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 - 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 - 2

Revision Notes - 1

Revision Notes - 1

Beta and Gamma Functions, its properties and 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

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 - 5

Revision Notes - 1

Revision Notes - 1

Differential Equation of first order and first degree. Exact differential equations, Equations reducible to exact equations by integrating factors.

Linear differential equations, equation reducible to linear form, Bernoulli’s equation.

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

Simple application of differential equation of first order and second order to electrical and Mechanical Engineering problem

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

Video Lessons - 5

Revision Notes - 1

Revision Notes - 1

Linear Differential Eqaution with constant coeffiecient‐ Complimentary function, particular integrals of differential equation of the type f(D)y = X where X is e^{ax}, sin (ax+b), cos (ax+b), x^{n}, e^{ax}V, xV

Cauchy’s homogeneous linear differential equation and Legendre’s differential equation, Method of variation of parameters.

Linear Differential Equation, Homogeneous Linear Differential Equation, LDE with constant coefficients, Homogeneous LDE with constant coefficients, Solving a Homogeneous LDE with constant coefficients, Concept of Auxillary Equation, Repeated Roots, Imaginary Roots, Repeated Imaginary Roots, and other topics.

Video Lessons - 4

Revision Notes - 2

Revision Notes - 2

Multiple Integrals‐Double integration‐definition, Evaluation of Double Integrals, Change of order of integration, Evaluation of double integrals by changing the order of integration and changing to polar form

Triple integration –definition and evaluation (Cartesian, cylindrical and spherical polar coordinates).

Application to double integrals to compute Area, Mass, Volume. Application of triple integral to compute volume.

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

Video Lessons - 2

Revision Notes - 1

Revision Notes - 1

(a)Taylor’s series method (b)Euler’s method (c) Modified Euler method (d) Runga‐Kutta fourth order formula

Introduction to Numerical Methods, Taylor's Series Method, Euler's Method, and other topics.

Video Lessons - 4

Revision Notes - 2

Revision Notes - 2

Numerical integration‐Different type of operators such as shift, forward, backward difference and their relation.

Interpolation, Newton interpolation, Newton‐Cotes formula. Integration by (a) Trapezoidal (b) Simpson’s 1/3rd (c)Simpson’s 3/8th rule

Interpolation and Extrapolation, Forward Difference Operator, Backward Difference Operator, Central Difference Operator, Averaging Operator, Shift Operator, and other topics.

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