This course on Advanced Calculus aims to teach students the convergence of infinite series, partial differentiation, Jacobian transformations, envelope and evolutes, maxima and minima of functions, gamma and beta functions, curve tracing, volumes and surface areas of solids of revolution, double and triple integrals, Taylor series, limits, continuity, differentiability, and important calculus formulas. The course uses a lecture-based teaching method and is intended for learners interested in advancing their knowledge of calculus and multivariable calculus.
Overview
Syllabus
Infinite Series - Convergence Of Infinite Series | Basic Concepts.
Infinite Series - Comparison Test For Convergence of Series | Calculus.
Infinite Series - Cauchy's Integral Test For Convergence of Series.
Infinite Series - D'Alembert's Ratio Test For Convergence of Series.
Infinite Series -Cauchy Root Test For Convergence of Series | Calculus.
Infinite Series -Raabe's Test For Convergence of Series | Calculus.
Infinite Series- De Morgan & Bertrand's Test For Convergence of Series.
Alternating Series | Leibniz Test | Convergence Of Infinite Series.
Absolute Convergence | Conditionally Convergent | Infinite Series.
Partial Differentiation Example And Solution | Multivariable Calculus.
Partial Differentiation - Euler's Theorem for Homogeneous Function.
Partial Differentiation - Total Differential Coefficient Problem & Solution.
Jacobian, Jacobian Transformation, Jacobian Method, Differential Calculus.
Jacobian, Jacobian Properties,Jacobian Example, Differential Calculus.
Jacobian, Jacobian of Implicit Function, Jacobian Example Par-III.
Envelope and Evolutes, Envelope Math, Differential Calculus By GP Sir.
Envelope and Evolutes, Evolute, Evolute of Curve Differential Calculus.
Maxima And Minima of Two Variables Function | Examples And Solution.
Maxima and Minima - Langrange's Method of Undetermined Multipliers.
Gamma Function - Properties & Its Application | Integral Calculus.
Beta Function - Properties with Example | Relation of Gamma & Beta Function.
Curve Tracing of Cartesian Curve By GP Sir.
Curve Tracing of Cartesian Curve | Lecture-II | Working Rule of Tracing.
Curve Tracing of Polar Curves | Cardioids, Limacon, Bernoulli | GP Sir.
Volume of Solids of Revolution | Cartesian & Parametric Form BY GP Sir.
Surface Area of Solids of Revolution | Cartesian & Parametric Form.
Double Integral & Area By Double Integration | Multiple Integral.
Double Integration - Change of Order of Integration | Cartesian & Polar.
Triple Integral | Integral Calculus | Multivariable Calculus | GP Sir.
Triple Integral | Integral Calculus | Multivariable Calculus | Volume By Triple Integral.
Triple Integral | Dirichlet Theorem | Integral Calculus | Multivariable Calculus.
Taylor Series | Taylor Series Expansion | For Function Of Two Variable | Part-I.
Taylor Series | Taylor Series Expansion | For Function Of Two Variable | Part-II.
Limit of a function | Two Variable Function | Epsilon Delta definition of Limit | Examples.
Limit of a function | Two Variable Function | Examples & Solution | Part-II.
Continuity of a Function | Two Variable Function | Multivariable Calculus.
Partial Derivative | Function Of Two Variable | Examples By Limit Definition.
Differentiability | Two Variable Function | Multivariable Calculus.
Calculus | Important formulae | Limit Continuity And Differentiability.
Calculus | Mean Value Theorem | Important formulae | Rolles, Lagrange & Cauchy.
Calculus | Taylor Series | Maclaurin Series | Important formulae.
Taught by
Gajendra Purohit
