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Calculus II - MTH301 - VU Video Lectures

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Introduction, Integral Calculus, Location of a point, Concept of a Function, Examples of function, Function of Several Variables.
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Values of functions, Function of One,two,three and n Variables.
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Distance formula in three dimension, Mid point of two points, Direction Angles, Direction Ratios, Direction cosines, Intesection of two surfaces and planes, Intersection of Cone and sphere, General Equation of Plane.
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Polar co-ordinates, Conversion formula from polar to Cartesian coordinates, Cylindrical co-ordinates, Spherical co-ordinates.
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Limit of multivariable function, Domains and Ranges,Rules for limit.
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Geometry of continuous functions, Continuity of functions of two and three variables, Partial derivative.
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Geometric meaning of partial derivative, Partial Derivatives of Higher Orders, Laplace’s Equation, Euler’s theorem.
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Order of differentiation, Chain rule in function of One variable.
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The Chain Rule for Functions of many variables.
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Introduction to vectors, Magnitude or Length Of vector, Unit vector, Addition Of vectors, Equal and Opposite vectors, Angle between two vectors, Right-hand rule.
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The triple scalar, Directional derivative, Properties of directional derivatives.
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Tangent planes to the surfaces, Normal line to the surfaces, General equation of straight line, Parametric equation of a line, Equation of a plane, Tangent Plane and Normal Line.
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Orthogonal Surface, Normal line, total differential for function of one and two variables.
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Extrema of functions of two variables, Extreme value theorm, Absolute maximum and manimum.
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Graph of f(x,y), The second partial derivative test.
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Extreme valued theorem.
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Revision of integration, Double integral,Iterated or repeated integral.
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Double integral for non-rectangular region.
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Polar coordinate systems, Lines in polar coordinates, Circle in polar coordinates, Equation of circle in polar coordinates.
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Sketching, Sketching of curves in polar coordinates, Cardioids and Limacons, Spiral.
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Double integrals in polar co-ordinates.
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Vector valued functions, Parametric equations in vector form.
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Limits of vector valued functions, Continuity of vector-valued functions, Derivative of vector-valued functions, Rules of differentiation, Integral vector-valued function, Properties of integral.
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Change of parameter.
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Exact differential, Integration Of exact differentials, Line integrals.
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Line integral, Properties of line integrals.
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Examples, Dependence of the line integral.
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Examples, Exact differentials in three independent variables, Green’s thorem.
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Examples, Gradient of a scalar function, Div(Divergence) and Curl of a vector function, Multiple operations.
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Definite integrals, Wallis sine formula, Integration by parts.
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Scalar and Vector fields.
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Examples, Conservative vector fields.
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Conservative vector fields, Divergence theorem (Gauss’ theorem), Stokes theorem.
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Periodic functions, Fourier series.
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Fourier series, Fourier coefficients, Result for fourier series, Dirichlet conditions.
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Examples, Odd And even functions.
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Examples, Half-range series.
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Functions with period-T, Half-wave rectifier.
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Laplace transform, Euler formaula.
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First shift theorem, Inverse transforms, Rules of partial fractions.