Engineering Mathematics - II
Video Lessons & Revision Notes1. Differential Equations
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
Featured Lesson in Differential Equations
Differential Equation : Introduction and Variable Separable Type
50 mins Video LessonIntroduction 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
Revision Notes - 1
Orthogonal Trajectories, Newton's Law of Cooling, Motion, One-Dimensional Conduction of Heat, Chemical Problems
Featured Lesson in Applications of Differential Equations
Orthogonal Trajectories and Newton’s Law of Cooling
38 mins Video LessonOrthogonal Trajectories, OT in Cartesian Coordinates, OT in Polar Coordinates, Newton's Law of Cooling, and other topics.
3. Fourier Series
Revision Notes - 2
Definition, Dirichlet's Conditions, Full Range Fourier Series, Half Range Fourier Series, Harmonic Analysis and Applications to Problems in Engineering.
Featured Lesson in Fourier Series
Fourier Series : Basic Concepts
46 mins Video LessonIntroduction 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
Revision Notes - 1
Reduction Formulae for different type of Algebraic, Exponential and Trigonometric Expressions and their usage in solving Integrals
Featured Lesson in Reduction Formulae
Reduction Formulae : Part 1
54 mins Video LessonConcept 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
Revision Notes - 1
Beta and Gamma Functions and their usage in solving Integrals
Featured Lesson in Beta and Gamma Functions
Beta Gamma Functions : Basic Concepts
30 mins Video LessonGamma Function and its Properties, Beta Functions and its Properties, and other topics.
6. Differentiation under the Integral Sign
Revision Notes - 1
Leibnitz's Integral Rule, Differentiation under the Integral Sign (DUIS), Solving Integrals using DUIS
Featured Lesson in Differentiation under the Integral Sign
Differentiation Under Integral Sign
44 mins Video LessonLeibnitz's Integral Rule and Introduction to DUIS, Typical Problems related to DUIS, and other topics.
7. Error Functions
Revision Notes - 1
Error Functions, their Properties and Applications
Featured Lesson in Error Functions
Error Functions
26 mins Video LessonError Function, Complimentary Error Function and Properties of Error Function, Applications of Error Function, and other topics.
8. Curve Tracing
Revision Notes - 1
Tracing of Curves in Cartesian, Polar and Parametric form
Featured Lesson in Curve Tracing
Curve Tracing in Cartesian Form : Part 1
74 mins Video LessonIntroduction 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
Revision Notes - 1
Rectification of Curves in Cartesian, Polar and Parametric form. Line Integrals.
Featured Lesson in Rectification of Curves
Rectification of Curves
55 mins Video LessonMeaning 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
Revision Notes - 4
Introduction to Lines and Planes. Spheres, Cones and Cylinders
Featured Lesson in Solid Geometry
Lines and Planes
37 mins Video LessonConcept 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
Revision Notes - 1
Cartesian, Polar, Spherical and Cylindrical Coordinate Systems
Featured Lesson in Coordinate Systems
Coordinate Systems
24 mins Video LessonCartesian 2D, Polar, Cartesian 3D, Cylindrical, Spherical, and other topics.
12. Multiple Integrals and their Applications
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
Featured Lesson in Multiple Integrals and their Applications
Iterated Integrals
47 mins Video LessonIntroduction 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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