MathLogic

Lec-118 Interior extremum theorem. If f has extremum then f'(c)=0, Real Analysis I, Bartle. (Urdu)

CSS Pure Maths 2024 Q # 2 : System of linear equations : unique solution : no solution : infinite so

CSS Pure Maths 2024 Q # 1. CSS Pure Mathematics Old Papers of 2024 Solution. (Urdu/Hindi)

Lec-117 Derivative of Inverse of a Function. Real Analysis I. Bartle. (Urdu/Hindi)

Lec-116 Derivative by definition. Derivative of x^2sin1/x. Real Analysis I : Bartle. (Urud/Hindi)

CSS Pure Maths 2023 Q # 8: Laurent Series : Residues at poles.

CSS Pure Maths 2023 Q # 7. Harmonic function, harmonic conjugate. Fundamental theorem of complex int

MCQ's, Differential Geometry, Lec_33. Diff. Geometry

Quadric surfaces, most general quadratic equation in three variables. Lec_32 Diff. Geometry

Smooth map between surface, Level surfaces, Method to prove level surface to b smooth. Lec_31.

Lec-115 proof of Chain Rule : Derivative of Composition of functions : Bartle : Real Analysis I

Lec-06 : Force on Inclined plane. May June 2017 P42 Q # 5. A levels mchanics. (Urdu/Hindi)

Continuity at a point continuity at isolated point. Real Analysis I. Bartle. Lec-90

Lec-08 A function having finite points of discontinuity is Riemann Stieltjes integrable.

f is monotonic increasing on (a,b), its left and right limits at c in (a,b) exist. (Bartle) Lec-85

If limit of a function is positive then in a neighborhood of limit point function is positive.Lec-82

limits of sum of functions is equal to sum of limits of functions. Real Analysis I, Bartle Lec-76

Sequential criteria limit of a function. Divergence Criteria non-existence limit of function.Lec-74

Plane Curves I, Calculus by S.M. Yusuf, Ex 6.2, Q # 27 and 28 Lec-32 (P)

Limit of Product of functions is equal to product of their limits. Bartle, Real Analysis I. Lec-77

Infinite Limits. f approaches to ∞ or -∞ as x approaches to 0. Real Analysis I. Bartle. Lec-87

Some Examples to Evaluate Limits of functions by definition. Bartle, Real Analysis I, Lec-72

sin, cosine and modulus f are continuous functions. Real Analysis I. Bartle. Lec-94

Lec_8.1-14, Mathematics 11 Chapter 8, Principle of extended mathematical induction. (Urdu/Hindi)

Lec_20, Number Theory, Radix conversion of positive integer a to an integer in base g greater than1.