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.
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.
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.
Reduction Formulae for different type of Algebraic, Exponential and Trigonometric Expressions and their usage in solving Integrals
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.
Beta and Gamma Functions and their usage in solving Integrals
Gamma Function and its Properties, Beta Functions and its Properties, and other topics.
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.
Error Functions, their Properties and Applications
Error Function, Complimentary Error Function and Properties of Error Function, Applications of Error Function, and other topics.
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.
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.
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.
Cartesian, Polar, Spherical and Cylindrical Coordinate Systems
Cartesian 2D, Polar, Cartesian 3D, Cylindrical, Spherical, and other topics.
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.