Road Maps

Subject overview

PAPER: APPLIED MATHEMATICS (100 MARKS)

Motion in a straight line with constant and variable acceleration; simple harmonic motion; conservative forces and principles of energy.

Motion in a straight line with constant and variable acceleration; simple harmonic motion; conservative forces and principles of energy.

Equations of first order; separable equations, exact equations; first order linear equations; orthogonal trajectories; nonlinear equations reducible to linear equations, Bernoulli and Riccati equations.

Equations of first order; separable equations, exact equations; first order linear equations; orthogonal trajectories; nonlinear equations reducible to linear equations, Bernoulli and Riccati equations.

Trigonometric Fourier series; sine and cosine series; Bessel inequality; summation of infinite series; convergence of the Fourier series.

Trigonometric Fourier series; sine and cosine series; Bessel inequality; summation of infinite series; convergence of the Fourier series.

Solution of nonlinear equations by bisection, secant and Newton -Raphson methods; the fixed- point iterative method; order of convergence of a method.

Solution of nonlinear equations by bisection, secant and Newton -Raphson methods; the fixed- point iterative method; order of convergence of a method.

Vector Calculus (10%)

Vector algebra; scalar and vector products of vectors; gradient divergence and curl of a vector; line, surface and volume integrals; Green’s, Stokes’ and Gauss theorems.

Tangential, normal, radial and transverse components of velocity and acceleration; motion under central forces; planetary orbits; Kepler laws;

Tangential, normal, radial and transverse components of velocity and acceleration; motion under central forces; planetary orbits; Kepler laws;

Equations with constant coefficients; homogeneous and inhomogeneous equations; Cauchy-Euler equations; variation of parameters.

Equations with constant coefficients; homogeneous and inhomogeneous equations; Cauchy-Euler equations; variation of parameters.

Partial differential equations of first order; classification of partial differential equations of second order; boundary value problems; solution by the method of separation of variables; problems associated with Laplace equation, wave equation and

Partial differential equations of first order; classification of partial differential equations of second order; boundary value problems; solution by the method of separation of variables; problems associated with Laplace equation, wave equation and the heat equation in Cartesian coordinates.

Solution of a system of linear equations; diagonally dominant systems; the Jacobi and Gauss-Seidel methods.

Solution of a system of linear equations; diagonally dominant systems; the Jacobi and Gauss-Seidel methods.

Statics (10%)

Composition and resolution of forces; parallel forces and couples; equilibrium of a system of coplanar forces; centre of mass of a system of particles and rigid bodies; equilibrium of forces in three dimensions.

Ordinary and singular points of a differential equation; solution in series; Bessel and Legen dre equations; properties of the Bessel functions and Legendre polynomials.

Ordinary and singular points of a differential equation; solution in series; Bessel and Legen dre equations; properties of the Bessel functions and Legendre polynomials.

Numerical differentiation and integration; trapezoidal rule, Simpson’s rules, Gaussian integration formulas.

Numerical differentiation and integration; trapezoidal rule, Simpson’s rules, Gaussian integration formulas.

Dynamics (10%)

Numerical solution of an ordinary differential equation; Euler and m odified Euler methods; Runge- Kutta methods.

Numerical solution of an ordinary differential equation; Euler and m odified Euler methods; Runge- Kutta methods.

Ordinary differential equations (20%)

Fourier series and partial differential equations (20%)

Numerical Methods (30%)

Subject overview

PAPER: APPLIED MATHEMATICS (100 MARKS)

Motion in a straight line with constant and variable acceleration; simple harmonic motion; conservative forces and principles of energy.

Motion in a straight line with constant and variable acceleration; simple harmonic motion; conservative forces and principles of energy.

Equations of first order; separable equations, exact equations; first order linear equations; orthogonal trajectories; nonlinear equations reducible to linear equations, Bernoulli and Riccati equations.

Equations of first order; separable equations, exact equations; first order linear equations; orthogonal trajectories; nonlinear equations reducible to linear equations, Bernoulli and Riccati equations.

Trigonometric Fourier series; sine and cosine series; Bessel inequality; summation of infinite series; convergence of the Fourier series.

Trigonometric Fourier series; sine and cosine series; Bessel inequality; summation of infinite series; convergence of the Fourier series.

Solution of nonlinear equations by bisection, secant and Newton -Raphson methods; the fixed- point iterative method; order of convergence of a method.

Solution of nonlinear equations by bisection, secant and Newton -Raphson methods; the fixed- point iterative method; order of convergence of a method.

Vector Calculus (10%)

Vector algebra; scalar and vector products of vectors; gradient divergence and curl of a vector; line, surface and volume integrals; Green’s, Stokes’ and Gauss theorems.

Tangential, normal, radial and transverse components of velocity and acceleration; motion under central forces; planetary orbits; Kepler laws;

Tangential, normal, radial and transverse components of velocity and acceleration; motion under central forces; planetary orbits; Kepler laws;

Equations with constant coefficients; homogeneous and inhomogeneous equations; Cauchy-Euler equations; variation of parameters.

Equations with constant coefficients; homogeneous and inhomogeneous equations; Cauchy-Euler equations; variation of parameters.

Partial differential equations of first order; classification of partial differential equations of second order; boundary value problems; solution by the method of separation of variables; problems associated with Laplace equation, wave equation and

Partial differential equations of first order; classification of partial differential equations of second order; boundary value problems; solution by the method of separation of variables; problems associated with Laplace equation, wave equation and the heat equation in Cartesian coordinates.

Solution of a system of linear equations; diagonally dominant systems; the Jacobi and Gauss-Seidel methods.

Solution of a system of linear equations; diagonally dominant systems; the Jacobi and Gauss-Seidel methods.

Statics (10%)

Composition and resolution of forces; parallel forces and couples; equilibrium of a system of coplanar forces; centre of mass of a system of particles and rigid bodies; equilibrium of forces in three dimensions.

Ordinary and singular points of a differential equation; solution in series; Bessel and Legen dre equations; properties of the Bessel functions and Legendre polynomials.

Ordinary and singular points of a differential equation; solution in series; Bessel and Legen dre equations; properties of the Bessel functions and Legendre polynomials.

Numerical differentiation and integration; trapezoidal rule, Simpson’s rules, Gaussian integration formulas.

Numerical differentiation and integration; trapezoidal rule, Simpson’s rules, Gaussian integration formulas.

Dynamics (10%)

Numerical solution of an ordinary differential equation; Euler and m odified Euler methods; Runge- Kutta methods.

Numerical solution of an ordinary differential equation; Euler and m odified Euler methods; Runge- Kutta methods.

Ordinary differential equations (20%)

Fourier series and partial differential equations (20%)

Numerical Methods (30%)