Advanced Calculus and Partial Differential Equations | As per NEP, BSC Second year Mathematics Handwritten Notes PDF Download

Description

Chapters and Topics Included on PDF

Module-I

• Field structure and ordered structure of R, intervals, bounded and unbounded sets, supremum and infimum, completeness in R, absolute value of a real number.
• Sequence of real numbers
• Limit of a sequence
• Bounded and monotonic sequences
• Cauchy’s general principle of convergence
• Algebra of sequence and some important theorems

Module – II

• Series of non-negative terms
• Convergence of positive term series
• Alternating series and Leibnitz’s test
• Absolute and Conditional Convergence of Series of real terms
• Uniform continuity
• Chain rule of differentiability
• Mean value theorems and their geometrical interpretations

Module – III

• Limit and continuity of functions of two variables
• Change of variables
• Euler’s theorem on homogeneous functions
• Taylor’s theorem for functions of two variables
• Jacobians
• Maxima and Minima of functions of two variables
• Lagrange’s multiplier method

Module – IV

• Partial differential equations of the first order
• Lagrange’s solution
• Some special types of equations which can be solved easily by methods other than the general method
• Charpit’s general method
• Partial differential equations of second and higher orders

Module – V

• Classification of partial differential equations of second order
• Homogeneous and non-homogeneous partial differential equations of constant coefficients
• Partial differential equations reducible to equations with constant coefficients