Unit 1Live Study Access
Matrices and Linear Algebra
Matrix basics and properties, Rank of a matrix, Consistency of linear systems, Eigenvalues and eigenvectors, Cayley-Hamilton theorem, Diagonalization and quadratic forms
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Read privacy policyEngineering Mathematics notes, chapter flow, practical concepts, and revision resources.
Units
18
Resources
0
Flow
18
Syllabus
Unit 1
Matrices and Linear Algebra
Matrix basics and properties, Rank of a matrix, Consistency of linear systems
Unit 2
Solved Examples
Rank example, Linear system solution, Eigenvalue and eigenvector example
Unit 3
Exercise and Revision
Basic practice set, Intermediate exam problems, Advanced high-scoring questions
Unit 4
Differential Calculus (Single Variable)
Successive differentiation, Leibniz theorem, Mean value theorems
Unit 5
Module 2 Solved Examples
Nth derivative using Leibniz theorem, LMVT verification, Maclaurin expansion
Unit 6
Module 2 Revision
Quick reference sheet, Exam focus, Common mistakes
Unit 7
Partial Differentiation and Applications
Partial derivatives and higher order derivatives, Total differential and chain rule, Euler's theorem
Unit 8
Module 3 Solved Examples
Mixed partial derivative example, Chain rule proof example, Euler theorem verification
Unit 9
Module 3 Revision
Quick reference sheet, Exam focus, Common mistakes
Unit 10
Multiple Integrals and Applications
Double integrals in Cartesian and polar form, Change of order of integration, Triple integrals and coordinate systems
Unit 11
Module 4 Solved Examples
Double integral over triangular region, Change of order example, Triple integral over hemisphere
Unit 12
Module 4 Revision
Exercise sets, Quick reference sheet, Exam focus
Unit 13
Ordinary Differential Equations
First order ODE types and solutions, Higher order linear ODEs, Variation of parameters
Unit 14
Module 5 Solved Examples
Linear first-order ODE example, Resonance case in higher order ODE, Variation of parameters example
Unit 15
Module 5 Revision
Exercise sets, Quick reference sheet, Exam focus
Unit 16
Infinite Series and Convergence
Convergence tests for positive term series, Alternating and conditional convergence, Power series and radius of convergence
Unit 17
Module 6 Solved Examples
Ratio test example, Conditional convergence example, Radius and interval of convergence example
Unit 18
Module 6 Revision
Exercise sets, Quick reference sheet, Exam focus
Overview
Ye subject page direct study workspace ki tarah bana hai. Left side me syllabus yaad rahega, aur right side me har unit ka actual study access, questions, revision, aur MCQ links milenge.
Matrix basics and properties, Rank of a matrix, Consistency of linear systems, Eigenvalues and eigenvectors, Cayley-Hamilton theorem, Diagonalization and quadratic forms
Rank example, Linear system solution, Eigenvalue and eigenvector example, Cayley-Hamilton inverse example, Quadratic form reduction
Basic practice set, Intermediate exam problems, Advanced high-scoring questions, Quick reference sheet, Exam focus and common mistakes
Successive differentiation, Leibniz theorem, Mean value theorems, Taylor and Maclaurin series, Curvature and radius of curvature, Curve tracing essentials
Nth derivative using Leibniz theorem, LMVT verification, Maclaurin expansion, Radius of curvature example
Quick reference sheet, Exam focus, Common mistakes, Study strategy
Partial derivatives and higher order derivatives, Total differential and chain rule, Euler's theorem, Jacobians and properties, Maxima and minima, Taylor theorem for two variables
Mixed partial derivative example, Chain rule proof example, Euler theorem verification, Jacobian evaluation, Lagrange multiplier optimization, Two-variable Taylor expansion
Quick reference sheet, Exam focus, Common mistakes, Key takeaways
Double integrals in Cartesian and polar form, Change of order of integration, Triple integrals and coordinate systems, Change of variables and Jacobian, Beta and Gamma functions, Applications to area, volume, mass, and center of mass
Double integral over triangular region, Change of order example, Triple integral over hemisphere, Jacobian substitution example, Gamma function example, Volume by polar integration
Exercise sets, Quick reference sheet, Exam focus, Study strategy, Key takeaways
First order ODE types and solutions, Higher order linear ODEs, Variation of parameters, Cauchy-Euler equation, Engineering applications
Linear first-order ODE example, Resonance case in higher order ODE, Variation of parameters example, Cauchy-Euler example, RL circuit application
Exercise sets, Quick reference sheet, Exam focus, Study strategy, Key takeaways
Convergence tests for positive term series, Alternating and conditional convergence, Power series and radius of convergence, Fourier series basics
Ratio test example, Conditional convergence example, Radius and interval of convergence example, Fourier series of x on (-pi,pi)
Exercise sets, Quick reference sheet, Exam focus, Study strategy, Key takeaways