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Mathematics-I (R-13)

University

JNTU Hyderabad

Department

Civil and Environmental Engineering

Semester

1 Year I Semester

- Introduction to Differential Equation
- Introduction to Differential Equation
- First Order First Degree Differential Equations
- Linear Differential Equations
- Linear Differential Equations
- Bernouli's Equation
- Bernouli's Equation
- Exact Differential Equations
- Exact Differential Equations
- Non Exact Differential Equations
- Non Exact Differential Equations
- Problems Related to Non Exact Differential Equations
- Problems Related to Non Exact Differential Equations
- Applications of 1st order and First Degree Differential equations
- Applications of 1st order and First Degree Differential equations
- Procedure to find Orthogonal Trajectory in polar coordinate system
- Procedure to find Orthogonal Trajectory in polar coordinate system
- Newtons Laws of Cooling
- Newtons Laws of Cooling
- Problems related to Newtons laws of cooling
- Problems related to Newtons laws of cooling
- Law of Natural Growth and Decay
- Law of Natural Growth and Decay
- Problems related to Newtons Laws of decay and growth
- Problems related to Newtons Laws of decay and growth
- Problems based on Newtons Law of Growth and Decay -1
- Problems based on Newtons Law of Growth and Decay-1
- Linear Differential Equation of 2nd and Higher Order
- Linear Differential Equation of 2nd and Higher Order
- Linear Differential Equation of 2nd and higher order-1
- Linear Differential Equation of 2nd and higher Order-1
- General Formula to Find Particular Integral
- General Formula to Find Particular Integral
- Rules to find PI in Some Special Cases
- Rules to find PI in Some Special Cases
- Method of Variation of Parameters
- Method of Variation of Parameters
- Rules for finding particular integrals I
- Rules for finding particular integrals I
- Finding particular integrals II
- Finding particular integrals II
- Finding particular integrals III
- Finding particular integrals III
- Electrical Circuits
- Electrical Circuits
- Unit-1 Short answer questions
- Unit-1 long answer question

- Types of Real Matrices and Complex Matrices
- Types of Real Matrices and Complex Matrices
- Rank of a Matrix - Echelon form
- Rank of a Matrix - Echelon form
- Problems on Echelon Form
- Problems on Echelon Form
- Rank of a Matrix - Normal form
- Rank of a Matrix - Normal form
- System of Homogeneous linear equations
- Consistency and solution of homogeneous linear systems
- Solving system of linear equations
- Consistency and solution of non homogeneous linear equations
- Indirect method or Method based on Ranks
- Indirect method and problems based on indirect method
- Problems based on consistency method
- Problems based on consistency method
- Problems based on consistency method
- Problems based on consistency method
- Continuation problem on consistency method
- Continuation problem on consistency method
- Gauss Elimination method
- Gauss Elimination method
- Gauus Jordan method
- Gauus Jordan method
- LU Decomposition method
- LU Decomposition method
- Unit-2 Short answer questions
- Unit-2 long answer question
- Unit-2 Multiple choice question and answer

- Eigen values, eigen vectors and quadratic forms
- Eigen values, eigen vectors and quadratic forms
- Properties of Eigen values
- Properties of Eigen values
- Problems on Eigen values and Eigen vectors
- Problems on Eigen values and Eigen vectors
- Problems on Eigen values Eigen and vectors 2
- Problems on Eigen values Eigen and vectors 2
- Finding eigen values and eigen vectors for complex matrices
- Finding eigen values and eigen vectors for complex matrices
- Diagonalisation of a matrix and power of a matrix
- Diagonalisation of a matrix and power of a matrix
- Problems on diagonal form
- Problems on diagonal form
- Cayley Hamilton's Theorem
- Cayley Hamilton's Theorem
- Quadratic forms and related problems
- Quadratic forms and related problems
- Methods to Reduce Quadratic forms to Canonical forms
- Methods to Reduce Quadratic forms to Canonical forms
- Diagonalisation Method
- Diagonalisation Method
- Problems Related to Lagrange's Reduction Method
- Problems Related to Lagrange's Reduction Method
- Properties and theorems of Eigen values
- Properties and theorems of Eigen values
- Properties and theorems of Eigen values 2
- Properties and theorems of Eigen values 2
- Methods of reduce Q.F to canonical form
- Methods of reduce Q.F to canonical form
- Unit-3 Short answer questions
- Unit-3 long answer question

- Limits of function and its derivatives
- Limits of function and its derivatives
- Continuity and its problems
- Continuity and its problems
- Partial derivatives and its problems
- Partial derivatives and its problems
- Total derivative and its problems
- Total derivative and its problems
- Chain rule of differentiation
- Chain rule of differentiation
- Homogeneous and its problems
- Homogeneous and its problems
- Homogeneous and its problems -2
- Homogeneous and its problems -2
- Jacobian and its problems
- Jacobian and its problems
- Jacobin and its problems - 2
- Jacobin and its problems - 2
- Functional Dependence and its Problem
- Functional Dependence and its Problem
- Taylor Series for Function of Two Variable and its Problems
- Taylor Series for Function of Two Variable and its Problems
- Taylor Series for a Function of Two Variables and its Problems - 2
- Taylor Series for a Function of Two Variables and its Problems - 2
- Maximum and Minimum for Function of Two Variables
- Maximum and Minimum for Function of Two Variables
- Problems based on Maximum and Minimum - 1
- Problems based on Maximum and Minimum - 1
- Problems based on Maximum and Minimum - 2
- Problems based on Maximum and Minimum - 2
- Lagrange Method of Multipliers and Its Problems - 1
- Lagrange Method of Multipliers and Its Problems - 1
- Unit-4 Short answer questions
- Unit-4 long answer question

- Partial Differential Equations of First order
- Partial Differential Equations of First order
- Elimination of Arbitrary Functions
- Elimination of Arbitrary Functions
- Solutions of Partial Differential Equations of 1st order
- Solutions of Partial Differential Equations of 1st order
- Method of Substitution
- Method of Substitution
- Non Linear Partial Differential Equations
- Non Linear Partial Differential Equations
- Standard form I
- Standard form I
- Standard Form II
- Standard Form II
- Standard Form III
- Standard Form III
- Unit-5 Short answer questions
- Unit-5 long answer question