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We discuss the remaining examples in this part. #trigonometric_equations #class_xi #ncert #a_mathematical_room

We start Section 11.8 - The Riemann-Stieltjes integral. In this part we define the α-length of a bounded interval and discuss the additive property of this new notion of length. #α-length #riemann_stieltjes_integral #analysis #tao #a_mathematical_room

We solve Exercise 4 of the Section 6.6 here. #jordan_canonical_form #linear_algebra #herstein #a_mathematical_room

In this part we discuss Exercises 39, 40, 41 and 42. #differentiation #thomascalculus #calculus #a_mathematical_room

The title is self-explanatory. #periodic_function #a_mathematical_room

We start Differential Equations from Ross. In this part we define and classify differential equations. #differential_equation #order #ordinarydifferentialequation #partialdifferentialequation #lineardifferentialequation #ross #a_mathematical_room

We prove that the converse to Fermat's little theorem is false. #fermat #number_theory #burton #a_mathematical_room

This is section 11.7. Here we see an example of a bounded function which is not Riemann integrable. #riemannintegral #analysis #tao #a_mathematical_room

In this part we solve Exercise 3. #jordan_canonical_form #linear_algebra #herstein #a_mathematical_room

In this part we discuss Exercises 29 - 38, and solve some of them. #derivatives #differentiation #thomascalculus #calculus #a_mathematical_room

Not everything needs to be long and complicated. #rational_number #irrational_number #analysis #tao #a_mathematical_room

We are starting topology from Munkres' book. In this part we define an order relation and discuss Examples 7 and 8. #order_relation #topology #munkres #a_mathematical_room

In this part we solve the equations cos x=cos y and tan x=tan y. We then discuss two examples. #trigonometric_equations #class_xi #ncert #a_mathematical_room

We complete the ongoing section in this part by proving Corollary 11.6.5. #monotonic_functions #riemann_integral #analysis #tao #a_mathematical_room

Canonical Forms, A Decomposition of V, Jordan Form (Part 5, Herstein)

Differentiation Rules (Part 6, Thomas and Finney)

Further Adjustments

Fermat's Theorem (Part 5, Burton)

Riemann Integrability of Monotonic Functions (Part 3, Tao)

Canonical Forms, A Decomposition of V, Jordan Form (Part 4, Herstein)

Differentiation Rules (Part 5, Thomas and Finney)

Why so careless?

Riemann Integrability of Monotonic Functions (Part 2, Tao)

Class XI, NCERT (Trigonometric Functions, Part 11)

Canonical Forms, A Decomposition of V, Jordan Form (Part 3, Herstein)

Differentiation Rules (Part 4, Thomas and Finney)

Fermat's Theorem (Part 4, Burton)

Riemann Integrability of Monotonic Functions (Part 1, Tao)

Canonical Forms, A Decomposition of V, Jordan Form (Part 2, Herstein)