# Engineering Mathematics - II

Video Lessons & Revision Notes

### 1. Differential Equations

Video Lessons - 5
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

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.

### 2. Applications of Differential Equations

Video Lessons - 4
Revision Notes - 1

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

All Lessons and Notes
##### 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.

### 3. Fourier Series

Video Lessons - 4
Revision Notes - 2

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

All Lessons and Notes
##### Fourier Series : Basic Concepts
46 mins Video Lesson

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.

### 4. Reduction Formulae

Video Lessons - 2
Revision Notes - 1

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

All Lessons and Notes
##### Reduction Formulae : Part 1
54 mins Video Lesson

Concept of a Reduction Formula, Reducing Sin nx & Cos nx, Typical Integrals solvable by reducing Sin nx & Cos nx, Reducing Sin nx.Cos nx, Typical Integrals solvable by reducing Sin nxCos nx, and other topics.

### 5. Beta and Gamma Functions

Video Lessons - 2
Revision Notes - 1

Beta and Gamma Functions 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.

### 6. Differentiation under the Integral Sign

Video Lessons - 1
Revision Notes - 1

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

All Lessons and Notes
##### Differentiation Under Integral Sign
44 mins Video Lesson

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

### 7. Error Functions

Video Lessons - 1
Revision Notes - 1

Error Functions, their Properties and Applications

All Lessons and Notes
##### Error Functions
26 mins Video Lesson

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

### 8. 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.

### 9. 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.

### 10. 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.

### 11. Coordinate Systems

Video Lessons - 1
Revision Notes - 1

Cartesian, Polar, Spherical and Cylindrical Coordinate Systems

All Lessons and Notes
##### Coordinate Systems
24 mins Video Lesson

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

### 12. Multiple Integrals and their Applications

Video Lessons - 4
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

All Lessons and Notes
##### 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.

##### In this Subject
• Around 30 Hours of Videos
• 36 Video Lessons
• 17 Revision Notes
• 12 Modules