GTU Syllabus:-
unit 1:-
- Indeterminate Forms and L’ Hospital’s Rule.
- Improper Integrals, Convergence and divergence of the integrals,
- Beta and Gamma functions and their properties.
- Applications of definite integral,
- Volume using cross-sections, Length of plane curves, Areas of Surfaces of Revolution
unit 2:-
- Convergence and divergence of sequences,
- The Sandwich Theorem for Sequences,
- The Continuous Function Theorem for Sequences,
- Bounded Monotonic Sequences,
- Convergence and divergence of an infinite series,
- geometric series,
- telescoping series,
- Nth term test for divergent series,
- Combining series, Harmonic Series, Integral test,
- The p - series, The Comparison test,
- The Limit Comparison test, Ratio test,
- Raabe’s Test, Root test, Alternating series test,
- Absolute and Conditional convergence,
- Power series, Radius of convergence of a power series,
- Taylor and Maclaurin series.
unit 3:-
- Fourier Series of 2𝑛 periodic functions,
- Dirichlet’s conditions for representation by a Fourier series,
- Orthogonality of the trigonometric system,
- Fourier Series of a function of period 2𝑛,
- Fourier Series of even and odd functions,
- Half range expansions.
unit 4:-
- Functions of several variables,
- Limits and continuity, Test for non existence of a limit,
- Partial differentiation, Mixed derivative theorem,
- differentiability, Chain rule, Implicit differentiation, Gradient, Directional derivative,
- tangent plane and normal line, total differentiation,
- Local extreme values,
- Method of Lagrange Multipliers.
unit 5:-
- Multiple integral,
- Double integral over Rectangles and general regions,
- double integrals as volumes, Change of order of integration,
- double integration in polar coordinates,
- Area by double integration,
- Triple integrals in rectangular,
- cylindrical and spherical coordinates,
- Jacobian, multiple integral by substitution.
unit 6:-
- Elementary row operations in Matrix,
- Row echelon and Reduced row echelon forms,
- Rank by echelon forms,
- Inverse by Gauss-Jordan method,
- Solution of system of linear equations by Gauss elimination and Gauss Jordan methods.
- Eigen values and eigen vectors,
- Cayley-Hamilton theorem,
- Diagonalization of a matrix.
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