - 24:59
Explore complex matrices and their complex conjugates, use transposed conjugates to identify hermitian and skew hermitian forms and determine unitary matrices that yield the identity.
- Solving System of Linear equations6:22
solving systems of linear equations covers a x = b, giving x = b/a for a ≠ 0, and infinite or no solutions when a = 0; includes graphical, substitution, elimination, and augmented-matrix methods.
- Row Operations and Equivalent Systems4:47
Explore how equivalent linear systems share same solutions and simplify them with elementary row operations, interchanging rows, scaling by a non-zero constant, and adding multiples of rows via augmented matrices.
- Gaussian Elimination or Row Reduction method3:58
Explore Gaussian elimination, transforming the augmented matrix to upper triangular form via forward elimination with elementary row operations, using pivots to reveal rank, determinant, and inverse.
- Echelon Form of a Matrix2:41
- Rank of a matrix by Echelon form4:58
Determine the rank of a matrix by reducing to row echelon form, identify pivots, and relate rank to the solution counts of linear systems using augmented and coefficient matrices.
- Rank of a matrix using Normal Form2:03
- Invertible Matrices - 14:54
- Theorems on Invertible Matrices6:28
Explore theorems on the inverse of matrices, linking invertibility to full rank, the identity matrix, and products of elementary matrices, with BA = I and AB = I.
- Inverse of a matrix using Gauss-Jordan method4:09
- Homogeneous and non homogeneous linear systems3:55
- Matrix Eigenvalues4:56
Explore eigenvalues and eigenvectors to diagonalize matrices, power computations, and fast vibrational analysis, with real-world applications in resonance, natural frequencies, and diverse scientific fields.
- Finding Eigenvalues and Eigenvectors
- Cayley-Hamilton Theorem2:44
The Cayley-Hamilton theorem states that every square matrix satisfies its own characteristic polynomial. It shows the matrix annihilates its own characteristic equation, enabling finding inverses and higher powers.
- Cayley-Hamilton Theorem-2
- Gram Schmidt method3:16
Apply the Gram-Schmidt method to form an orthogonal (and optionally normalized) set that spans subspace, using projections and noting Householder transformation, Given's rotation, and singular value decomposition for numerical stability.
- Gram Schmidt method - 2
- Diagonalization5:24
- Matrix Decomposition4:02
Explore matrix decomposition, the factorization of a matrix into upper and lower triangular matrices, such as the LU decomposition, and its use in solving linear systems, inverses, and determinants.
- Sequence5:16
Define sequences as ordered lists and as mappings from natural numbers to real numbers, exploring domain, range, codomain, monotone behavior, and bounded above or below.
- Convergence & Divergence3:38
- Convergence & Divergence - 2
- Series5:35
- Numerical Series3:56
Classify series as positive-term, alternating, and geometric, with convergence criteria for geometric sums and 0≤R<1. Address harmonic and B-series, noting 1/n^2 converges while harmonic diverges.
- Tests for Convergence and Divergence4:01
- Tests for Convergence and Divergence - 2
- D'Alembert's Ratio Test3:00
- D'Alembert's Ratio Test - 2
- Raabe’s Test2:39
- Raabe’s Test - 2
- Cauchy’s Integral test5:02
- Cauchy’s root test2:07
- Cauchy’s root test - 2
- Logarithmic Test3:01
Apply the logarithmic test to determine convergence of positive-term series, with outcomes for L>1, L<1, and inconclusive L=1. Compare with the ratio test via an example with factorials and powers.
- Logarithmic Test - 2
- Alternating series test3:41
- Basics6:34
- Mean value theorem4:59
Explore how the mean value theorem links change to the derivative, ensuring an instantaneous velocity equals the average velocity, and illustrate Rolle's theorem with a tangent parallel to the x-axis.
- Lagrange’s Mean Value Theorem3:19
- Cauchy’s Mean Value Theorem4:51
Explore Cauchy's mean value theorem, also called the extended or second mean value theorem, linking derivatives to changes in two functions on a closed interval.
- Generalized mean value theorems: Taylor series6:14
- Taylor’s Theorem-24:26
Explains Taylor's theorem and its conditions on intervals, then derives Maclaurin series expansions, including the log(1+x) expansion: x - x^2/2 + x^3/3 - x^4/4.
- Applications of definite integrals4:18
Explore applications of definite integrals in Cartesian coordinates to compute areas under curves, arc lengths, surface areas of revolution, and volumes generated by revolving regions about the x-axis or y-axis.
Requirements
- NO
Description
In this course you will learn about Engineering Mathematics in a playful way. Each and every topic is prepared in such a way that explains conceptually. This engineering mathematics course covers matrices, eigen values and eigen vectors, sequences and series, calculus, partial differentiation and applications. Some of the topics contain infographic information to get a clear view.
Who this course is for:
- ENGINEERS