# Applied Mathematics ‐ II

Video Lessons & Revision Notes

### 1. Curve Tracing

Video Lessons - 5
Revision Notes - 1

Tracing of Curves in Cartesian, Polar and Parametric form

All Lessons and Notes
##### Curve Tracing in Cartesian Form : Part 1
74 mins Video Lesson

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.

### 2. Solid Geometry

Video Lessons - 6
Revision Notes - 4

Introduction to Lines and Planes. Spheres, Cones and Cylinders

All Lessons and Notes
##### Lines and Planes
37 mins Video Lesson

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.

### 3. Beta and Gamma Functions

Video Lessons - 2
Revision Notes - 1

Beta and Gamma Functions, its properties and  their usage in solving Integrals

All Lessons and Notes
##### Beta Gamma Functions : Basic Concepts
30 mins Video Lesson

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

### 4. Rectification of Curves

Video Lessons - 1
Revision Notes - 1

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

All Lessons and Notes
##### Rectification of Curves
55 mins Video Lesson

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.

### 5. Differential Equations

Video Lessons - 5
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.

All Lessons and Notes
##### Differential Equation : Introduction and Variable Separable Type
50 mins Video Lesson

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.

### 6. Applications of Differential Equations

Video Lessons - 4
Revision Notes - 1

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

All Lessons and Notes
##### Applications of Differential Equations : Orthogonal Trajectories and Newton\'s Law of Cooling
38 mins Video Lesson

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

### 7. Linear Differential Equations of Higher Order

Video Lessons - 5
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 eax, sin (ax+b), cos (ax+b), xn, eaxV, xV

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

All Lessons and Notes
##### Solving a Homogeneous Linear DE
80 mins Video Lesson

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.

### 8. Multiple Integrals and their Applications

Video Lessons - 4
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.

All Lessons and Notes
##### Multiple Integrals : Iterated Integrals
47 mins Video Lesson

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

### 9. Numerical solution of Ordinary Differential Equations

Video Lessons - 2
Revision Notes - 1

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

All Lessons and Notes
##### Differential Equations : Numerical Techniques - Part 1
43 mins Video Lesson

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

### 10. Interpolation and Numerical Integration

Video Lessons - 4
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

All Lessons and Notes
##### Finite Difference Operators - Part 1
51 mins Video Lesson

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

##### In this Subject
• Around 30 Hours of Videos
• 38 Video Lessons
• 15 Revision Notes
• 10 Modules