Applied Mathematics - I
Mumbai University - Biomedical Engineering - SEM I


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  • Lectures
  • 164 Lectures
  • Videos
  • 25.78 Hrs Video

Course Description

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Curriculum

Total Chapters: 12 164 Videos

Chapter No. 1 : Review of Complex Numbers

   

Standard form of Complex Numbers - Concept

Preview 7.35

Problem 1 based on Standard form of Complex Number

Preview 6.44

Problem 2 based on Standard form of Complex Number

7.02

Conjugate of Complex Numbers - Concept

4.58

Problem 1 based on Conjugate of Complex Numbers

4.22

Problem 2 based on Conjugate of Complex Numbers

5.19

Algebra of Complex Numbers - Concept

9.43

Problem 1 based on Algebra of Complex Numbers

5.22

Problem 2 based on Algebra of Complex Numbers

9.22

Problem 3 based on Algebra of Complex Numbers

8.25

Equality of Complex Numbers - Concept

4.28

Problem 1 based on Equality of Complex Numbers

2.41

Problem 2 based on Equality of Complex Numbers

9.35

Problem 1 based on Square root of Complex Numbers

14.27

Modulus and Argument of Complex Number - Concept

10.15

Problem 1 based on Modulus and Argument of Complex Number

11.59

Problem 2 based on Modulus and Argument of Complex Number

8.59

Problem 3 based on Modulus and Argument of Complex Number

9.43

Polar form of Complex Numbers - Concept

4.57

Miscellaneous Problem no. 1 on Complex Number

10.21

Miscellaneous Problem no. 2 on Complex Number

5.48

Miscellaneous Problem no. 3 on Complex Number

8.32

Miscellaneous Problem no. 4 on Complex Number

12.07

Chapter No. 2 : DeMoivre's Theorem

   

De Moivre's theorem with Corollaries

Preview 4.52

Problem 1 based on Power of Complex Number

Preview 10.52

Problem 2 based on Power of Complex Number

9.51

Problem 3 based on Power of Complex Number

8.24

Problem 1 based on roots of quadratic equation

11.45

Problem 2 based on roots of quadratic equation

8.25

Miscellaneous Problem no. 1 on De Moivre's theorem

9.55

Problem 2 based on Expansion of sin nq, cos nq in powers of sinq, cosq

11.58

Problem 1 based on cube root of unity

12.4

Problem 2 based on cube root of unity

6.44

Problem 3 based on cube root of unity

3.05

Problem 4 based on cube root of unity

3.31

Problem 2 based on multiple roots of equation

9.29

Problem 3 based on multiple roots of equation

9.3

Problem 4 based on multiple roots of equation

16.11

Problem 5 based on multiple roots of equation

10.21

Problem 1 based on Exponential form of Complex Numbers

5.53

Problem 2 based on Exponential form of Complex Numbers

12.14

Problem 3 based on Exponential form of Complex Numbers

9.08

Problem 4 based on Exponential form of Complex Numbers

10.33

Chapter No. 3 : Hyperbolic Functions

   

Euler's form of Circular function- Concept

Preview 4.4

Problem 1 based on Euler's form of Circular function

Preview 3.57

Problem 2 based on Euler's form of Circular function

6.34

Problem 3 based on Euler's form of Circular function

6.53

Problem 4 based on Euler's form of Circular function

8.4

Problem 1 based on Hyperbolic functions

6

Problem 2 based on Hyperbolic functions

12.3

Problem 3 based on Hyperbolic functions

6.35

Problem 4 based on Hyperbolic functions

10.02

Relationship between Hyperbolic and Circular functions

7.18

Problem 1 based on Formulae of Hyperbolic Functions

4.21

Problem 2 based on Formulae of Hyperbolic Functions

6.41

Problem 3 based on Formulae of Hyperbolic Functions

14.45

Problem 4 based on Formulae of Hyperbolic Functions

8.01

Problem 5 based on Formulae of Hyperbolic Functions

7.17

Chapter No. 4 : Logarithms of complex numbers

   

How to find log of Complex number?

Preview 9.02

Miscellaneous Problem no. 1 on logarithm of complex number

Preview 6.09

Miscellaneous Problem no. 2 on logarithm of complex number

7.12

Miscellaneous Problem no. 3 on logarithm of complex number

6.06

Miscellaneous Problem no. 4 on logarithm of complex number

9.1

Miscellaneous Problem no. 5 on logarithm of complex number

15.25

Chapter No. 5 : Matrices

   

Orthogonal Matrices - Concept

Preview 3.07

Problem 1 based on Orthogonal Matrices

Preview 5.26

Problem 2 based on Orthogonal Matrices

8.54

Problem 3 based on Orthogonal Matrices

5.4

Unitary Matrices - Concept

3.32

Problem 1 based on Unitary Matrices

7.09

Problem 2 based on Unitary Matrices

12.2

Chapter No. 7 : Successive Differentiation

   

Nth derivative of Algebraic Functions - Formula

Preview 8.42

Gauss Elimination Method with Example

Preview 21.51

Jacobi's Method with Example

Preview 15.26

Nth derivative of Algebraic Functions - Formula

Preview 11.36

Nth derivative of Transcedental Functions - Formula

9.04

Gauss-Seidel Method with Example

14.32

Nth derivative of Transcedental Functions - Formula

9.44

Nth derivative of Transcedental Functions - Formula

6.47

Chapter No. 8 : Partial Differentiation

   

Partial Derivative of First Order - Problem 1

Preview 8.05

Partial Derivative of First Order - Problem 3

Preview 12.04

Partial Derivative of First Order - Problem 4

11.36

Partial Derivative of First Order - Problem 5

9.1

Partial Derivative of First Order - Problem 6

3.57

Partial Derivative of First Order - Problem 7

12.26

Partial Derivative of Second Order - Problem 1

13.22

Partial Derivative of Second Order - Problem 2

11.14

Partial Derivative of Second Order - Problem 3

14.05

Partial Derivative of Second Order - Problem 4

9.19

Partial Derivative of Second Order - Problem 5

Preview 19.59

Partial Derivative of Second Order - Problem 6

Preview 9.48

Partial Derivative of Second Order - Problem 7

14.3

Partial Derivative of Second Order - Problem 8

15.26

Partial Derivative of Second Order - Problem 9

8.56

Partial Derivative of Second Order - Problem 10

12.59

Composite Function - Definition & Example

12.08

First Order Partial Derivation of Composite Function - Problem 1

16.34

First Order Partial Derivation of Composite Function - Problem 2

13.14

First Order Partial Derivation of Composite Function - Problem 3

12.09

First Order Partial Derivation of Composite Function - Problem 4

12.59

First Order Partial Derivation of Composite Function - Problem 6

27.15

Chapter No. 9 : Homogenous Functions

   

Problem 1 based on Euler's Theorem

Preview 5.34

Problem 2 based on Euler's Theorem

Preview 12.4

Problem 3 based on Euler's Theorem

16.12

Problem 4 based on Euler's Theorem

5.01

Problem 5 based on Euler's Theorem

13.5

Problem 2 based on Corollary 1 of Euler's Theorem

14.35

Problem 3 based on Corollary 1 of Euler's Theorem

4.36

Problem 1 based on Corollary 2 of Euler's Theorem

9.04

Problem 2 based on Corollary 2 of Euler's Theorem

9.14

Problem 3 based on Corollary 2 of Euler's Theorem

17.32

Problem 1 based on Corollary 3 of Euler's Theorem

8.54

Problem 2 based on Corollary 3 of Euler's Theorem

11.44

Problem 3 based on Corollary 3 of Euler's Theorem