Explore a comprehensive 11-hour course on Differential Calculus designed for B.Sc. and Engineering students. Delve into a wide range of topics including asymptotes, curve tracing, maxima and minima, partial differentiation, radius of curvature, Jacobian transformations, envelopes and evolutes, infinite series, successive differentiation, Leibnitz theorem, and Taylor and Maclaurin series. Learn through detailed explanations, examples, and solutions provided by Dr. Gajendra Purohit. Master important theorems, formulas, and concepts in calculus, including limit continuity, differentiability, and mean value theorems. Gain a solid foundation in differential calculus applicable to various scientific and engineering fields.
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
