Advanced Calculus Advanced Calculus

Advanced Calculus

Calculus (from Latin calculus, literally "small pebble used for counting") is the mathematical study of change, in the same way that geometry is the study of shape and algebra is the study of operations and their application to solving equations. It has two major branches, differential calculus (concerning rates of change and slopes of curves), and integral calculus (concerning accumulation of quantities and the areas under and between curves); these two branches are related to each other by the fundamental theorem of calculus. Both branches make use of the fundamental notions of convergence of infinite sequences and infinite series to a well-defined limit. Generally, modern calculus is considered to have been developed in the 17th century by Isaac Newton and Gottfried Leibniz. Today, calculus has widespread uses in science, engineering and economicsand can solve many problems that elementary algebra alone cannot

Calculus is a part of modern mathematics education. A course in calculus is a gateway to other, more advanced courses in mathematics devoted to the study of functions and limits, broadly called mathematical analysis. Calculus has historically been called "the calculus of infinitesimals", or "infinitesimal calculus". Calculus (plural calculi) is also used for naming some methods of calculation or theories of computation, such as propositional calculus, calculus of variations, lambda calculus, and process calculus.

Chapter 1 : Continuity
Chapter 2 : Differentiability
Chapter 3 : Limit and Continuity of Functions of Two Variables
Chapter 4 : Jacobians
Chapter 5 : Envelopes, Evolutes and Involutes
Chapter 6 : Maxima and Minima (Of Functions of Two Variables)
Chapter 7 : Maxima and Minima (Of Functions of Sever al Independent Variables
Chapter 8 : Beta and Gamma Functions
Chapter 9 : Multiple Integrals (Double and Triple Integrals,Change of Order of Integration)
Chapter 10 : Dirichlet's and Liouville's Integrals
Chapter 11 : Convergence of Improper Integrals