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Gujarat Technological University, Gujarat, Information Technology Semester 1, Mathematics - I Syllabus
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Unit - 1 Intermediate forms
Unit 1
Content
1.1 Indeterminate forms and l’hospital rule
1.2 Improper integrals
1.3 Convergence and divergence of the integrals
1.4 Beta and gamma function and their properties
1.5 Application of define integral
1.6 Volume using crosssection
1.7 Length of plane curves
1.8 Area of surfaces of revolution
1.1 Indeterminate forms and l’hospital rule
1.2 Improper integrals
1.3 Convergence and divergence of the integrals
1.4 Beta and gamma function and their properties
1.5 Application of definite integral
1.6 Volume using crosssection
1.7 Length of plane curves
1.8 Area of surfaces of revolution
Unit - 2 Convergence & Divergence Rule
Unit – 2
Content
2.1 Convergence and Divergence of Sequences
2.2 The Sandwich Theorem for Sequences
2.3 The Continuous Function Theorem for Sequences
2.4 Bounded Monotonic Sequences
2.5 Convergence and Divergence of an Infinite Series
2.6 Combining Series
2.7 Harmonic Series
2.8 Integral Test
2.9 The PSeries test
2.10 The Comparison Test
2.11 The Limit Comparison Test
2.12 Ratio Test
2.13 Raabe’s Test
2.14 Root Test
2.15 Alternation Series Test
2.16 Absolute and Conditional Convergence
2.17 Power Series
2.18 Radius of Convergence Of A Power Series
2.19 Taylor and Maclaurin Series
2.1 Convergence and Divergence of Sequences
2.2 The Sandwich Theorem for Sequences
2.3 The Continuous Function Theorem for Sequences
2.4 Bounded Monotonic Sequences
2.5 Convergence and Divergence of an Infinite Series
2.6 Combining Series
2.7 Harmonic Series
2.8 Integral Test
2.9 The PSeries test
2.10 The Comparison Test
2.11 The Limit Comparison Test
2.12 Ratio Test
2.13 Raabe’s Test
2.14 Root Test
2.15 Alternation Series Test
2.16 Absolute and Conditional Convergence
2.17 Power Series
2.18 Radius of Convergence Of A Power Series
2.19 Taylor and Maclaurin Series
Unit - 3 Fourier series
Unit – 3
Fourier series
3.2 Dirichlet’s conditions for representation by a Fourier series
3.3 Orthogonality of the trigonometric system
3.4 Fourier series of a function of period 2L
3.5 Fourier series of even and odd function
3.6 Half Range expansions
3.2 Dirichlet’s conditions for representation by a Fourier series
3.3 Orthogonality of the trigonometric system
3.4 Fourier series of a function of period 2L
3.5 Fourier series of even and odd function
3.6 Half Range expansions
Unit - 4 Function of several variables
Unit – 4
Content
4.1 Function of several variables
4.2 Limits and continuity
4.3 Test for nonexistence of a limit
4.4 Partial differentiation
4.5 Mixed derivative theorem
4.6 Differentiability
4.7 Chain rule
4.8 Implicit differentiation
4.9 Gradient
4.10 Directional derivative
4.11 Tangent plane and normal line
4.12 Total differentiation
4.13 Local extreme values
4.14 Method of Lagrange multipliers
4.1 Function of several variables
4.2 Limits and continuity
4.3 Test for nonexistence of a limit
4.4 Partial differentiation
4.5 Mixed derivative theorem
4.6 Differentiability
4.7 Chain rule
4.8 Implicit differentiation
4.9 Gradient
4.10 Directional derivative
4.11 Tangent plane and normal line
4.12 Total differentiation
4.13 Local extreme values
4.14 Method of Lagrange multiplier
Unit - 5 Multiple integral
Unit 5
Content
5.1 Multiple integral
5.2 Double Integral over Rectangular and general regions
5.3 Double integrals as volumes
5.4 Change of order of integration
5.5 Double integration in polar coordination
5.6 Area of double integration
5.7 Triple integrals in rectangular
5.8 Cylindrical and spherical coordinates
5.9 Jacobian
5.10 Multiple integral by substitution
5.1 Multiple integral
5.2 Double Integral over Rectangular and general regions
5.3 Double integrals as volumes
5.4 Change of order of integration
5.5 Double integration in polar coordination
5.6 Area of double integration
5.7 Triple integrals in rectangular
5.8 Cylindrical and spherical coordinates
5.9 Jacobian
5.10 Multiple integral by substitution
Unit - 6 Elementary row operations in matrix
Unit – 6
Content
6.1 Elementary row operations in matrix
6.2 Row echelon and reduced row echelon froms
6.3 Rank by echelon form
6.4 Inverse by gauss – Jordan method
6.5 Solution of system of linear equation by gauss elimination and gauss Jordan method
6.6 Eigen values and Eigen vector
6.7 Cayley – Hamilton theorem
6.8 Diagonalization of a matrix
6.1 Elementary row operations in matrix
6.2 Row echelon and reduced row echelon forms
6.3 Rank by echelon form
6.4 Inverse by gauss – Jordan method
6.5 Solution of system of linear equation by gauss elimination and gauss Jordan method
6.6 Eigen values and Eigen vector
6.7 Cayley – Hamilton theorem
6.8 Diagonalization of a matrix
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