This course on Differential Calculus aims to teach students the following learning outcomes and goals: understanding asymptotes, curve tracing of Cartesian and Polar curves, finding maxima and minima of functions, applying partial differentiation, calculating radius of curvature, working with Jacobians, studying envelopes and evolutes, analyzing convergence of infinite series, mastering successive differentiation, and exploring Leibnitz, Maclaurin, and Taylor series. The course teaches individual skills such as identifying asymptotes, tracing curves, finding extrema, differentiating partially, calculating radii of curvature, working with Jacobians, analyzing series convergence, and applying differentiation theorems. The teaching method includes lectures, examples, and solutions presented in Hindi. The course is intended for B.Sc. and engineering students seeking to deepen their understanding of differential calculus concepts and applications.
Overview
Syllabus
Definition of Asymptotes with Working Rule in Hindi By GP Sir.
Asymptotes Example & Solution When Roots are Equal | Definition & Rule.
Intersection of Curve and Its Asymptotes Definition & Method | GP Sir.
Asymptotes By Inspection Method | Parallel Asymptotes | By Gp Sir.
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.
Maxima And Minima of Two Variables Function | Examples And Solution.
Maxima and Minima - Langrange's Method of Undetermined Multipliers.
Partial Differentiation Example And Solution | Multivariable Calculus.
Partial Differentiation - Euler's Theorem for Homogeneous Function.
Partial Differentiation - Total Differential Coefficient Problem & Solution.
Radius of Curvature | Radius of Curvature Formula & Example & Solution.
Radius of Curvature Part-2 Example and Solutions Differential Calculus.
Radius of Curvature Part-3 Example and Solutions Differential Calculus.
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.
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.
Successive Differentiation | Differential Calculus | Concepts & Examples.
Successive Differentiation | nth Derivative | Differential Calculus.
Leibnitz Theorem | Successive Differentiation | nth Derivative | Part-I.
Leibnitz Theorem | Successive Differentiation | nth Derivative | Part-II.
Leibnitz Theorem | nth Differential Coefficient For Special Value of x | Part-III.
Maclaurin Series | Maclaurin Theorem | Proof & Series Expansion | Part-I.
Maclaurin Series | Maclaurin Theorem | Example & Solutions | Part-II.
Taylor Series | Taylor Theorem | Proof & Series Expansion | Part-I.
Taylor Series | Taylor Theorem | Example & Solutions | Part-II.
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
