Matrices and Calculus

Matrices and Calculus - Engineering Subject

Matrices and Calculus - MA3151 1st semester | 2021 Regulation | Anna University Engineering Subject Paper

Unit I: Matrices

1. Matrices: Vector - Worked Solved Examples

2. Eigen Values and Eigen Vectors - Definition, Properties, Worked Examples

3. Properties of eigen values - Matrices

4. Cayley-Hamilton Theorem - Worked Example Problems

5. Similarity Transformation and Orthogonal Transformation - Theorem, Properties, Solved Example Problems | Matrices

6. Real Quadratic Form Reduction to Canonical Form - Matrices

7. Worked Examples of Real Quadratic Form Reduction to Canonical Form - Solved Example Problems

8. Application of Eigen Value Problem: Stretching of an Elastic Membrane

9. Worked Examples of Application of Eigen Value Problem: Stretching of an Elastic Membrane

10. Questions and Answers - Solved Example Problems | Matrices

Unit II: Differential Calculus

1. Differential Calculus - Introduction

2. Differential Calculus: Function - Definition, Methods of Representing, Examples, Solved Example Problems

3. New Functions from given functions - Definition, Solved Example Problems | Differential Calculus

4. Limit of a Function - Definition, Theorem, Solved Example Problems | Differential Calculus

5. Continuity - Definition, Theorem, Solved Example Problems | Differential Calculus

6. Derivative - Definition, Theorem, Solved Example Problems | Differential Calculus

7. Derivative Problems Based on General Rules of Differentiation

8. Chain Rule or Derivative of Composite Function - Worked Examples, Exercise problems with Answers | Differential Calculus

9. Derivative of Inverse Functions - Trigonometric Functions, Worked Examples, Exercise with Answers | Differential Calculus

10. Implicit Differentiation - Worked Examples | Differential Calculus

11. Logarithmic Differentiation - Worked Examples | Differential Calculus

12. Differentiation of Parametric Equations - Definition, Worked Examples, Exercise with Answers | Differential Calculus

13. Hyperbolic Functions - Definition, Worked Examples, Exercise with Answers | Differential Calculus

14. Geometrical Interpretation of Derivative - Worked Examples, Exercise with Answers | Differential Calculus

15. Applications: Maxima and Minima of Function of One Variable - Definition, Theorem, Worked Examples | Differential Calculus

16. Maxima and Minima of a Function of one variable - Definition, Theorem, Geometrical Meaning, Tests, Worked Examples, Exercise with Answers | Differential Calculus

17. Concavity - Definition, Theorem, Worked Examples, Exercise with Answers | Differential Calculus

18. Questions and Answers - Solved Problems | Differential Calculus | Matrices and Calculus

Unit III: Functions of Several Variables

1. Functions of Several Variables - Introduction | Calculus

2. Limit and Continuity - Definition, Worked Examples, Exercise with Answers

3. Partial Derivatives - Definition, Theorem, Worked Examples, Exercise with Answers

4. Jacobians - Definition, Properties, Worked Examples, Exercise with Answers

5. Taylor's Expansion for Function of Two Variables - Theorem, Worked Examples, Exercise with Answers

6. Applications: Maxima and Minima for Functions of Two Variables - Definition, Worked Examples, Exercise with Answers

7. Questions and Answers - Solved Example Problems | Functions of Several Variables | Matrices and Calculus

Unit IV: Integral Calculus

1. Integral Calculus - Introduction

2. Definite Integral (Rectangle Method of Finding Area) - Worked Examples, Fundamental Theorem of Calculus

3. Indefinite Integral - Worked Examples, Exercise with Answers | Integral Calculus

4. Integration by Parts - Worked Examples, Exercise with Answers | Integral Calculus

5. Improper Integrals - Theorem, Worked Examples, Exercise with Answers | Integral Calculus

6. Applications of Integral - Definition, Worked Examples, Exercise with Answers, Hydrostatic Force and Pressure, Moments and Centre of Mass | Integral Calculus

7. Questions and Answers - Solved Problems | Integral Calculus | Matrices and Calculus | Matrices and Calculus

Unit V: Multiple Integrals

1. Double Integration - Worked Examples, Exercise with Answers

2. Triple Integral in Cartesian Coordinates - Worked Examples, Exercise with Answers

3. Change of Variables in Double and Triple Integrals - Worked Examples, Exercise with Answers

4. Integrals: Centre of Mass and Centre of Gravity - Worked Examples, Exercise with Answers | Multiple Integrals

5. Integrals: Moment of Inertia - Worked Examples, Exercise with Answers

6. Questions and Answers - Solved Problems | Multiple Integrals | Matrices and Calculus