Video Lessons - 5

Revision Notes - 1

Revision Notes - 1

Definition, Order and Degree of DE, Formation of DE. Solutions of Variable Separable DE, Exact DE, Linear DE and reducible to these types

Introduction to DE, Ordinary DE, Partial DE, Order, Degree, Formation of DE, Variable Separable DE, Concept of Particular and General Solution, Solving by Substitution, and other topics.

Video Lessons - 4

Revision Notes - 1

Revision Notes - 1

Orthogonal Trajectories, Newton's Law of Cooling, Motion, One-Dimensional Conduction of Heat, Chemical Problems

Orthogonal Trajectories, OT in Cartesian Coordinates, OT in Polar Coordinates, Newton's Law of Cooling, and other topics.

Video Lessons - 4

Revision Notes - 2

Revision Notes - 2

Definition, Dirichlet's Conditions, Full Range Fourier Series, Half Range Fourier Series, Harmonic Analysis and Applications to Problems in Engineering.

Introduction to Fourier series, Fourier Series in an arbitrary period of 2L, Even and Odd functions in (-L,L), Dirichlet's Conditions, and other topics.

Video Lessons - 2

Revision Notes - 1

Revision Notes - 1

Reduction Formulae for different type of Algebraic, Exponential and Trigonometric Expressions and their usage in solving Integrals

Concept of a Reduction Formula,
Reducing Sin ^{n}x & Cos ^{n}x,
Typical Integrals solvable by reducing Sin ^{n}x & Cos ^{n}x,
Reducing Sin ^{n}x.Cos ^{n}x,
Typical Integrals solvable by reducing Sin ^{n}xCos ^{n}x,
and other topics.

Video Lessons - 2

Revision Notes - 1

Revision Notes - 1

Beta and Gamma Functions andÂ their usage in solving Integrals

Gamma Function and its Properties, Beta Functions and its Properties, and other topics.

Video Lessons - 1

Revision Notes - 1

Revision Notes - 1

Leibnitz's Integral Rule, Differentiation under the Integral Sign (DUIS), Solving Integrals using DUIS

Leibnitz's Integral Rule and Introduction to DUIS, Typical Problems related to DUIS, and other topics.

Video Lessons - 1

Revision Notes - 1

Revision Notes - 1

Error Functions, their Properties and Applications

Error Function, Complimentary Error Function and Properties of Error Function, Applications of Error Function, and other topics.

Video Lessons - 5

Revision Notes - 1

Revision Notes - 1

Tracing of Curves in Cartesian, Polar and Parametric form

Introduction to tracing curves, Point of intersection with Axes, Critical Points and Concavity, Tracing a Parabola, Transformations, Symmetry, Region of non-existence, Tracing a Circle, Tracing a Cubic Curve (point of Inflection), and other topics.

Video Lessons - 1

Revision Notes - 1

Revision Notes - 1

Rectification of Curves in Cartesian, Polar and Parametric form. Line Integrals.

Meaning of Rectification of a curve, Rectification of a cartesian curve, Rectification of a parametric curve, Rectification of a polar curve, Typical problems based on rectification, Line Integral, and other topics.

Video Lessons - 6

Revision Notes - 4

Revision Notes - 4

Introduction to Lines and Planes. Spheres, Cones and Cylinders

Concept of Direction Cosines, Direction Ratios, Distance between 2 points and DRs of line Joining them, Angle between Lines, Equation of a Line, Equation of a Plane, Angle between Planes, Prependicular distance from a point to a plane, and other topics.

Video Lessons - 1

Revision Notes - 1

Revision Notes - 1

Cartesian, Polar, Spherical and Cylindrical Coordinate Systems

Cartesian 2D, Polar, Cartesian 3D, Cylindrical, Spherical, and other topics.

Video Lessons - 4

Revision Notes - 2

Revision Notes - 2

Double and Triple Integrations, Applications to Area, Volume, Mean and Root Mean Square Value, Mass, Center of Gravity and Moment of Inertia

Introduction to Iterated Integrals, Region of Integration, Change of Order of Integration, Important results when region is rectangular, Areas, and other topics.

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