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Calculus And Analytical Geometry - MTH101 - VU Video Lectures

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Real numbers, Set theory, Interval, Inequlities, Oder properties of real numbers.
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Absolute Values, Inequlities involving Absolute Values, Theorem inequlities.
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Graphs in coordinate plane, Intercepts, Symmetry.
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Slop of line (steepness), Angel of inclination.
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Distance formula, Pythagors theorem, Midpoint formula, Circle, Center and Radius of Circle, Quadratic equation.
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What is function, Notation of function, Domain of function, Rang of function.
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Opration of function, Function can be added, subtracted, multiplied, divided, and composed with each other.
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Repersent function by graphs, Visualize behaviour of function, Use of graphs.
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Limits (Intuitive Introduction).
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Limits and Computational Approach, Algebric techniques, Use limits of basic function to comlicated function.
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Formal definition of limit, Left-hand and Right-hand limits.
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Mathematical definition of Continuity of function, Properties of continuous function, Continuity of polynomials, Rational and Composite funcions, Intermediate value theorem.
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Continuity of sine, cosine and other trigonometric function, Squeeze theorem, Limit of sine and cosine.
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Tangent lines and Rates of change, Slope of Tangent lines.
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Definition of Derivative, Existence of derivative, Relationship between differentiability and Continuity, derivative at the endpoint of the interval.
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Techniques of Differentiation,Derivatives of special, Constant, power, And constant multipal functions.
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Derivatives of f(x)=sin(x), cos(x), tan(x), sec(x), cosec(x), cot(x) and other function made by these funcion.
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Chain rule, Generalized derivatives formula, Alternative approach to using chai rule.
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Implicit differentiation, Derivatives of rational power of x, Differentiability of implicit function.
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Derivatives of Logarithmic, Exponential and Invers functions.
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Applications of differentiation, Related rates, Increasing, Decreasing And Concavity of functions.
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Relative maxima and minima, Critical points, First and Second derivative test, Graphs of polynomials and Rational functions.
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Maximum and Minimum values of functions.
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Newton’s method, Rolle’s theorem and Mean value theorem.
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Integration, Integration formulas, Indefinite integral, Properties of indefinite integral.
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Integration by substitution.
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Definition of Sigma Notation, Index summation, Properties of sigma notation, Summation formulas.
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Area as limit, Definition of Area, Some technical considerations, Numerical approximation of area.
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Definite integral of Continuous and Discontinuous functions, Properties of definite integral, Inequalities involving definite integral.
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First fundamental theorem of calculus, Relationship between definite and indefinite integrals, Mean value theorem itegration, Average value of function.
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Evaluating definite integral by substitution, Approximation of Riemann sums.
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Dummy variable, definite integrals with vriable upper limit, Second fundamental theorem of calculus, Existence of antiderivatives for continuous functions, Functions defind by integral.
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Application of the definite integral.
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Volume by Slicing, Disks and Washers.
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Cylindrical shell, Volume of a cylindrical shell, Cylindrical shells centered on y-axis, Volume through surface area.
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Length of Plane Curve.
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Definition of Surface Area, Surface area formulas.
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Work done by constant and variable force, Fluid pressure, Pascal's principle.
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Integrals over infinite interval, Integrals whose Integrands become infinite.
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L’Hopital’s Rule and Indeterminate forms.
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Definition of sequence, Graph of sequences, Limit of sequence, Recursive sequence, Testing for Monotonicity, Eventually monotonic sequences, Convergence of monotonic sequence.
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Additional Convergence Tests.
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Alternating Series, Conditional convergence.