Engineering Mathematics

Lecture Repository • Course Index

Chapter 1: Matrix Foundations

Matrix Basics RREF & Rank Determinants Eigenvalues Diagonalization

10 lectures • fully available

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Chapter 2: Calculus

Limits Continuity Differentiability Partial Derivatives

10 lectures • fully available

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Chapter 3: First Order Differential Equations

Separable Linear Exact Applications

8 lectures • fully available

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Chapter 4: Higher Order Differential Equations

Constant Coefficients Cauchy–Euler Undetermined Coefficients Variation of Parameters

8 lectures • fully available

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Weekly Assignments

Matrix Limits and Continuity Differential Equations

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Practice Questions

Matrix Limits and Continuity Differential Equations

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Chapter 1: Matrix Foundations10 lectures
  1. Lecture 1: Introduction to Matrices
  2. Lecture 2: Elementary Operations-1
  3. Lecture 3: Elementary Operations-2
  4. Lecture 4: Rank of a Matrix
  5. Lecture 5: System of Linear equations-1
  6. Lecture 6: System of Linear equations-2
  7. Lecture 7: Eigenvalues & Eigenvectors
  8. Lecture 8: Cayley–Hamilton Theorem & Diaganlozation
  9. Lecture 9: Quadratic Forms & Canonical form-1
  10. Lecture 10: Quadratic Forms & Canonical form-2
Chapter 2: Calculus10 lectures
  1. Lecture 1: Introduction to Functions
  2. Lecture 2: Limits, Continuity, and Differentiation – Basic rules, interpretation, and examples
  3. Lecture 3: Increasing and Decreasing Functions
  4. Lecture 4: Mean Value Theorems and Applications
  5. Lecture 5: Indeterminate Forms and L’Hospital’s Rule
  6. Lecture 6: Maxima and Minima (One Variable)
  7. Lecture 7: Taylor’s Theorem and Approximations
  8. Lecture 8: Introduction – Limits and Continuity of Several Variables
  9. Lecture 9: Partial Derivatives and Taylor’s Theorem
  10. Lecture 10: Maxima and Minima in Several Variables & Method of Lagrangian Multipliers
Chapter 3: First Order Differential Equations8 lectures
  1. Lecture 1: Introduction to Differential Equations
  2. Lecture 2: Formation of First Order DEs
  3. Lecture 3: Separable Equations
  4. Lecture 4: Linear Equations
  5. Lecture 5: Homogeneous Equations
  6. Lecture 6: Exact Equations
  7. Lecture 7: Integrating Factors
  8. Lecture 8: Applications (Growth & Decay)
Chapter 4: Higher Order Differential Equations8 lectures
  1. Lecture 1: Higher Order DEs with Constant Coefficients
  2. Lecture 2: Auxiliary Equation & Solution Structure
  3. Lecture 3: Cauchy–Euler Equations
  4. Lecture 4: Method of Undetermined Coefficients
  5. Lecture 5: Method of Variation of Parameters
  6. Lecture 6: Applications in Mechanical Vibrations
  7. Lecture 7: Coupled Differential Equations
  8. Lecture 8: Modeling with Higher Order DEs
Practice Questions4
  1. Matrix Theory-1
    2. & Solutions of-1
  2. Matrix theorey-2
    3. & Solutions of-2
  3. Matrix theorey-3
    4. & Solutions of-3
  4. ODE-1
  5. ODE-2
List of Assignments12
  1. Assignment 1: Matrix theorey-1
  2. Assignment 2: Matrix theorey-2
  3. Assignment 3: Matrix theorey-3
  4. Assignment 4: Limits and Continuity
  5. Assignment 5: Function of One Variables
  6. Assignment 6: Function of Several Variables

Assignment-1 (Matrix Theorey-1)

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