Let Us C - Yashwant Kanetkar
Mathematics-I
Partial Differentiation and its applications:
Functions of Two or More Variables, Partial Derivatives, Homogeneous Functions- Euler’s Theorem, Total Derivative. Differentiation of Implicit Functions, Geometrical Interpretation- Tangent Plane and Normal to a surface. Change of Variables, Jacobians, Taylor’s Theorem for functions of two variables. Jacobians, Taylor’s Theorem for functions of two variables. Errors and approximations. Total Differential, Maxima and Minima of functions two variables. Lagrange’s method of undetermined multiples, Differentiation under the integral sign – Leibnitz Rule. Involutes and evolutes.
Multiple integrals and their applications:
Double integrals. Change of order of integration. Double integrals in Polar Co-ordinates, Areas enclosed by plane curves. Triple integrals. Volume of solids. Change of variables. Area of a curve of a curved surface. Calculation of Mass, Center of gravity, Center of pressure, Moment of inertia. Product of inertia. Principle Axes. Beta function, Gamma function. Relation between Beta and Gamma functions. Error function or Probability integral.
Solid geometry ( Vector Treatment ):
Equation of a plane. Equations of Straight line. Condition for a line to lie in a plane. Coplanar lines. Shortest distance between two lines. Interaction of three planes. Equation of Sphere, Tangent plane to a sphere. Cone, cylinder, Quadric surfaces.
Infinite series:
Definitions. Convergence, Divergence and oscillation of a series, General properties, series of Positive terms, comparison tests, Integral test. D’Alembert’s ratio test. Raabe’s test. Logarithmic test. Cauchy’s Root test. Alternating series- Leibnitz’s rule, Series of positive or negative terms. Power series. Convergence of exponential. Logerithmic and Bionomial series. Uniform convergence. Weirstrass M-test. Properties of uniformly convergent series.
Fourier series:
Euler’s formulae, Conditions for a Fourier expansion, Functions having points of discontinuity, Change of interval, Odd and even functions – Expansions of odd or even periodic function. Half range series. Parsevel formula, Practical Harmonic analysis.
Text Books:
1. Higher Engineering Mathematics by B.S.Grewal
2. Mathematics for Engineering by Chandrica Prasad.
Reference Books:
1. Higher Engineering Mathematics by M.K.Venkatraman.
2. Advanced Engineering Mathematics by Erwin Kreyszig.
Functions of Two or More Variables, Partial Derivatives, Homogeneous Functions- Euler’s Theorem, Total Derivative. Differentiation of Implicit Functions, Geometrical Interpretation- Tangent Plane and Normal to a surface. Change of Variables, Jacobians, Taylor’s Theorem for functions of two variables. Jacobians, Taylor’s Theorem for functions of two variables. Errors and approximations. Total Differential, Maxima and Minima of functions two variables. Lagrange’s method of undetermined multiples, Differentiation under the integral sign – Leibnitz Rule. Involutes and evolutes.
Multiple integrals and their applications:
Double integrals. Change of order of integration. Double integrals in Polar Co-ordinates, Areas enclosed by plane curves. Triple integrals. Volume of solids. Change of variables. Area of a curve of a curved surface. Calculation of Mass, Center of gravity, Center of pressure, Moment of inertia. Product of inertia. Principle Axes. Beta function, Gamma function. Relation between Beta and Gamma functions. Error function or Probability integral.
Solid geometry ( Vector Treatment ):
Equation of a plane. Equations of Straight line. Condition for a line to lie in a plane. Coplanar lines. Shortest distance between two lines. Interaction of three planes. Equation of Sphere, Tangent plane to a sphere. Cone, cylinder, Quadric surfaces.
Infinite series:
Definitions. Convergence, Divergence and oscillation of a series, General properties, series of Positive terms, comparison tests, Integral test. D’Alembert’s ratio test. Raabe’s test. Logarithmic test. Cauchy’s Root test. Alternating series- Leibnitz’s rule, Series of positive or negative terms. Power series. Convergence of exponential. Logerithmic and Bionomial series. Uniform convergence. Weirstrass M-test. Properties of uniformly convergent series.
Fourier series:
Euler’s formulae, Conditions for a Fourier expansion, Functions having points of discontinuity, Change of interval, Odd and even functions – Expansions of odd or even periodic function. Half range series. Parsevel formula, Practical Harmonic analysis.
Text Books:
1. Higher Engineering Mathematics by B.S.Grewal
2. Mathematics for Engineering by Chandrica Prasad.
Reference Books:
1. Higher Engineering Mathematics by M.K.Venkatraman.
2. Advanced Engineering Mathematics by Erwin Kreyszig.
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