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]]>Objective: The objective of the paper is to facilitate the student with the basics of Applied Mathematics that are required for an engineering student
Successive differentiation: Leibnitz theorem for nth derivative (without proof). Infinite series: Convergence and divergence of infinite series, positive terms infinite series, necessary condition, comparison test (Limit test), D’Alembert ratio test, Integral Test, Cauchy’s root test, Raabe’s test and Logarithmic test(without proof). Alternating series, Leibnitz test, conditional and absolutely convergence. Taylor’s and Maclaurin’s expansion(without proof) of function ( ex , log(1+x), cos x , sin x) with remainder terms ,Taylor’s and Maclaurin’s series, Error and approximation.
Asymptotes to Cartesian curves. Radius of curvature and curve tracing for Cartesian, parametric and polar curves. Integration: integration using reduction formula for. Application of integration : Area under the curve, length of the curve, volumes and surface area of solids of revolution about axis only .Gamma and Beta functions
Matrices: Orthogonal matrix, Hermitian matrix, Skew-Hermitian matrix and Unitary matrix. Inverse of matrix by Gauss-Jordan Method (without proof). Rank of matrix by echelon and Normal (canonical) form. Linear dependence and linear independence of vectors. Consistency and inconsistency of linear system of homogeneous and non homogeneous equations . Eigen values and Eigen vectors. Properties of Eigen values (without proof). Cayley-Hamilton theorem (without proof). Diagonlization of matrix. Quadratic form, reduction of quadratic form to canonical form.
Ordinary differential equations: First order linear differential equations, Leibnitz and Bernaulli’s equation. Exact differential equations , Equations reducible to exact differential equations. Linear differential equation of higher order with constant coefficients, Homogeneous and non homogeneous differential equations reducible to linear differential equations with constant coefficients. Method of variation of parameters. Bessel’s and Legendre’s equations (without series solutions), Bessel’s and Legendre’s functions and their properties.
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]]>The main objectives of this course are to introduce the students to the exciting world of Differential Equations, Mathematical Modelling and their applications.
The course will enable the students to:
Syllabus Content May vary as per curriculum by university
Differential equations and mathematical models, Order and degree of a differential equation, Exact differential equations and integrating factors of first order differential equations, Reducible second order differential equations, Application of first order differential equations to equations to acceleration-velocity model, Growth and decay model.
Introduction to compartmental models, Lake pollution model (with case study of Lake Burley Griffin), Drug assimilation into the blood (case of a single cold pill, case of a course of cold pills, case study of alcohol in the bloodstream), Exponential growth of population, Limited growth of population, Limited growth with harvesting.
General solution of homogeneous equation of second order, Principle of superposition for a homogeneous equation; Wronskian, its properties and applications, Linear homogeneous and non-homogeneous equations of higher order with constant coefficients, Euler’s equation, Method of undetermined coefficients, Method of variation of parameters, Applications of second order differential equations to mechanical vibrations.
Interacting population models, Epidemic model of influenza and its analysis, Predator-prey model and its analysis, Equilibrium points, Interpretation of the phase plane, Battle model and its analysis.
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]]>The primary objective of this course is to introduce the basic tools of theory of equations, complex numbers, number theory and matrices to understand their linkage to the real-world problems. Perform matrix algebra with applications to Computer Graphics.
This course will enable the students to:
Syllabus Content May vary as per curriculum by university
Elementary theorems on the roots of an equation, Polynomials, The remainder and factor theorem, Synthetic division, Factored form of a polynomial, The Fundamental theorem of algebra, Relations between the roots and the coefficients of polynomial equations, Imaginary roots occur in pairs, Integral and rational roots; Polar representation of complex numbers, The nth roots of unity, De Moivre’s theorem for integer and rational indices and its applications.
Equivalence relations, Functions, Composition of functions, Invertibility and inverse of functions, One-to-one correspondence and the cardinality of a set.
The division algorithm, Divisibility and the Euclidean algorithm, The fundamental theorem of arithmetic, Modular arithmetic and basic properties of congruences; Principles of mathematical induction and well ordering principle.
Systems of linear equations, Row reduction and echelon forms, Vector equations, The matrix equation Ax = b, Solution sets of linear systems, Linear independence, The rank of a matrix and applications; Introduction to linear transformations, The matrix of a linear transformation; Matrix operations, The inverse of a matrix, Characterizations of invertible matrices, Applications to Computer Graphics, Eigenvectors and eigenvalues, The characteristic equation and the Cayley-Hamilton theorem.
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]]>The post B.Sc Mathematics Tuition Of Calculus appeared first on Online Math Tutor.
]]>The Primary Objective Of Live Tuition Class Of Calculus Course Is To Introduce The Basic Tools Of Calculus And Geometric Properties Of Different Conic Sections Which Are Helpful In Understanding Their Applications In Planetary Motion, Design Of Telescope And To The Real-World Problems. Also, To Carry Out The Hand On Sessions In Computer Lab To Have A Deep Conceptual Understanding Of The Above Tools To Widen The Horizon Of Students’ Self-Experience.
We Teach All university Syllabus. The Below syllabus may vary as per university.
The First-Derivative Test For Relative Extrema, Concavity And Inflection Points, Second-Derivative Test For Relative Extrema, Curve Sketching Using First And Second Derivative Tests; Limits To Infinity And Infinite Limits, Graphs With Asymptotes, L’hôpital’s Rule; Applications In Business, Economics And Life Sciences; Higher Order Derivatives, Leibniz Rule.
Parametric Representation Of Curves And Tracing Of Parametric Curves (Except Lines In 3), Polar Coordinates And Tracing Of Curves In Polar Coordinates; Techniques Of Sketching Conics, Reflection Properties Of Conics, Rotation Of Axes And Second Degree Equations, Classification Into Conics Using The Discriminant.
Volumes By Slicing Disks And Method Of Washers, Volumes By Cylindrical Shells, Arc Length, Arc Length Of Parametric Curves, Area Of Surface Of Revolution; Hyperbolic Functions; Reduction Formulae.
Introduction To Vector Functions And Their Graphs, Operations With Vector Functions, Limits And Continuity Of Vector Functions, Differentiation And Integration Of Vector Functions; Modeling Ballistics And Planetary Motion, Kepler’s Second Law; Unit Tangent, Normal And Binormal Vectors, Curvature.
1. Anton, Howard, Bivens, Irl, & Davis, Stephen (2013). Calculus (10th Ed.). John Wiley & Sons Singapore Pte. Ltd. Indian Reprint (2016) By Wiley India Pvt. Ltd. Delhi.
2. Osborne, George. A. (1906). Differential And Integral Calculus With Examples And Applications. Revised Edition. D. C. Health & Co. Publishers. Boston, U.S.A.
3. Strauss, Monty J., Bradley, Gerald L., & Smith, Karl J. (2007). Calculus (3rd Ed.). Dorling Kindersley (India) Pvt. Ltd. (Pearson Education). Delhi. Indian Reprint 2011.
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