Mathematics Videos

Lecture 3 : The Derivative of a Complex Function

Lecture 4 : Solved Examples

Lecture 5 : Cauchy Riemann equations (Derivation)

Lecture 6 : Important result

Lecture 7 : Sufficient Condition of Differentiability

Lecture 8 : Cauchy Riemann polar coordianates

Lecture 9 : Expression Of Derivative And Sufficient Condition of Differentiability In Polar Coordinates

Lecture 10 : Example1,2,3 Complex Derivatives

Lecture 11 : Exercise Q.1 (section 23 J.Brown)

Lecture 12 : Q.2 ( Section 23 J.Brown)

Lecture 13 : Q.3 (All parts)

Lecture 14 : Exercise Q.4 (all parts)

Lecture 15 : Q.5 Q.6

Lecture 16 : Q.7, Q.8 (PU Annual)

Lecture 17 : Analytic Function (definition And Examples), Singularity, Some Results

Lecture 18 : Theorem 1

Lecture 19 : Example 1,2

Lecture 20 : Example 3,4

Lecture 21 : Harmonic Function (definition), Example

Lecture 22 : Theorem1 (harmonic Function)

Lecture 23 : Harmonic Conjugate, Theorem 2

Lecture 24 : Example 3 (how to find harmonic conjugate)

Lecture 25 : Exercise Q.1,2

Lecture 26 : Exercise Q.3,4

Lecture 27 : Exercise Q.5,6

Lecture 28 : Exponential Functions, Theorem 1mp4

Lecture 29 : Theorem 2

Lecture 30 : Thorem 3

Lecture 31 : Theorem 4

Lecture 32 : Definition Of Complex Cosine And Sine Function

Lecture 33 : Properties of Trigonometric Functions

Lecture 34 : Exercise Q.1 to 3

Lecture 35 : Exercise Q.4 to 7

Lecture 36 : Exercise Q.8,9,10

Lecture 37 : Exercise Q.11 To Q.13

Lecture 38 : Exercise Q.14,15,16

Lecture 39 : Hyperbolic Fuctions, Their Derivatives And Relation With Trigonometric Functions

Lecture 41 : Integrals of Complex functions of real Variables

Lecture 42 : Exercises Questions

Lecture 43,44,45,46 : Contours

Lecture 47,48 : Contour Integration (part1)

Lecture 49 : Green's Theorem and its Complex Form

Lecture 50 : Cauchy's Integral Theorem

Lecture 51 : Green's Theorem and its Complex Form

Lecture 52 : Cauchy's Integral Theorem

Lecture 53, 54 : Cauchy-goursat Theorem

Lecture 55, 56 : Q.4.20, 4.21, 4.22 Of Schaum Series (important)

Lecture 57,58 : Cauchy Integral Formula, Example 1

LECTURE 59,60: An extension of Cauchy Integral Formula

Lecture 61,62,63 : Morera's Theorem, Therem Of Section 44 Of J.brown R.churchil, Therem 1 Of Section 52-1

Lecture 64,65 : Solved Exercise Problems

Lecture 66 : Cauchy Inequality, Liouville's Theorem

Lecture 67, 68 Fundamental Theorem Of Algebra, with corollary

lecture 1,2,3,4,5 Convergence of sequence and series ad basic theorems, Taylor and Maclaurin Series, Theorem-1 (Taylors Theorem)

Lecture 6,7 Examples (Exampe 1 to Example 5)